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Porro, Cristina Shino. "Quantum mechanical/molecular mechanics studies of Cytochrome P450BM3." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/quantum-mechanical--molecular-mechanics-studies-of-cytochrome-p450bm3(ad4255e7-b779-47a2-a2c5-8dbf6b603ca5).html.
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Cytochrome P450 (P450) enzymes are found in all kingdoms of life, catalysing a wide range of biosynthetic and metabolic processes. They are, in fact, of particular interest in a variety of applications such as the design of agents for the inhibition of a particular P450 to combat pathogens or the engineering of enzymes to produce a particular activity. Bacterial P450BM3 is of particular interest as it is a self-sufficient multi-domain protein with high reaction rates and a primary structure and function similar to mammalian isoforms. It is an attractive enzyme to study due to its potential for engineering catalysts with fast reaction rates which selectively produce molecules of high value.In order to study this enzyme in detail and characterise intermediate species and reactions, the first step was to design a general hybrid quantum mechanical /molecular mechanics (QM/MM) computational method for their investigation. Two QM/MM approaches were developed and tested against existing experimental and theoretical data and were then applied to subsequent investigations.The dissociation of water from the water-bound resting state was scrutinised to determine the nature of the spin conversion that occurs during this transformation. A displacement of merely 0.5 Å from the starting state was found to trigger spin crossing, with no requirement for the presence of a substrate or large conformational changes in the enzyme.A detailed investigation of the sulfoxidation reaction was undertaken to establish the nature of the oxidant species. Both reactions involving Compound 0 (Cpd0) and Compound I (CpdI) confirmed a concerted pathway proceeding via a single-state reactivity mechanism. As the reaction involving Cpd0 was found to be unrealistically high, the reaction proceeds preferentially via the quartet state of CpdI. This QM/MM study revealed that the preferred spin-state and the transition state structure for sulfoxidation are influenced by the protein environment. P450cam and P450BM3 were found to have CpdI species with different Fe-S distances and spin density distributions, and the latter having a larger reaction barrier for sulfoxidation.A novel P450 species, the doubly-reduced pentacoordinated system, was characterised using gas-phase and QM/MM methods. It was discovered to have a heme radical coupled to two unpaired electrons on the iron centre, making it the only P450 species to have similar characteristics to CpdI. Calculated spectroscopic parameters may assist experimentalists in the identification of the elusive CpdI.
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Vanini, Paolo. "A mixed quantum mechanical problem /." [S.l.] : [s.n.], 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10912.
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Grummt, Robert. "On quantum mechanical decay processes." Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-166215.
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This thesis is concerned with quantum mechanical decay processes and their mathematical description. It consists out of three parts:
In the first part we look at Laser induced ionization, whose mathematical description is often based on the so-called dipole approximation. Employing it essentially means to replace the Laser's vector potential $\vec A(\vec r,t)$ in the Hamiltonian by $\vec A(0, t).$ Heuristically this is justified under usual experimental conditions, because the Laser varies only slowly in $\vec r$ on atomic length scales. We make this heuristics rigorous by proving the dipole approximation in the limit in which the Laser's length scale becomes infinite compared to the atomic length scale. Our results apply to $N$-body Hamiltonians.
In the second part we look at alpha decay as described by Skibsted (Comm. Math. Phys. 104, 1986) and show that Skibsted's model satisfies an energy-time uncertainty relation. Since there is no self-adjoint time operator, the uncertainty relation for energy and time can not be proven in the same way as the uncertainty relation for position and momentum. To define the time variance without a self-adjoint time operator, we will use the arrival time distribution obtained from the quantum current. Our proof of the energy-time uncertainty relation is then based on the quantitative scattering estimates that will be derived in the third part of the thesis and on a result from Skibsted. In addition to that, we will show that this uncertainty relation is different from the well known {\it linewidth-lifetime relation}.
The third part is about quantitative scattering estimates, which are of interest in their own right. For rotationally symmetric potentials having support in $[0,R_V]$ we will show that for $R\geq R_V$, the time evolved wave function $e^{-iHt}\psi$ satisfies
\begin{align}\nonumber
\|\1_R e^{-iHt}\psi\|_2^2\leq c_1t^{-1}+c_2t^{-2}+c_3t^{-3}+c_4t^{-4}
\end{align}
with explicit quantitative bounds on the constants $c_n$ in terms of the resonances of the $S$-Matrix. While such bounds on $\|\1_R e^{-iHt}\psi\|_2$ have been proven before, the quantitative estimates on the constants $c_n$ are new. These results are based on a detailed analysis of the $S$-matrix in the complex momentum plane, which in turn becomes possible by expressing the $S$-matrix in terms of the Jost function that can be factorized in a Hadamard product.Gegenstand dieser Arbeit ist die mathematische Beschreibung von quantenmechanischen Zerfallsprozessen. Im ersten von drei Teilen, werden wir die durch Laser induzierte Ionisation von Atomen untersuchen, die üblicherweise mit Hilfe der sogenannten Dipolapproximation beschrieben wird. Bei dieser Approximation wird das Vektorpotential $\vec A(\vec r,t)$ des Lasers im Hamiltonoperator durch $\vec A(0, t)$ ersetzt, was oft dadurch gerechtfertigt ist, dass sich das Vektorpotential des Lasers auf atomaren Längenskalen in $\vec r$ kaum verändert. Ausgehend von dieser Heuristik werden wir die Dipolapproximation in dem Limes beweisen, in dem die Wellenlänge des Lasers im Verhältnis zur atomaren Längenskala unendlich groß wird. Unsere Resultate sind auf $N$-Teilchen Systeme anwendbar. Im zweiten Teil wenden wir uns dem Alphazerfallsmodell von Skibsted (Comm. Math. Phys. 104, 1986) zu und beweisen, dass es eine Energie-Zeit Unschärfe erfüllt. Da kein selbstadjungierter Zeitoperator existiert, kann die Energie-Zeit Unschärfe nicht auf gleiche Weise wie die Orts-Impuls Unschärfe bewiesen werden. Um ohne einen selbstadjungierten Zeitoperator Zugriff auf die Zeitvarianz zu bekommen, werden wir mit Hilfe des quantenmechanischen Wahrscheinlichkeitsstroms eine Ankunftszeitverteilung definieren. Der Beweis der Energie-Zeit Unschärfe folgt dann aus einem Resultat von Skibsted und aus den quantitativen Streuabschätzungen, die im dritten Teil der Dissertation bewiesen werden. Darüber hinaus werden wir zeigen, dass diese Unschärfe von der {\it linewidth-lifetime relation} zu unterscheiden ist. Hauptresultat des dritten Teils sind quantitative Streuabschätzungen, die als eigenständiges Resultat von Interesse sind. Für rotationssymmetrische Potentiale mit Träger in $[0,R_V]$ werden wir für alle $R\geq R_V$ die Abschätzung \begin{align}\nonumber \|\1_R e^{-iHt}\psi\|_2^2\leq c_1t^{-1}+c_2t^{-2}+c_3t^{-3}+c_4t^{-4} \end{align} beweisen und darüber hinaus, das ist das Novum, quantitative Schranken für die Konstanten $c_n$ angeben, die von den Resonanzen der $S$-Matrix abhängen. Um zu diesen Schranken zu gelangen, werden wir die analytische Struktur der $S$-Matrix studieren, indem wir die Beziehung der $S$-Matrix zur Jost-Funktion ausnutzen und die wiederum in ein Hadamard-Produkt zerlegen.
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Lever, Greg. "Large scale quantum mechanical enzymology." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/246261.
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There exists a concerted and continual e ort to simulate systems of genuine biological interest to greater accuracy with methods of increasing transferability. More accurate descriptions of these systems at a truly atomistic and electronic level are irrevocably changing our understanding of biochemical processes. Broadly, classical techniques do not employ enough rigour, while conventional quantum mechanical approaches are too computationally expensive for systems of the requisite size. Linear-scaling density-functional theory (DFT) is an accurate method that can apply the predictive power of quantum mechanics to the system sizes required to study problems in enzymology. This dissertation presents methodological developments and protocols, including best practice, for accurate preparation and optimisation, combined with proof-of-principle calculations demonstrating reliable results for a range of small molecule and large biomolecular systems. Previous authors have shown that DFT calculations yield an unphysical, negligible energy gap between the highest occupied and lowest unoccupied molecular orbitals for proteins and large water clusters, a characteristic reproduced in this dissertation. However, whilst others use this phenomenon to question the applicability of Kohn-Sham DFT to large systems, it is shown within this dissertation that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Furthermore, practical solutions are demonstrated for ensuring a physical gap is maintained upon increasing system size. Harnessing these advances, the rst application using linear-scaling DFT to optimise stationary points in the reaction pathway for the Bacillus subtilis chorismate mutase (CM) enzyme is made. Averaged energies of activation and reaction are presented for the rearrangement of chorismate to prephenate in CM and in water, for system sizes comprising up to 2000 atoms. Compared to the uncatalysed reaction, the calculated activation barrier is lowered by 10.5 kcal mol-1 in the presence of CM, in good agreement with experiment. In addition, a detailed analysis of the interactions between individual active-site residues and the bound substrate is performed, predicting the signi cance of individual enzyme sidechains in CM catalysis. These proof-of-principle applications of powerful large-scale DFT methods to enzyme catalysis will provide new insight into enzymatic principles from an atomistic and electronic perspective.
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Giannelli, Luigi [Verfasser]. "Quantum Opto-Mechanical Systems for Quantum Technologies / Luigi Giannelli." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1214640788/34.
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Hayes, Anthony. "Quantum enhanced metrology : quantum mechanical correlations and uncertainty relations." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/78385/.
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The foundational theory of quantum enhanced metrology for parameter estimation is of fundamental importance to the progression of science and technology as the scientific method is built upon empirical evidence, the acquisition of which is entirely reliant on measurement. Quantum mechanical properties can be exploited to yield measurement results to a greater precision (lesser uncertainty) than that which is permitted by classical methods. This has been mathematically demonstrated by the derivation of theoretical bounds which place a fundamental limit on the uncertainty of a measurement. Furthermore, quantum metrology is of immediate interest in the application of quantum technologies since measurement plays a central role. This thesis focuses on the role of quantum correlations and uncertainty relations which govern the precision bounds. We show how correlations can be distributed amongst limited resources in realistic scenarios, as permitted by current experimental capabilities, to achieve higher precision measurements than current approaches. This is extended to the setting of multiparameter estimation in which we demonstrate a more technologically feasible method of correlation distribution than those previously posited which perform as well as, or worse than, our scheme. Furthermore, a quantum metrology protocol is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. We consider the more realistic sensing scenario of time being a limited resource which is divided amongst the three stages and demonstrate the most efficient use of this resource. Additionally, we take an information theoretic approach to quantum mechanical uncertainty relations and derive a one-parameter class of uncertainty relations which supplies more information about the quantum mechanical system of interest than conventional uncertainty relations. Finally, we demonstrate how we can use this class of uncertainty relations to reconstruct information of the state of the quantum mechanical system.
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Schöneboom, Jan Claasen Curd. "Combined quantum mechanical - molecular mechanical calculations on cytochrome P450cam." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968865267.
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Liu, Zi-Wen. "Quantum correlations, quantum resource theories and exclusion game." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/100108.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 131-138).
This thesis addresses two topics in quantum information theory. The first topic is quantum correlations and quantum resource theory. The second is quantum communication theory. The first part summarizes an ongoing work about quantum correlations beyond entanglement and quantum resource theories. We systematically explain the concept quantum correlations beyond entanglement, and introduce a unified framework of measuring such correlations with entropic quantities. In particular, a new measure called Diagonal Discord (DD), which is simpler to compute than discord but still possesses several nice properties, is proposed. As an application to real physical scenarios, we study the scaling behaviors of quantum correlations in spin lattices with these measures. On its own, however, the theory of quantum correlations is not yet a satisfactory quantum resource theory. Some partial results towards this goal are introduced. Furthermore, a unified abstract structure of general quantum resource theories and its duality is formalized. The second part shows that there exist (one-way) communication tasks with an infinite gap between quantum communication complexity and quantum information complexity. We consider the exclusion game, recently introduced by Perry, Jain and Oppenheim [80], which exhibits the property that for appropriately chosen parameters of the game, there exists an winning quantum strategy that reveals vanishingly small amount of information as the size of the problem n increases, i.e., the quantum (internal) information cost vanishes in the large n limit. For those parameters, we prove the quantum communication cost (the size of quantum communication to succeed) is lower bounded by Q (log n), thereby proving an infinite gap between quantum information and communication costs. This infinite gap is further shown to be robust against sufficiently small error. Some other interesting features of the exclusion game are also discovered as byproducts.
by Zi-Wen Liu.
S.M.
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Wang, Lihui. "Quantum Mechanical Effects on MOSFET Scaling." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-07072006-111805/.
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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2007.Philip First, Committee Member ; Ian F. Akyildiz, Committee Member ; Russell Dupuis, Committee Member ; James D. Meindl, Committee Chair ; Willianm R. Callen, Committee Member.
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Bhutta, Imran Ahmed. "A quantum mechanical semiconductor device simulator." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06072006-124213/.
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Gandhi, Sunil Kumar. "Quantum mechanical properties of the supermembrane." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47443.
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Tahir, Muhammed. "Quantum behaviour in nano-mechanical systems." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/5676.
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The emerging field of nano-electro-mechanical systems (NEMS), in which the single mode of a nanomechanical oscillator plays the role of an active device, is receiving much attention due to its technological importance. The characteristic component that gives the name to these devices is an oscillator of nanometer size coupled to the electrons on the dot that transfer electrons one-by-one between a source and a drain lead. From a fundamental point of view, it is important to understand the interplay between the electronic transport and the nanomechanical motion of the oscillator quantum mechanically. This thesis contains the description and analysis of the dynamics of a nanomechanical oscillator coupled to a resonant tunnel junction (RTJ) and its realization as a shuttle device. The models we consider describe both the mechanical and electrical degrees of freedom quantum mechanically; Firstly, a RTJ coupled to a nanomechanical oscillator. Secondly, we report a first complete quantum mechanical analysis of a charge shuttle. We introduce a new non-perturbative quantum mechanical description for the strong interaction of both the electrical and the mechanical object, which is beyond the existing experiments. We describe a nonequilibrium Green’s function formalism: a well suited technique to treat this kind of far from equilibrium systems, which can deal with very small to very large applied bias. The numerical implementation of these models are discussed in detail, and the transient and the steady state behavior of the system is also considered here for the quantum dynamics of the oscillator as a function of time. This will provide useful insight for the design of experiments aimed at studying the quantum behavior of an oscillator.
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Yasuda, Koji, and Daisuke Yamaki. "Simple minimum principle to derive a quantum-mechanical/molecular-mechanical method." American Institute of Physics, 2004. http://hdl.handle.net/2237/8738.
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Otte, Alexander-Nikolaj. "Combined quantum mechanical, molecular mechanical investigation of enantioselective reactions in lipases." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980565707.
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Rotter, Ingrid. "Description of an open quantum mechanical system." Forschungszentrum Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-32397.
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Karlsson, Ulf. "Semi-classical approximations of Quantum Mechanical problems." Doctoral thesis, KTH, Mathematics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3440.
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Zheng, Xiao. "Quantum mechanical simulation of open electronic systems." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B38717657.
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Zheng, Xiao, and 鄭曉. "Quantum mechanical simulation of open electronic systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B38717657.
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Bagwell, Philip F. (Philip Frederick). "Quantum mechanical transport in submicron electronic devices." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/44264.
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De, Fouquieres Pierre-Louis Becq. "Control of quantum mechanical systems through optimisation." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610642.
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Rotter, Ingrid. "Description of an open quantum mechanical system." Forschungszentrum Rossendorf, 1994. https://hzdr.qucosa.de/id/qucosa%3A22066.
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Salmon, Carrie R. "Chlorophosphazenes: Formation, Propagation, and Quantum Mechanical Calculations." University of Akron / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=akron1618769901438216.
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Adhikari, Upendra. "Quantum Mechanical Study of Weak Molecular Interactions." DigitalCommons@USU, 2014. https://digitalcommons.usu.edu/etd/2184.
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Noncovalent interactions have a long history and have received huge attention since their discovery almost a century ago. The prevalence of noncovalent interactions can be seen in the formation of simple dimers to structural and functional modification of large biomolecules. Even though plenty of experimental and theoretical studies are performed to understand various noncovalent interactions, the nature and variety of those interactions are still subject of study. And still they are receiving tremendous attention due to their significant role in the stability and conformation of biomolecules, catalysis of organic and inorganic reactions, crystal packing and material design. This dissertation explores various new sorts of noncovalent interactions, compares them with existing ones, and extensively studies the relevance of noncovalent interactions to various biological systems of interest by applying quantum mechanical tools. A new sort of noncovalent interaction has been identified where two electronegative atoms interact directly with each other with no intervening hydrogen or halogen atoms. These interactions are found to be surprisingly strong, even stronger than regular OH···O and NH···O hydrogen bonds in some cases, and are stabilized by the charge transfer from electron donor to electron acceptor. The major portion of this dissertation deals with the rigorous investigation of new sorts of interactions like P···N, S···N, Cl···N and several other charge transfer types of interactions with side by side comparison with hydrogen and halogen bonds. Similarly, a new carbonyl-carbonyl stacking geometry in peptide-peptide interactions is explored. These stacking geometries are energetically close to stronger NH···O hydrogen bonds, and get some assistance from CH···O hydrogen bonds. Carbon is considered one of the potent H-bond donors, albeit weaker, due to its ubiquitous presence in biomolecules. So, another portion of this dissertation is focused on the study of neutral and charged CH hydrogen bonds simulating various interpeptide interactions and enzyme catalysis. And the last part of this dissertation deals with the putative H-bonds that might be present in tip functionalized carbon nanotubes.
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Russell, Caroline. "Quantum mechanical wavepacket calculations on chemical reactions." Thesis, University of Oxford, 1998. https://ora.ox.ac.uk/objects/uuid:bc8fa8c2-7fbd-4fb4-bddf-8086442e36b7.
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The quantum mechanical time-dependent wavepacket method is introduced in the context of the field of chemical dynamics. The theory of the method is presented for two processes of interest in dynamics: molecular photodissociation, and reactive scattering. For the first of these processes, an expression is derived for the absorption spectrum of a molecule undergoing an electronic bound-continuum transition. For the second process, a time-dependent formulation is obtained for the S-matrix, and the "flux formulation" for the calculation of initial state-selected reaction probabilities (ISSRPs) is shown to be equivalent to summing over appropriate S-matrix elements. The time-dependent wavepacket theory for molecular photodissociation is used in the calculation of the photodetachment spectrum of the FHÌ
â anion. Spectra are calculated for two different energy resolutions, and previously unobserved structure is seen in the higher resolution spectrum. The structure is assigned by studying energy-dependent wavefunctions corresponding to each peak in the spectrum. Some peaks are assigned to direct scattering states, while others are assigned to quantum mechanical resonance states localised in the reactant and product valleys of the potential energy surface. The implication of this is that a high-resolution photodetachment experiment may provide the first experimental evidence for resonances in the F + H2 reaction. For reactive scattering, the time-dependent wavepacket method is used (in conjunction with the rotationally adiabatic approximation for J > 0 calculations) to calculate ISSRPs for various initial states of the nearly-thermoneutral ionmolecule reaction: N+(3P)+H2(1Σ+g)âNH+(X2II)+H(2S). Dense resonance structure in the reaction probabilities for J = 0 is attributed to the influence of the deep wells in. the potential energy surface for the reaction. The ISSRPs are used to calculate initial state-selected cross sections and rate constants which are compared with the results of some earlier trajectory calculations and with experimental data. The implications of the results for the astrophysical significance of the reaction are discussed.
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Ahn, Kwang Jun. "Fully quantum mechanical description of ultrashort time dynamics of semiconductor quantum dots." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=978946391.
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Engel, Ulf Martin. "On quantum chaos, stochastic webs and localization in a quantum mechanical kick system." Berlin Logos-Verl, 2003. http://deposit.d-nb.de/cgi-bin/dokserv?id=3004810&prov=M&dok_var=1&dok_ext=htm.
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Persson, E. "Threshold phenomena in an open quantum mechanical system." Forschungszentrum Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-32021.
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Hays, Mark Hanna IV. "Classical and quantum mechanical studies of nonlinear lattices." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187122.
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A class of nonlinear Hamiltonian lattice models that includes both the nonintegrable discrete nonlinear Schrodinger and the integrable Ablowitz-Ladik models is investigated classically and quantum mechanically. In general, the model under consideration is nonintegrable and its Hamiltonian structure is derived from a nonstandard Poisson bracket. It is shown that solutions of the classical model can, under appropriate and well-defined conditions, become infinite in finite time (blowup). Under suitable restrictions, it is demonstrated that an associated quantum lattice does not exhibit this singular behavior. In this sense, quantum mechanics can regularize a singular classical phenomenon. A fully nonlinear modulation theory for plane wave solutions of the classical lattice is developed. For cases of the model exhibiting blowup, numerical evidence is presented that suggests the existence of both stable and unstable modulated wavetrains. At the present time, it is unclear the extent to which one may relate the onset of instability to blowup. The Hartree approximation is applied to a generalized discrete self-trapping equation (GDST), with the result that the effective Hartree dynamics are described by a rescaled version of the GDST itself. In this manner, the Hartree approximation gives a direct connection between classical and quantum lattice models. Finally, Weyl's ordering prescription is shown to reproduce perturbative results for a weakly nonlinear oscillator. These results are extended to Hamiltonians that are nonpolynomial functions of the number operator. Extensions to the methodology that permit the treatment of other ordering prescriptions are given and compared with Weyl's rule.
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Han, Pin 1967. "Chaotic dynamics in classical and quantum mechanical systems." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/282102.
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This dissertation describes mainly researches on the chaotic properties of some classical and quantum mechanical systems. New phenomena like the three-dimensional uniform stochastic web and multiply riddled behavior are presented with numerical results. In the introduction, a short history and basic principles about chaotic dynamical systems are reviewed, which include the concepts of Lyapunov exponents and Poincare sections. In Chapter 2, we first discuss the Hamiltonian system, followed by the perturbation and KAM theory, then introduce Arnold diffusion and the existence of stochastic webs. We close this chapter with a system which can generate a three-dimensional uniform stochastic web. In Chapter 3, the relationship between deterministic chaos and quantum mechanics is studied. A quantum mechanical system called the tetrahedral array of Josephson junctions in which the deterministic chaos can exist is presented. At the end, we generalize such systems to any dimension and expect that chaos should survive in a higher dimensional case. In Chapter 4, in addition to the introduction of the riddled behavior, three examples in which multiply riddled behavior can occur are given and illustrated by graphs. The generalization of these systems is also made and we still expect that multiply riddled behavior will exist in these generalized systems containing more degrees of freedom.
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Backman, Carl-Johan, and Johannes Wennberg. "Quantum Mechanical Conduction of Electrons in 1DFibonacci Quasicrystals." Thesis, KTH, Teoretisk fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127013.
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In this report we model and study the propagation of electrons in one-dimensional (1D) Fibonacci quasicrystals. The quasicrystals are modeled with delta function potentials and created by either arranging their strengths or their spacings as a 2 letter Fibonacci word. The transmission and reflection amplitudes are calculated using an iterative method. A comparison is made against an ordinary crystal and a semi-random setup. The transmission of electrons are investigated and related to the electrical conduction in the different types of materials. We also investigate how sensitive the quasicrystals are to perturbations, compared to crystals. Finally, a quasicrystal modeled with a 3 letter Fibonacci word is discussed. We find that the Fibonacci structure increases the resistance by a relatively large factor, which makes the quasicrystals act like semiconductors. We also find tendencies that the quasicrystals are more sensitive to perturbations compared to ordinary crystals. The results are in good agreement with similar, earlier studies, both theoretical and experimental.
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Samaniego, Reyna Jose Cuauhtemoc. "Ab initio quantum mechanical approaches in solid state." Thesis, University of Birmingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289791.
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Godfrey, Michael John. "Quantum-mechanical theory of stress and its applications." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279694.
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Bruno, Juan Diderot 1970. "Quantum mechanical studies of Heisenberg antiferromagnetic spin chains." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/84735.
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Persson, E. "Threshold phenomena in an open quantum mechanical system." Forschungszentrum Rossendorf, 1995. https://hzdr.qucosa.de/id/qucosa%3A22028.
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Melin, Valdemar. "Quantum Mechanical Propagators Related to Classical Orthogonal Polynomials." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297558.
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A few quantum systems on the line with weighted classical orthogonal polynomials as eigenstates are studied. Explicit expressions of the propagators,i.e. the integral kernels of the time evolution operators, are derived. In the case of Hermite polynomials, the system is the harmonic oscillator, while forgeneralized Laguerre and Gegenbauer polynomials, the corresponding quanutum system are equivalent to two-particle Calogero-Sutherland systems.
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Moore, Darren William. "Quantum state reconstruction and computation with mechanical networks." Thesis, Queen's University Belfast, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728195.
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Networks of mechanical resonators embedded in the platform of optomechanics are studied in two quantum information contexts: quantum state reconstruction and measurement based quantum computation. The optomechanical setup considered consists of a harmonically interacting network of resonators one of which is coupled via radiation pressure to a resonant mode of a cavity electromagnetic field. We develop a protocol for reconstructing the state of the network from measurements on the output cavity field. An interaction profile tuned to a set of mechanical quadratures ensures that the cavity field carries a copy of the quadratures’ information. Homodyne detection of the output field provides measurement statistics directly linked to the statistics of the mechanical quadratures from which their marginals can be estimated and standard tomographic techniques applied, recovering the phase space distribution for the network. We provide a method for determining the interaction profiles required and analyse the effectiveness of the scheme for Gaussian states in the case of finite measurements. We also provide some further examples of state reconstruction in similar optomechanics settings. An equivalent setup is that in which the cavity field interacts simultaneously with a collection of noninteracting mechanical modes. Here we implement measurement based quantum computation, giving a summary of cluster state generation in optomechanics and providing a scheme for applying multimode Gaussian operations. Adapting QND measurements on movable mirrors we continuously monitor individual resonators in order to assess the feasibility of using indirect measurements for computation compared to projective measurements performed directly on the cluster. Using a linear cluster state of five modes and taking advantage of the decomposition of single-mode Gaussian operations into four steps, we perform a numerical assessment of a large array of experimental parameters, paring down the list until those that most significantly affect the outcome are distilled. These are the mechanical bath temperature, the mechanical dissipation rate and the cluster squeezing. They place strong restrictions on the experimental parameters in order to ensure high fidelities, with stronger requirements for more highly squeezed clusters. We conclude with a small discussion of currently available experimental settings and remarks on further research possibilities.
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King, Elizabeth Margaret. "Hydrocarbons on metallic surfaces : a quantum mechanical study." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/15166.
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The binding of liquid crystal molecules to surfaces in liquid crystal cells is a difficult interaction to characterise as the environment which surrounds the liquid crystal molecules makes the systems inaccessible to experimental and theoretical studies. However, insight may be gained from an examination of simplified systems which represent specific aspects of this interaction. First principles electronic structures calculations based on planewave density functional theory allow the adsorption of an isolated molecule on an extended surface to be examined and compared with studies on complex molecules. One possible binding interaction between a liquid crystal molecule and a metallic surface may be represented by the interaction of a conjugated p system with a metal. In order to characterise this interaction, this thesis examines the interaction of ethylene with aluminium and copper, and benzene with copper. The electronic interaction which occurs between the species can be rationalised by an identification of criteria which are important for the formation of a chemical bond in a complex molecule and an examination of whether these criteria can be met on adsorption of the hydrocarbon on an extended surface. It is found that ethylene is physisorbed on the s-p metal aluminium surface, but can be chemisorbed on the transition metal copper surface. Benzene can also be chemisorbed on a copper surface at certain sties. These results are explained by an examination of the Al(C2H4), Cu(C2H4) and Cu(C6H6) complexes.
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Deyirmenjian, Vatche Berj. "Quantum mechanical simulation of the mechanical behaviour and metallic bonding of defective aluminium." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338279.
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Weinstein, Yaakov Shmuel 1974. "Experimental implementations of quantum information processing." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/88834.
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Kiani, Bobak Toussi. "Quantum artificial intelligence : learning unitary transformations." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/127158.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, May, 2020Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 77-83).
Linear algebra is a simple yet elegant mathematical framework that serves as the mathematical bedrock for many scientific and engineering disciplines. Broadly defined as the study of linear equations represented as vectors and matrices, linear algebra provides a mathematical toolbox for manipulating and controlling many physical systems. For example, linear algebra is central to the modeling of quantum mechanical phenomena and machine learning algorithms. Within the broad landscape of matrices studied in linear algebra, unitary matrices stand apart for their special properties, namely that they preserve norms and have easy to calculate inverses. Interpreted from an algorithmic or control setting, unitary matrices are used to describe and manipulate many physical systems.
Relevant to the current work, unitary matrices are commonly studied in quantum mechanics where they formulate the time evolution of quantum states and in artificial intelligence where they provide a means to construct stable learning algorithms by preserving norms. One natural question that arises when studying unitary matrices is how difficult it is to learn them. Such a question may arise, for example, when one would like to learn the dynamics of a quantum system or apply unitary transformations to data embedded into a machine learning algorithm. In this thesis, I examine the hardness of learning unitary matrices both in the context of deep learning and quantum computation. This work aims to both advance our general mathematical understanding of unitary matrices and provide a framework for integrating unitary matrices into classical or quantum algorithms. Different forms of parameterizing unitary matrices, both in the quantum and classical regimes, are compared in this work.
In general, experiments show that learning an arbitrary dxd² unitary matrix requires at least d² parameters in the learning algorithm regardless of the parameterization considered. In classical (non-quantum) settings, unitary matrices can be constructed by composing products of operators that act on smaller subspaces of the unitary manifold. In the quantum setting, there also exists the possibility of parameterizing unitary matrices in the Hamiltonian setting, where it is shown that repeatedly applying two alternating Hamiltonians is sufficient to learn an arbitrary unitary matrix. Finally, I discuss applications of this work in quantum and deep learning settings. For near term quantum computers, applying a desired set of gates may not be efficiently possible. Instead, desired unitary matrices can be learned from a given set of available gates (similar to ideas discussed in quantum controls).
Understanding the learnability of unitary matrices can also aid efforts to integrate unitary matrices into neural networks and quantum deep learning algorithms. For example, deep learning algorithms implemented in quantum computers may leverage parameterizations discussed here to form layers in a quantum learning architecture.
by Bobak Toussi Kiani.
S.M.
S.M. Massachusetts Institute of Technology, Department of Mechanical Engineering
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Benighaus, Tobias [Verfasser]. "Boundary Potentials for Hybrid Quantum Mechanical / Molecular Mechanical Simulations of Solvated Biomolecules / Tobias Benighaus." Düsseldorf : Universitäts- und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf, 2011. http://d-nb.info/101545853X/34.
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Erhan, Inci. "Quantum Mechanical Computation Of Billiard Systems With Arbitrary Shapes." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1104082/index.pdf.
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An expansion method for the stationary Schrodinger equation of a particle moving freely in an arbitrary axisymmeric three dimensional region defined by an analytic function is introduced. The region is transformed into the unit ball by means of coordinate substitution. As a result the Schrodinger equation is considerably changed. The wavefunction is expanded into a series of spherical harmonics, thus, reducing the transformed partial differential equation to an infinite system of coupled ordinary differential equations. A Fourier-Bessel expansion of the solution vector in terms of Bessel functions with real orders is employed, resulting in a generalized matrix eigenvalue problem.
The method is applied to two particular examples. The first example is a prolate spheroidal billiard which is also treated by using an alternative method. The numerical results obtained by using both the methods are compared. The second exampleis a billiard family depending on a parameter. Numerical results concerning the second example include the statistical analysis of the eigenvalues.
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Ristow, Gerald H. "A quantum mechanical investigation of the Arnol'd cat map." Thesis, Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/27568.
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Baniahmad, Ata. "QUANTUM MECHANICAL Study and Modelling of MOLECULAR ELECTRONIC DEVICES." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13193/.
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Molecular electronics pursues the use of molecules as fundamental electronic components. The inherent properties of molecules such as nano-size, low cost, scalability, and self-assembly are seen by many as a perfect complement to conventional silicon electronics. Molecule based electronics has captured the attention of a broad cross section of the scientific community.
In molecular electronic devices, the possibility of having channels that are just one atomic layer thick, is perhaps the most attractive feature that takes the attention to graphene.The conductivity, stability, uniformity, composition, and 2D nature of graphene make it an excellent material for electronic devices.
In this thesis we focused on Zigzag Graphene NanoRibbon(ZGNR) as a transmission channel. Due to the importance of an accurate description of the quantum effects in the operation of graphene devices, a full-quantum transport model has been adopted: the electron dynamics has been described by Density Functional Theory(DFT) and transport has been solved within the formalism of Non-Equilibrium Green’s Functions (NEGF). Using DFT and NEGF methods, the transport properties of ZGNR and ZGNR doped with Si are studied by systematically computing the transmission spectrum. It is observed that Si barrier destroyed the electronic transport properties of ZGNR, an energy gap appeared for ZGNR, and variations from conductor to semiconductor are displayed. Its followed by a ZGNR grown on a SiO2 crystal substrate, while substituting the Graphene electrodes with the Gold ones, and its effect on transmission properties have been studied. Improvement in transmission properties observed due to the formation of C-O bonds between ZGNR and substrate that make the ZGNR corrugated. Finally, we modeled a nano-scale Field Effect Transistor by implementing a gate under SiO2 substrate. A very good I-ON/I-OFF ratio has been observed although the device thickness.
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Höhr, Timm. "Quantum-mechanical modeling of transport parameters for MOS devices /." Konstanz : Hartnung-Gorre, 2006. http://www.loc.gov/catdir/toc/fy0707/2007358987.html.
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Originally presented as the author's thesis (Swiss Federal Institute of Technology), Diss. ETH No. 16228.Summary in German and English, text in English. Includes bibliographical references (p. 123-132).
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Ye, Lin Holder Andrew J. "Application of quantum mechanical QSAR to dental molecule design." Diss., UMK access, 2007.
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Thesis (Ph. D.)--Dept. of Chemistry and School of Pharmacy. University of Missouri--Kansas City, 2007."A dissertation in chemistry and pharmaceutical science." Advisor: Andrew J. Holder. Typescript. Vita. Description based on contents viewed Apr. 15, 2008; title from "catalog record" of the print edition. Includes bibliographical references (leaves 89-93). Online version of the print edition.
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Tan, Keng Ean. "Quantum mechanical modelling of refractory transition metal carbide films." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294188.
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Haynes, P. "Linear-scaling methods in ab initio quantum-mechanical calculations." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603888.
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The work described in this dissertation concerns the development of new methods for performing computer simulations of real materials from first principles or ab initio i.e. using the fundamental equations of quantum mechanics and only well-controlled approximations. In particular, these methods have been developed within the framework of density-functional theory and therefore lie in the realms of both quantum chemistry and computational condensed matter physics. The work is particularly concerned with methods which are efficient in the sense that the computational effort required scales only linearly with system-size (i.e. the volume or number of electrons) whereas traditional methods have scaled with the cube of the system-size which has restricted their range of applicability. The aim of this work is therefore to extend the scope of ab initio quantum-mechanical calculations beyond what is currently possible. Density-functional theory has traditionally been applied by making use of a mapping from the system of interacting electrons to a fictitious system of non-interacting particles. However, the need to maintain the mutual orthogonality of the wave functions of the fictitious system leads to the cubic scaling mentioned above, and is ultimately responsible for limiting the maximum size of systems which can be treated. Making use of a reformulation of the problem in terms of the single-particle density-matrix eliminates the need to work with the wave functions directly. Moreover, exploiting the short-ranged nature of the density-matrix leads in principle to a linear-scaling method. The dissertation tackles two issues which are relevant to obtaining practical schemes for performing linear-scaling calculations. Firstly a localised basis set is developed which is used to describe the density-matrix computationally. Analytic results for several key quantities required by the calculation are derived, namely the overlap, kinetic energy and non-local pseudopotential matrix elements. These results allow accurate calculation of the total energy of the system and have been implemented and tested computationally. Secondly, the dissertation discusses several methods for imposing the difficult non-linear idempotency constraint on the density-matrix.
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Mirsakiyeva, Amina. "Quantum Mechanical Calculations of Thermoelectrical Polymers and Organic Molecules." Licentiate thesis, KTH, Materialfysik, MF, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168430.
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The subject of the present licentiate thesis is density functional theorybased electronic structure calculations of organic thermoelectric materials and novel organic molecules. We used the Car-Parrinello molecular dynamics method in order to investigate the electronic structure of “green energy” and “greenchemistry” compounds. First, we have investigated the electronic structure of the poly(3,4-ethylene-dioxythiophene) (PEDOT) and its derivatives - the best studied and successfully implemented by industry organic thermoelectric material. Its transparency, low toxicity and high stability in the oxidized state are combined withan ability to produce electrical current when applying a temperature gradient. This makes PEDOT a perfect “organic metal” and a first candidate for organic thermoelectrogenerators - devices that can produce “green energy” from a temperature difference. The average structures found in these quantum dynamical simulations agree well with earlier static electronic structure studies. The energy gap of two, four and six unit oligomers of PEDOT was calculated and was found to lie in the range of previous theoretical studies. We have also calculatedthe point-charge distributions along the polymer backbone in order to investigate the polaron formed by doping agents of PEDOT. Our analysis allowed us to predict possible localization of the charge in the center of the polymer chain. However, further calculations of the twelve unit PEDOT and its selenium and tellurium derivatives will provide more information. First-principles calculations for the tellurium derivative of PEDOT are here presented for the first time. The second part of our investigation concerns theoretical calculations of novel piperidine-containing acetylene glycols. These molecules were newly synthesized by our experimental collaborators and are expected to provideplant growth stimulation properties, the same as its diacetylene analogs. We performed quantum mechanical calculations of four compounds, presented ananalysis of the highest occupied and lowest unoccupied molecular orbitals and collected detailed information on point-charges for further parametrization of novel molecules for future computational studies. According to these results, the low production yield found in the experiments cannot be attributed to chemical instability in these novel compounds.QC 20150629
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Jason, Peter. "Comparisons between classical and quantum mechanical nonlinear lattice models." Licentiate thesis, Linköpings universitet, Teoretisk Fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-105817.
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In the mid-1920s, the great Albert Einstein proposed that at extremely low temperatures, a gas of bosonic particles will enter a new phase where a large fraction of them occupy the same quantum state. This state would bring many of the peculiar features of quantum mechanics, previously reserved for small samples consisting only of a few atoms or molecules, up to a macroscopic scale. This is what we today call a Bose-Einstein condensate. It would take physicists almost 70 years to realize Einstein's idea, but in 1995 this was finally achieved. The research on Bose-Einstein condensates has since taken many directions, one of the most exciting being to study their behavior when they are placed in optical lattices generated by laser beams. This has already produced a number of fascinating results, but it has also proven to be an ideal test-ground for predictions from certain nonlinear lattice models. Because on the other hand, nonlinear science, the study of generic nonlinear phenomena, has in the last half century grown out to a research field in its own right, influencing almost all areas of science and physics. Nonlinear localization is one of these phenomena, where localized structures, such as solitons and discrete breathers, can appear even in translationally invariant systems. Another one is the (in)famous chaos, where deterministic systems can be so sensitive to perturbations that they in practice become completely unpredictable. Related to this is the study of different types of instabilities; what their behavior are and how they arise. In this thesis we compare classical and quantum mechanical nonlinear lattice models which can be applied to BECs in optical lattices, and also examine how classical nonlinear concepts, such as localization, chaos and instabilities, can be transfered to the quantum world.