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Relevant bibliographies by topics / Quantum integrable system

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Academic literature on the topic 'Quantum integrable system'

Author: Grafiati

Published: 11 December 2022

Last updated: 25 January 2023

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Journal articles on the topic "Quantum integrable system"

1

GARCÍA, MARCOS A. G., and ALEXANDER V. TURBINER. "THE QUANTUM H3 INTEGRABLE SYSTEM." International Journal of Modern Physics A 25, no. 30 (2010): 5567–94. http://dx.doi.org/10.1142/s0217751x10050597.

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The quantum H3 integrable system is a three-dimensional system with rational potential related to the noncrystallographic root system H3. It is shown that the gauge-rotated H3 Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H3, is in algebraic form: it has polynomial coefficients in front of derivatives. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector [Formula: see text]. One among possible integrals is found (of the second order) as we

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GARCÍA, MARCOS A. G., and ALEXANDER V. TURBINER. "THE QUANTUM H4 INTEGRABLE SYSTEM." Modern Physics Letters A 26, no. 06 (2011): 433–47. http://dx.doi.org/10.1142/s0217732311034839.

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The quantum H4 integrable system is a 4D system with rational potential related to the non-crystallographic root system H4 with 600-cell symmetry. It is shown that the gauge-rotated H4 Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H4, is in algebraic form: it has polynomial coefficients in front of the derivatives. Any eigenfunction is a polynomial multiplied by ground-state function (factorization property). Spectra correspond to one of the anisotropic harmonic oscillators. The Hamiltonian has infinitely-many finite-dimensional invar

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Kupershmidt, B. A. "Quantum mechanics as an integrable system." Physics Letters A 109, no. 4 (1985): 136–38. http://dx.doi.org/10.1016/0375-9601(85)90002-7.

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CASTRO-ALVAREDO, O. A., and A. FRING. "APPLICATIONS OF QUANTUM INTEGRABLE SYSTEMS." International Journal of Modern Physics A 19, supp02 (2004): 92–116. http://dx.doi.org/10.1142/s0217751x04020336.

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We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demonstrating that the emission spectrum of a minimally coupled laser field of frequency ω to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, by evaluating expressions for the conductance in the high temperature regime we show that multiples of the characteristic filling fractions of the Jain sequence, which occur in the fractional quantum Hall effect, can be obtained from quantum wires which are desc

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Sun, Li-Zhen, Qingmiao Nie, and Haibin Li. "Randomness of Eigenstates of Many-Body Quantum Systems." Entropy 21, no. 3 (2019): 227. http://dx.doi.org/10.3390/e21030227.

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The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies th

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YAN, MU-LIN, and BAO-HENG ZHAO. "QUANTUM INTEGRABLE SYSTEM WITH MULTI-COMPONENTS IN TWO DIMENSIONS." Modern Physics Letters B 16, no. 23n24 (2002): 871–83. http://dx.doi.org/10.1142/s021798490200441x.

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A quantum N-body problem with 2-component in (2 + 1) dimensions deduced from an integrable model in (2 + 1) dimensions is investigated. The Davey–Stewartson 1 (DS1) system9 is an integrable model in two dimensions. A quantum DS1 system with 2 color components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 color components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimension. For the latter with δ-function interactions and being so

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GERASIMOV, A., S. KHARCHEV та D. LEBEDEV. "ON A CLASS OF INTEGRABLE SYSTEMS CONNECTED WITH GL(N,ℝ)". International Journal of Modern Physics A 19, supp02 (2004): 205–16. http://dx.doi.org/10.1142/s0217751x04020415.

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In this paper we define a new class of the quantum integrable systems associated with the quantization of the cotangent bundle T*(GL(N)) to the Lie algebra [Formula: see text]. The construction is based on the Gelfand-Zetlin maximal commuting subalgebra in [Formula: see text]. We discuss the connection with the other known integrable systems based on T*GL(N). The construction of the spectral tower associated with the proposed integrable theory is given. This spectral tower appears as a generalization of the standard spectral curve for an integrable system.

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Nepomechie, Rafael I. "The Am(1) Q-system." Modern Physics Letters A 35, no. 31 (2020): 2050260. http://dx.doi.org/10.1142/s0217732320502600.

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Zhang, Yufeng, Xiangzhi Zhang, Yan Wang, and Jiangen Liu. "Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws." Zeitschrift für Naturforschung A 72, no. 1 (2017): 77–86. http://dx.doi.org/10.1515/zna-2016-0347.

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AbstractWith the help ofR-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula byR-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional gen

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Steeb, W. H., and A. J. van Tonder. "Quantum Mechanics and a Completely Integrable Dynamical System." Zeitschrift für Naturforschung A 42, no. 8 (1987): 819–24. http://dx.doi.org/10.1515/zna-1987-0809.

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From the eigenvalue equation (H0 + λV) \ ψn(λ)) = En (λ) | ψn( λ ) ) one can derive an autonomous system of first order differential equations for the eigenvalues En (λ) and the matrix elements Vmn(X) = ( ψm(λ) \ V \ ψn(λ), where λ is the independent variable. If the initial values En (λ = 0) and ψn (λ = 0) are known the differential equations can be solved. Thus one finds the “motion” of the energy levels En(λ). Here we give two applications of this technique. Furthermore we describe the connection with the stationary state perturbation theory. We also derive the equations of motion for the e

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Dissertations / Theses on the topic "Quantum integrable system"

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Kawaguchi, Io. "Integrable deformations of principal chiral models and the AdS/CFT correspondence." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188477.

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Ma, Tao. "Statistics of Quantum Energy Levels of Integrable Systems and a Stochastic Network Model with Applications to Natural and Social Sciences." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1378196433.

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Crivelli, Dawid Wiesław. "Particle and energy transport in strongly driven one-dimensional quantum systems." Doctoral thesis, Katowice: Uniwersytet Śląski, 2016. http://hdl.handle.net/20.500.12128/5879.

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This Dissertation concerns the transport properties of a strongly–correlated one–dimensional system of spinless fermions, driven by an external electric field which induces the flow of charges and energy through the system. Since the system does not exchange information with the environment, the evolution can be accurately followed to arbitrarily long times by solving numerically the time–dependent Schrödinger equation, going beyond Kubo’s linear response theory. The thermoelectric response of the system is here characterized, using the ratio of the induced energy and particle currents,

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Sun, Yi Ph D. Massachusetts Institute of Technology. "Quantum intertwiners and integrable systems." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104579.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 223-229).<br>We present a collection of results on the relationship between intertwining operators for quantum groups and eigenfunctions for quantum integrable systems. First, we study the Etingof-Kirillov Jr. expression of Macdonald polynomials as traces of intertwiners of quantum groups in the Gelfand-Tsetlin basis. In the quasiclassical limit, we obtain a new Harish-Chandra type integral formula for Heckman- Opdam hype

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Pehlivan, Yamac. "Matrix Quantum Mechanics And Integrable Systems." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605065/index.pdf.

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In this thesis we improve and extend an algebraic technique pioneered by M. Gaudin. The technique is based on an infinite dimensional Lie algebra and a related family of mutually commuting Hamiltonians. In order to find energy eigenvalues of such Hamiltonians one has to solve the equations of Bethe ansatz. However, in most cases analytical solutions are not available. In this study we examine a special case for which analytical solutions of Bethe ansatz equations are not needed. Instead, some special properties of these equations are utilized to evaluate the energy eigenvalues. We use this met

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Adamopoulou, Panagiota-Maria. "Differential equations and quantum integrable systems." Thesis, University of Kent, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.655223.

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This thesis explores several aspects of the correspondence between classes of linear ordinary differential equations (ODEs) in the complex plane and certain quantum integrable models (IMs), also known as the ODE/IM correspondence. First, we enlarge the set of ordinary differential equations that enter the correspondence. Differential equations satisfied by Wronskians between solutions of specific ODEs are obtained and are associated to nodes of particular Dynkin diagrams. In the second part of the thesis we generalise the correspondence to encompass massive IMs. Starting from an integrable non

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Bianchini, D. "Entanglement entropy in integrable quantum systems." Thesis, City, University of London, 2016. http://openaccess.city.ac.uk/17490/.

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In this thesis I present the results I have been developing during my PhD studies at City University London. The original results are based on D Bianchini et al, D Bianchini, O Castro-Alvaredo and B Doyon, D Bianchini and F Ravanini, D Bianchini et al and D Bianchini and O Castro-Alvaredo. In all but one publications, we compute the entanglement of various systems. Using the celebrated “replica trick” we compute the entanglement entropy of non unitary systems using integrable tools in continuum and discrete models. In particular, in the first article we generalise the method described in the s

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Sorrell, Mark. "Quantum integrable systems and Schrodinger Eigenvalue problems." Thesis, Heriot-Watt University, 2008. http://hdl.handle.net/10399/2176.

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Hawkins, Michael Stuart. "Local conservation laws in quantum integrable systems." Thesis, University of Birmingham, 2009. http://etheses.bham.ac.uk//id/eprint/282/.

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One of the phenomena associated with quantum integrable systems is the possibility of persistent currents, i.e. currents which do not decay away entirely, but have some portion that continues to flow undiminished and indefinitely. These residual currents are shown to be the conserved part of the current operator, and calculable from the conservation laws of the system. In a particular system, previous attempts to calculate a known residual current from the conservation laws have failed. A numerical investigation is undertaken, and this disparity with the formal results is resolved by the inclu

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Evangelisti, Stefano <1983&gt. "Quantum Correlations in Field Theory and Integrable Systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amsdottorato.unibo.it/5161/.

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In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical

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Books on the topic "Quantum integrable system"

1

Anindya, Ghose Choudhury, ed. Quantum integrable systems. Chapman & Hall/CRC, 2003.

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Donagi, Ron, Boris Dubrovin, Edward Frenkel, and Emma Previato. Integrable Systems and Quantum Groups. Edited by Mauro Francaviglia and Silvio Greco. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0094791.

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GIFT, International Seminar on Recent Problems in Mathematical Physics (23rd 1992 Salamanca Spain). Integrable systems, quantum groups, and quantum field theories. Kluwer Academic, 1993.

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Ibort, L. A., and M. A. Rodríguez, eds. Integrable Systems, Quantum Groups, and Quantum Field Theories. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1980-1.

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Ibort, L. A. Integrable Systems, Quantum Groups, and Quantum Field Theories. Springer Netherlands, 1993.

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6

From quantum cohomology to integrable systems. Oxford University Press, 2008.

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7

Quantum dissipative systems. 3rd ed. World Scientific, 2008.

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Quantum dissipative systems. World Scientific, 1993.

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9

1944-, Kulish P. P., Manojlovic Nenad 1962-, and Samtleben Henning, eds. Infinite dimensional algebras and quantum integrable systems. Birkhäuser Verlag, 2005.

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Helminck, G. F., ed. Geometric and Quantum Aspects of Integrable Systems. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0021439.

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Book chapters on the topic "Quantum integrable system"

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Shastry, B. S. "The 1/r 2 Integrable System: The Universal Hamiltonian for Quantum Chaos." In Correlation Effects in Low-Dimensional Electron Systems. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-85129-2_2.

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Braak, Daniel. "What Kind of Insight Provide Analytical Solutions of Quantum Models?" In International Symposium on Mathematics, Quantum Theory, and Cryptography. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_2.

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Abstract There are several concepts of what constitutes the analytical solution of a quantum model, as opposed to the mere “numerically exact” one. This applies even if one considers only the determination of the discrete spectrum of the corresponding Hamiltonian, setting aside such important questions as the asymptotic dynamics for long times. In the simplest case, the spectrum can be given in closed form, the eigenvalues $$E_{j}, j=0,\ldots ,N\le \infty $$ read $$E_{j} =f(j,\{p_{k}\})$$, where f is a known function of the label $$j\in \mathbb {N}_{0}$$ and the $$\{p_k\}$$ are a set of numbers parameterizing the Hamilton operator. This kind of solution exists only in cases where the classical limit of the model is Liouville-integrable. Some quantum-mechanical many-body systems allow the determination of the spectrum in terms of auxiliary parameters $$[\{k_j\},\{n_l\}]$$ as $$E(\{n_l\}) = f(\{k_{j}(\{n_{l}\})\})$$ where the $$\{k_{j}(\{n_{l}\})\}$$ satisfy a coupled set of transcendental equations, following from a certain ansatz for the eigenfunctions. These systems (integrable in the sense of Yang-Baxter (Eckle 2019)) may have a Hilbert space dimension growing exponentially with the system size L, i.e., $$N\sim e^{L}$$. The simple enumeration of the energies with the label j is replaced by the multi-index $$\{n_{l}\}$$. Although no priori knowledge about the spectrum is available, its statistical properties can be computed exactly (Berry and Tabor 1977). Other integrable and also non-integrable models exist where N depends polynomially on L and the energies $$E_j$$ are the zeroes of an analytically computable transcendental function, the so-called G-function $$G(E,\{p_k\})$$ (Braak 2013a, 2016), which is proportional to the spectral determinant. Although no closed formula for $$E_j$$ as function of the index j exists, detailed qualitative insight into the distribution of the eigenvalues can be obtained (Braak 2013b). Possible applications of these concepts to information compression and cryptography are outlined.

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Gutzwiller, Martin C. "Integrable Systems." In Chaos in Classical and Quantum Mechanics. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0983-6_4.

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Turbiner, Alexander. "Perturbations of integrable systems and Dyson-Mehta integrals." In Superintegrability in Classical and Quantum Systems. American Mathematical Society, 2004. http://dx.doi.org/10.1090/crmp/037/21.

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Arutyunov, Gleb. "Quantum-Mechanical Integrable Systems." In Elements of Classical and Quantum Integrable Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24198-8_3.

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Kulish, Petr P. "Quantum Groups and Integrable Models." In Factorization and Integrable Systems. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8003-9_3.

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Chari, Vyjayanthi, and Andrew Pressley. "Quantum Affine Algebras and Integrable Quantum Systems." In Quantum Fields and Quantum Space Time. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4899-1801-7_10.

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Leznov, A. N., and M. V. Saveliev. "Exactly integrable quantum dynamical systems." In Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems. Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8638-3_7.

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Semenov-Tian-Shansky, M. A. "Quantum and Classical Integrable Systems." In Integrability of Nonlinear Systems. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40962-5_9.

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Cariñena, José F., Alberto Ibort, Giuseppe Marmo, and Giuseppe Morandi. "Integrable and Superintegrable Systems." In Geometry from Dynamics, Classical and Quantum. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-9220-2_8.

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Conference papers on the topic "Quantum integrable system"

1

YAN, MU-LIN, and BAO-HENG ZHAO. "QUANTUM INTEGRABLE SYSTEM WITH MULTI-COMPONENTS IN TWO DIMENSIONS." In In Celebration of the 80th Birthday of C N Yang. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812791207_0028.

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Bekenstein, R., E. N. Knall, C. M. Knaut, et al. "On-demand single photon source integrated into a nanophotonic platform." In Quantum 2.0. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/quantum.2022.qth2b.3.

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Ge, Mo-Lin. "QUANTUM GROUP AND QUANTUM INTEGRABLE SYSTEMS." In Nankai Lectures on Mathematical Physics. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814538534.

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Carfora, M., M. Martellini, and A. Marzuoli. "Integrable Systems and Quantum Groups." In Conference. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814537483.

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Koroteev, Peter, Niklas Beisert, and Marvin L. Marshak. "Integrable Systems and Quantum Deformations." In 10TH CONFERENCE ON THE INTERSECTIONS OF PARTICLE AND NUCLEAR PHYSICS. AIP, 2009. http://dx.doi.org/10.1063/1.3293858.

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Malbouisson, Adolfo P. C. "Time Evolution of confined quantum systems - a non-perturbative approach." In Workshop on Integrable Theories, Solitons and Duality. Sissa Medialab, 2002. http://dx.doi.org/10.22323/1.008.0025.

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Maillet, Jean-Michel. "Correlation functions of quantum integrable systems." In Non-perturbative Quantum Effects 2000. Sissa Medialab, 2000. http://dx.doi.org/10.22323/1.006.0051.

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Wang, Yan. "Simulating Stochastic Diffusions by Quantum Walks." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12739.

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Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the major challenges of computational efficiency in solving FPE numerically. In this paper, a generic continuous-time quantum walk formulation is developed to simulate stochastic diffusion processes. Stochastic

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GIORDANO, M., G. MARMO, A. SIMONI, and F. VENTRIGLIA. "INTEGRABLE AND SUPER-INTEGRABLE SYSTEMS IN CLASSICAL AND QUANTUM MECHANICS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0025.

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LeTourneux, Jean, and Luc Vinet. "Quantum Groups, Integrable Models and Statistical Systems." In 1992 CAP/NSERC Summer Institute. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535137.

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Reports on the topic "Quantum integrable system"

1

Danilov, Viatcheslav, and Sergei Nagaitsev. On Quantum Integrable Systems. Office of Scientific and Technical Information (OSTI), 2011. http://dx.doi.org/10.2172/1036292.

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