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Books on the topic 'Non Equilibrium Green's Function'
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1
Pourfath, Mahdi. The Non-Equilibrium Green's Function Method for Nanoscale Device Simulation. Vienna: Springer Vienna, 2014. http://dx.doi.org/10.1007/978-3-7091-1800-9.
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2
Kadanoff, Leo P. Quantum statistical mechanics: Green's function methods in equilibrium and nonequilibrium problems. Redwood City, Calif: Addison-Wesley Pub. Co., Advanced Book Program, 1989.
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3
Pourfath, Mahdi. Non-Equilibrium Green's Function Method for Nanoscale Device Simulation. Springer Wien, 2014.
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4
Pourfath, Mahdi. The Non-Equilibrium Green's Function Method for Nanoscale Device Simulation. Pourfath Mahdi, 2016.
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5
Pourfath, Mahdi. The Non-Equilibrium Green's Function Method for Nanoscale Device Simulation. Pourfath Mahdi, 2014.
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6
Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.
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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.
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Nikolic, Branislav K., Liviu P. Zarbo, and Satofumi Souma. Spin currents in semiconductor nanostructures: A non-equilibrium Green-function approach. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.24.
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This article examines spin currents and spin densities in realistic open semiconductor nanostructures using different tools of quantum-transport theory based on the non-equilibrium Green function (NEGF) approach. It begins with an introduction to the essential theoretical formalism and practical computational techniques before explaining what pure spin current is and how pure spin currents can be generated and detected. It then considers the spin-Hall effect (SHE), and especially the mesoscopic SHE, along with spin-orbit couplings in low-dimensional semiconductors. It also describes spin-current operator, spindensity, and spin accumulation in the presence of intrinsic spin-orbit couplings, as well as the NEGF approach to spin transport in multiterminal spin-orbit-coupled nanostructures. The article concludes by reviewing formal developments with examples drawn from the field of the mesoscopic SHE in low-dimensional spin-orbit-coupled semiconductor nanostructures.
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Thygesen, K. S., and A. Rubio. Correlated electron transport in molecular junctions. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.23.
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This article focuses on correlated electron transport in molecular junctions. More specifically, it considers how electronic correlation effects can be included in transport calculations using many-body perturbation theory within the Keldysh non-equilibrium Green’s function formalism. The article uses the GW self-energy method (G denotes the Green’s function and W is the screened interaction) which has been successfully applied to describe quasi-particle excitations in periodic solids. It begins by formulating the quantum-transport problem and introducing the non-equilibrium Green’s function formalism. It then derives an expression for the current within the NEGF formalism that holds for interactions in the central region. It also combines the GW scheme with a Wannier function basis set to study electron transport through two prototypical junctions: a benzene molecule coupled to featureless leads and a hydrogen molecule between two semi-infinite platinum chains. The results are analyzed using a generic two-level model of a molecular junction.
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Golizadeh-Mojarad, Roksana, and Supriyo Datta. NEGF-based models for dephasing in quantum transport. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.3.
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This article describes the use of NEGF-based models for elastic dephasing in quantum transport. The non-equilibrium Green's function (NEGF) method provides a rigorous prescription for including any kind of dephasing mechanisms to any order starting from a microscopic Hamiltonian through an appropriate choice of the self-energy function. The article first introduces the general approach to quantum transport that provides a general method for modelling a wide class of nanotransistor and spin devices. It then discusses the effect of different types of dephasing on momentum and spin relaxation before considering three simple phenomenological choices of the self-energy function that allows one to incorporate spin, phase and momentum relaxation independently. It also looks at an example that takes into account these three types of dephasing mechanisms: the ‘spin-Hall’ effect.
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Yang, Jinlong, and Qunxiang Li. Theoretical simulations of scanning tunnelling microscope images and spectra of nanostructures. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.15.
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This article presents theoretical simulations of scanning tunnelling microscope (STM) images and spectra of nanostructures. It begins with an overview of the theories of STM and scanning tunnelling spectroscopy (STS), focusing on four main approaches: the perturbation or Bardeen approach, the Tersoff–Hamann approach and its extension, the scattering theory or Landauer–Bütticker approach, and the non-equilibrium Green's function or Keldysh approach. It then considers conventional STM and STS experimental investigations of various systems including clean surfaces, ad-atoms, single molecules, self-assembled monolayers, and nanostructures. It also discusses STM activities that go beyond conventional STM images and STS, such as functionalized STM tip, inelastic spectroscopy identification, manipulation, molecular electronics and molecular machines.
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Horing, Norman J. Morgenstern. Quantum Statistical Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.001.0001.
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The methods of coupled quantum field theory, which had great initial success in relativistic elementary particle physics and have subsequently played a major role in the extensive development of non-relativistic quantum many-particle theory and condensed matter physics, are at the core of this book. As an introduction to the subject, this presentation is intended to facilitate delivery of the material in an easily digestible form to students at a relatively early stage of their scientific development, specifically advanced undergraduates (rather than second or third year graduate students), who are mathematically strong physics majors. The mechanism to accomplish this is the early introduction of variational calculus with particle sources and the Schwinger Action Principle, accompanied by Green’s functions, and, in addition, a brief derivation of quantum mechanical ensemble theory introducing statistical thermodynamics. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green’s function equations of motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and non-equilibrium Green’s functions, and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions includes quantum plasma dynamic, nonlocal screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low-dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as superconductors, superfluids and graphene.
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Succi, Sauro. Transport Phenomena. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0004.
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The previous Chapter presented a discussion of the notion of local and global equilibria and shown that these equilibria represent the special forms taken by the distribution function once direct and inverse collisions come into balance. This Chapter provides an elementary introduction to transport phenomena and discusses their intimate relation to non-equilibrium processes at the microscopic scale. In particular it shall deal with the connection between the transport coefficients, such as mass, momentum and energy diffusivity with the molecular mean free path, namely the distance traveled by a representative molecules between two subsequent collisions. The discussion also highlights the fundamental role of inhomogeneity in fueling non-equilibrium processes.
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Sklar, Lawrence. Causation in Statistical Mechanics. Edited by Helen Beebee, Christopher Hitchcock, and Peter Menzies. Oxford University Press, 2010. http://dx.doi.org/10.1093/oxfordhb/9780199279739.003.0033.
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In statistical mechanics causation appears at the micro-level as the postulation that the full state of a system at one time can be specified by the dynamical state of all its micro-constituents (the positions and momenta of the molecules in a gas or, alternatively the wave function of these at one time), and that this state at one time generates, following the laws of dynamics (classical or quantum) the future dynamical state of the system characterized in these micro-constituent terms. So what is ‘non-causal’ in nature in explanations in statistical mechanics? This article explores two issues: The peculiar ‘transcendental’ nature of explanation in equilibrium theory in statistical mechanics; The need for introducing some a priori probability posit over initial conditions of systems in non-equilibrium theory.
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Sabharwal, Nikant, Parthiban Arumugam, and Andrew Kelion. Radionuclide ventriculography. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198759942.003.0005.
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Radionuclide ventriculography (RNV) was the first reliable non-invasive method of assessing left ventricular (LV) function, and established nuclear cardiology as a clinical discipline. The subsequent development of other imaging modalities, particularly echocardiography, has led to a sharp decline in the number of studies performed, but RNV still has a role in situations where reproducible serial assessments of LV ejection fraction are required. Equilibrium RNV (ERNV) is the most straightforward and commonly performed style of RNV, and this chapter therefore focuses on ERNV, covering blood-pool labelling, principles of electrocardiogram (ECG) gating, acquisition, processing and interpretation, and clinical value in relation to ERNV. A section on first-pass radionuclide ventriculography is also included.
15
McDougal, Topher L. The Political Economy of Rural-Urban Conflict. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198792598.001.0001.
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In some cases of insurgency, the combat frontier is contested and erratic, as rebels target cities as their economic prey. In other cases, it is tidy and stable, seemingly representing an equilibrium in which cities are effectively protected from violent non-state actors. What factors account for these differences in the interface urban-based states and rural-based challengers? To explore this question, this book examines two regions representing two dramatically different outcomes. In West Africa (Liberia and Sierra Leone), capital cities became economic targets for rebels, who posed dire threats to the survival of the state. In Maoist India, despite an insurgent ideology aiming to overthrow the state via a strategy of progressive city capture, the combat frontier effectively firewalls cities from Maoist violence. This book argues that trade networks underpinning the economic relationship between rural and urban areas—termed “interstitial economies”—may differ dramatically in their impact on (and response to) the combat frontier. It explains rebel predatory tendencies toward cities as a function of transport networks allowing monopoly profits to be made by urban-based traders. It explains combat frontier delineation as a function of the social structure of the trade networks: hierarchical networks permit elite–elite bargains that cohere the frontier. These factors represent what might be termed respectively the “hardware” and “software” of the rural–urban economic relationship. Of interest to any student of political economy and violence, this book presents new arguments and insights about the relationships between violence and the economy, predation and production, core and periphery.
16
Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.
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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.
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Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.
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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.