Recent conceptual advances in the theory of physics of highly excited semiconductors are based on two formalisms, the real-time non-equilibrium Green's function techniques and the coherently controlled truncation of the many-particle problems. These approaches apply to completely different but complementary experimental conditions. We present a novel many-particle theory, which contains both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first numerical rigorous solutions of the four-particle problem in a semiconductor. They are in excellent agreement with experimental data.
Recent conceptual advances in the theory of physics of highly excited semiconductors are based on two formalisms, the real-time non-equilibrium Green's function techniques and the coherently controlled truncation of the many-particle problems. These approaches apply to completely different but complementary experimental conditions. We present a novel many-particle theory, which contains both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first numerical rigorous solutions of the four-particle problem in a semiconductor. They are in excellent agreement with experimental data.
Recent theories of highly excited semiconductors are based on two formalisms, referring to complementary experimental conditions, the real-time nonequilibrium Green's function techniques and the coherently controlled truncation of the many-particle problem. We present a novel many-particle theory containing both of these methods as limiting cases. As a first example of its application, we investigate four-particle correlations in a strong magnetic field including dephasing resulting from the growth of incoherent one-particle distribution functions. Our results are the first rigorous solution concerning formation and decay of four-particle correlations in semiconductors. They are in excellent agreement with experimental data.
This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.
Nonequilibrium Green's Functions: History, General Problems, Plasmas: Real-Time Nonequilibrium Green's Functions (L V Keldysh) Theory of High-Tc Superconductivity in Layered Cuprates (A A Abrikosov) Correlated Quantum Plasmas in Strong Laser Fields (M Schlanges et al.) Quantum Transport in Semiconductors: Non-Equilibrium Green's Functions in Semiconductor Device Modeling (R Lake et al.) Nonequilibrium Green Function Modelling of Transport in Mesoscopic Systems (A-P Jauho) Bohm Trajectories in Quantum Transport (J R Barker) Optical and Electronic Properties of Semiconductors: Coulomb Correlations in the Quantum Kinetics of Electron Phonon Systems (W Schafer et al.) Excitonic Quantum Coherences and Correlations in Semiconductor Quantum Wells (R Binder et al.) Nuclear Matter and High Energy Physics: Renormalization of Self-Consistent F-Derivable Approximations (H van Hees & J Knoll) Crossover from Neutron-Proton Superfluidity to Bose-Einstein Condensation of Deuterons in Nuclear Matter (A A Isayev) Kinetics of Vacuum Pair Creation in Strong Electromagnetic Fields (A V Tarakanov et al.) Alternative Computational Methods: Time-Dependent Density Functional Theory from a Practitioners Perspective (K Andrae et al.) Combination of Quantum Kinetic Theory and First-Principle Simulations for Strongly Correlated Quantum Plasmas (M Bonitz et al.) Tunneling of Interacting Identical Particles (Yu E Lozovik et al.) and other papers.
We study theoretically electron transients in semiconductor alloys excited by light pulses shorter than 100 fs and tuned above the absorption edge during and shortly after the pulse, when disorder scattering is dominant. We use nonequilibrium Green functions employing the field-dependent self-consistent Born approximation. The propagators and the particle correlation function are obtained by a direct numerical solution of the Dyson equations in differential form. For the purely elastic scattering in our model system the solution procedures for the retarded propagator and for the correlation function can be decoupled. The propagator is used as an input in calculating the correlation function. Numerical results combined with a cumulant expansion permit one to separate in a consistent fashion the dark and the induced parts of the self-energy. The dark behavior reduces to propagation of strongly damped quasiparticles; the field induced self-energy leads to an additional time nonlocal coherence. The particle correlation function is formed by a coherent transient and an incoherent back-scattered component. The particle number is conserved only if the field induced coherence is fully incorporated. The transient polarization and the energy balance are also obtained and interpreted.
Abstract In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
The quantum theory of many-particle systems is deeply connected to the mathematical formalism and techniques of quantum field theory, which are crucial in order describe the emergent phenomena that arise in condensed matter physics. The main goal of this thesis is to provide a unified description of quantum field theory methods in the context of many-particle physics in order to extend and develop these techniques to better understand the different quantum properties of matter. This both furthers the conceptual understanding of quantum many-body correlation and also allows for the development of novel theoretical techniques that combine the different formalisms employed in condensed matter theory, quantum chemistry and nuclear physics. To achieve this aim, the thesis is composed of two parts. Part I deals with many-body fermion-fermion interactions and is physically motivated by the non-relativistic electronic structure problem. Here, we introduce the Keldysh contour formulation of quantum field theory to provide a unified presentation of quantum systems both in and out-ofequilibrium. Then, we extend the conventional quantum theory of many-particle systems, based on hermitian quantum mechanics, to describe systems governed by non-hermitan Hamiltonians. This allows us to present a natural unification of two major pillars in the ab initio quantum theory of many-particle systems: coupled-cluster theory and the Green’s function formalism. This unification is further demonstrated through the emergence of the coupled-cluster amplitude equations from the Green’s function formalism. In particular, this analysis has direct bearing on the development of novel theoretical approaches to the electronic structure and nuclear many-body problems. Our findings are also relevant to the study of general non-hermitian as well as open quantum systems. Part II focuses on the quantum field theory of electron-nuclear interactions in infinite solids. Here, we use the Keldysh contour representation presented in Part I to understand excited state dynamics that include electron-electron and electron-lattice interactions in materials. We also derive the analytic continuation of the Green’s function for systems that have continuous eigenspectra. This analysis demonstrates the relationship between the Green’s function formalism and scattering theory, making the role of the continuum and causality conditions explicitly clear in the context of the pole condition of the Dyson equation. Using the analytic continuation of the propagator, we provide an in-depth analysis of electron-phonon and exciton-phonon scattering channels, with a particular focus on phonon-driven exciton dissociation scattering. Our theoretical analysis then firmly demonstrates the connection between the extension of the Bethe-Salpeter equation approach to include electron-phonon interactions and effective field theories based on composite exciton-phonon coupling. We subsequently combine the techniques presented in Part I, based on the Dyson supermatrix formulation, with the analysis presented in Part II to calculate, from first principles, the effects of including electron-phonon interactions on the excited states of heterogeneous semiconductors. Finally, we provide a summary of the fundamental contributions presented in this thesis and the potential further research directions to be pursued.