Abstract We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.
Abstract We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.
This thesis explores non-equilibrium phenomena in quantum many-body systems, with a focus on correlated electron systems and photon Bose-Einstein condensates. The first part develops the theoretical foundation, beginning with the Lindblad master equation and the construction of non-equilibrium quantum field theory. The two-particle irreducible effective action formalism is introduced, from which the Kadanoff-Baym equations for real-time evolution and the Dyson equation for steady-states are derived. The theoretical groundwork continues with a treatment of strongly correlated electron systems, where non-equilibrium dynamical mean-field theory (DMFT), auxiliary particles, and the non-crossing approximation (NCA) are introduced. These techniques, together with the Lindblad and Kadanoff-Baym approaches, are used throughout the subsequent chapters. The second part presents the main research projects of this thesis. The first two projects are concerned with the fate of the heavy fermion state under irradiation of light. To accurately incorporate light-matter interactions in this case, dipole transitions must be included. In the first project a periodically driven system is considered, where the light can be treated semiclassically. A Floquet DMFT+NCA framework is developed, revealing the mechanisms and conditions under which the heavy fermion state is most strongly suppressed. The second project analyzes a THz spectroscopy experiment performed on CeCu6. In this case a semi-classical treatment of the light field is no longer sufficient, and a full two-time evolution of all the non-equilibrium Green functions is necessary. This approach reveals the microscopic mechanisms underlying the collapse and revival of the Kondo state observed in the experiment. The next project investigates a recent experiment regarding an observation of a non-Hermitian phase transition in EuO. The equilibrium properties of EuO are first analyzed, and then an exciton model is constructed that gives rise to the non-Hermitian phase transition, in good agreement with experimental observations. In the final project, a photon Bose-Einstein condensate in a dye-filled microcavity is studied. A stabilization mechanism, distinct from thermalization, is revealed which admits a condensate phase for orders of magnitude longer than the experimentally relevant timescales.
Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.
This book presents an up-to-date formalism of non-equilibrium Green's functions covering different applications ranging from solid state physics, plasma physics, cold atoms in optical lattices up to relativistic transport and heavy ion collisions. Within the Green's function formalism, the basic sets of equations for these diverse systems are similar, and approximations developed in one field can be adapted to another field. The central object is the self-energy which includes all non-trivial aspects of the system dynamics. The focus is therefore on microscopic processes starting from elementary principles for classical gases and the complementary picture of a single quantum particle in a random potential. This provides an intuitive picture of the interaction of a particle with the medium formed by other particles, on which the Green's function is built on.
Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resummed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the “bare” number density function, and the second one is formulated on the basis of “physical” number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system.
We present a relativistic covariant form of many-body theory. The many-body covariant Lagrangian is derived from QED by integrating out the internal non-quantized electromagnetic field. The ordinary many-body Hamiltonian is recovered as an approximation to the exact covariant theory that contains many-body terms beyond the solely electrostatic interaction, e.g. the Lorentz force among electrons, spin-spin etc. Spin and relativistic terms, e.g. spin-orbit, are also automatically accounted. Moreover, the theory is compact, gauge-invariant and respects causality.
This paper introduces a novel Self-Consistent WKB-Variational Theory designed to investigate the complex dynamics of non-equilibrium quantum fields. Traditional approaches often struggle with strongly correlated systems or those far from thermal equilibrium, necessitating methods that capture both semiclassical evolution and quantum fluctuations. Our proposed framework unifies the Wentzel-Kramers-Brillouin (WKB) approximation, which provides a semiclassical description of the background field, with a time-dependent variational principle applied to quantum fluctuations around this background. The core of the theory lies in the self-consistent determination of the classical background field dynamics, influenced by quantum backreaction, and the evolution of the quantum fluctuations. This intricate interplay allows for a comprehensive description of non-perturbative phenomena, particle production, and phase transitions in dynamic settings. We elaborate on the theoretical derivation, outlining the coupled equations of motion for the background field and the variational parameters that characterize the quantum state. The advantages of this approach include its ability to address strong coupling regimes and provide a physically intuitive understanding of the interplay between classical and quantum degrees of freedom. Potential applications span diverse areas, from early universe cosmology to heavy-ion collisions and quantum quenches in condensed matter systems.