Related papers: Quantum Kinetic Equations and Evolution of Many-Pa…

Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time…

We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual…

We consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the…

We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and…

We review curvature-based hyperbolic forms of the evolution part of the Cauchy problem of General Relativity that we have obtained recently. We emphasize first order symmetrizable hyperbolic systems possessing only physical characteristics.

We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin…

We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity mode, in the presence of decoherence and dissipation for both fermions and cavity photons. The analytic solutions are derived for a broad…

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…

We solved the Quantum Kinetic Equations (QKEs) for an active-sterile neutrino system in the early universe. While on the surface this may seem to be an overly simplistic system, other linear two-state systems can be mapped onto the…

Many-particle quantum systems often give rise to exotic behaviors in their nonequilibrium dynamics that are rather challenging to reveal with analytical methods or with classical computation. Here, we consider the case of a system of many…

We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This…

We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is…

Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the…

By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained…

We study the dynamics of open quantum many-body systems driven across a critical point by quenching an Hamiltonian parameter at a certain velocity. General scaling laws are derived for the density of excitations and energy produced during…

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of…

A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as…

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…