Related papers: Effective equations for quantum dynamics
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
We provide an error bound for approximating the time evolution of N bosons by a generalized nonlinear Hartree equation. The bosons are assumed to interact via permutation symmetric bounded many-particle potentials and the initial…
Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research, showcasing surprising behaviors that include apparent violation of the adiabatic theorem…
We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences…
This work is devoted to the study of relaxation--dissipation processes in systems described by Quantum Field Theory. In the first part, I focus on the phi^4 scalar quantum field theory in finite volume in the large N limit. I find that the…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for…
Based on classical transport theory, we present a general set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out-of-equilibrium. A procedure to obtain the…
Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the…
We investigate the behaviour of the QCD evolution towards high-energy, in the diffusive approximation, in the limit where the fluctuation contribution is large. Our solution for the equivalent stochastic Fisher equation predicts the…
The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated…
Far-from-equilibrium situations are ubiquitous in nature. They are responsible for a wealth of phenomena, which are not simple extensions of near-equilibrium properties, ranging from fluid flows turning turbulent to the highly organized…
Einstein conjectured long ago that much of quantum mechanics might be derived as a statistical formalism describing the dynamics of classical systems. Bell's Theorem experiments have ruled out complete equivalence between quantum field…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
A quantum-kinetic formulation of the dynamical evolution of a high-energy non-equilibrium gluon system at finite density is developed, to study the interplay between quantum fluctuations of high-momentum (hard) gluons and the low-momentum…
Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of…
We analytically derive the exact -- though formal -- master equation for a two-level quantum system (qubit) interacting with a bosonic environment within the rotating-wave approximation, assuming the environment is initially in an arbitrary…
We consider the evolution of quasi-free states describing $N$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $N$, we study the convergence towards the classical Vlasov equation. For a…
It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…