Related papers: Random density matrices versus random evolution of…
A simplified model of an initially excited oscillator as a quantum system interacting with a large number of oscillators acting as a reservoir has been developed in this work. All these oscillators are in their ground state uncoupled each…
This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a…
We discuss two methods of an exact stochastic representation of the non-Markovian quantum dynamics of open systems. The first method employs a pair of stochastic product vectors in the total system's state space, while the second method…
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
We study two types of random matrix ensembles that emerge when considering the same probability measure on partitions. One is the Meixner ensemble with a hard wall and the other are two families of unitary matrix models, with weight…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a…
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to…
We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are…
We study the evolution of an open quantum system using a Langevin unravelling of the density matrix evolution over matrix product states. As the strength of coupling to and temperature of the environment is increased, we find a transition…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…
We introduce a density tensor hierarchy for open system dynamics, that recovers information about fluctuations lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution,…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
Studies of density matrices for random quantum states lead naturally to the fixed trace Laguerre ensemble in random matrix theory. Previous studies have uncovered explicit rational function formulas for moments of purity statistic (trace of…
In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering…
The dynamics of a single qubit interacting by a sequence of pairwise collisions with an environment consisting of just two more qubits is analyzed. Each collision is modeled in terms of a random unitary operator with a uniform probability…
An "almost diagonal" reduced density matrix (in coordinate representation) is usually a result of environment induced decoherence and is considered the sign of classical behavior. We point out that the proton of a ground state hydrogen atom…
We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In…