Related papers: Equilibration properties of small quantum systems:…
How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular…
We address the problem of understanding from first principles the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand previously known general upper bounds on the time scales…
We consider different properties of small open quantum systems coupled to an environment and described by a non-Hermitian Hamilton operator. Of special interest is the non-analytical behavior of the eigenvalues in the vicinity of singular…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time…
We study two classes of open systems: discrete-time quantum walks (a type of Floquet-engineered discrete quantum map) and the Lindblad master equation (a general framework of dissipative quantum systems), focusing on the non-equilibrium…
Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. Using concurrence as the entanglement…
We consider a nonlinear autonomous random dynamical system of $N$ degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum $n_{\mu}(\lambda)$ of real positive relaxation rates. Using Kac-Rice…
We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
We study the dynamical process of equilibration of topological properties in quantum many-body systems undergoing a parameter quench between two topologically inequivalent Hamiltonians. This scenario is motivated by recent experiments on…
We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT…
For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any…
Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and…
Designing a good transfer channel for arbitrary quantum states in spin chains implies optimizing a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles…
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 consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such…