Related papers: Spectral Statistics, Hydrodynamics and Quantum Cha…
Under unitary evolution, chaotic quantum systems initialized in simple states rapidly develop high complexity, precluding any efficient classical description. Quantum chaos is traditionally characterized by spectral properties of the…
We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a…
We investigate universal signatures of quantum chaos in the presence of time reversal symmetry (TRS) in generic many body quantum chaotic systems (gMBQCs). We study three classes of minimal models of gMBQCs with TRS, realized through random…
Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean…
Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean field basis to…
Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in many- body systems. In the classical case, chaos is a…
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We…
We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which in particular describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic…
We introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define…
In this work, we perform a holographic study to estimate the effect of backreaction on the correlation between two subsystems forming the thermofield double (TFD) state. Each of these subsystems is described as a strongly coupled…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
We study a microscopic Hamiltonian model describing an N-level quantum system S coupled to an infinitely extended thermal reservoir R. Initially, the system S is in an arbitrary state while the reservoir is in thermal equilibrium at…
The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral…
A closed quantum system thermalizes if for time $t \to \infty$, the function ${\rm Tr} (A \rho(t))$ tends asymptotically to ${\rm Tr} (A \rho_{\rm eq})$. Here $A$ is an operator that represents an observable, $\rho(t)$ is the time-dependent…
We extend the results of two of our papers [Phys. Rev. A 94, 041603R (2016) and Phys. Rev. B 97, 060303R (2018)] that touch upon the intimately connected topics of quantum chaos and thermalization. In the first, we argued that when the…
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found…
Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities such as matter, energy and charge flow from outer reservoirs across a system, and how they irreversibly degrade from one form to another. Stochastic…