Related papers: Structural Stability Hypothesis of Dual Unitary Qu…
We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form…
In recent years dual-unitary circuits and their multi-unitary generalizations have emerged as exactly solvable yet chaotic models of quantum many-body dynamics. However, a systematic picture for the solvability of multi-unitary dynamics…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient…
The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $\Delta_3(L)$. It is shown that some standard unfolding procedures,…
We address the longstanding challenge in quantum many-body theory of reconciling unitary dynamics with irreversible relaxation. In classical chaos, the unitary evolution operator develops Ruelle-Pollicott (RP) resonances inside the unit…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and…
Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can…
We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
We semiclassically derive the leading off-diagonal correction to the spectral form factor of quantum systems with a chaotic classical counterpart. To this end we present a phase space generalization of a recent approach for uniformly…