Related papers: Spectral Statistics, Hydrodynamics and Quantum Cha…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
Recent work highlighted the importance of higher-order correlations in quantum dynamics for a deeper understanding of quantum chaos and thermalization. The full Eigenstate Thermalization Hypothesis, the framework encompassing correlations,…
Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle.…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations. The definitions of work and heat and the microscopically reversible condition are two key concepts…
Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, $\Delta T$. However, experimental studies have exhibited a finite value of $\Delta T$ for a transition to TC. This paper explores…
The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems.…
The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as $10^{23}$ degrees of…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
It was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form, belongs to the family of cohomological…
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…
In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which…
We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix…
A classical dynamical system can be viewed as a probability space equipped with a measure-preserving time evolution map, admitting a purely algebraic formulation in terms of the algebra of bounded functions on the phase space. Similarly, a…
The problem of the insensitivity of the macroscopic behavior of any thermodynamical system to partitioning generates a bias between the reproducibility of its macroscopic behavior viewed as the simplest form of causality and its long-term…
Temperature chaos is a striking phenomenon in spin glasses, where even slight changes in temperature lead to a complete reconfiguration of the spin state. Another intriguing effect is the reentrant transition, in which lowering the…
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases,…
Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify ``ergodicity'', including the presence of underlying macroscopic symmetries, in generic quantum systems…