Related papers: Nonuniversality in level dynamics
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Absence of level repulsion between extended states in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of level spacing of diffusive metals in the usual Hermitian systems is replaced by the…
We study the distribution of particle number in extended subsystems of a one-dimensional non-interacting Fermi gas confined in a potential well at zero temperature. Universal features are identified in the scaled bulk and edge regions of…
We study the dynamics of a quantum system in which an intermediate property $m$ is measured in between initial and final measurements of two different non-commuting properties $a$ and $b$. Since this intermediate measurement must involve an…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the…
We consider the classical dynamics of bosonic and fermionic matrix variables in complex Hilbert space, defined by a trace action, assuming cyclic invariance under the trace and the presence of a global unitary invariance. With plausible and…
Symmetric random walks in $R^d$ and $Z^d$ are considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all $x$ and $t$) asymptotic…
An interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of the Anderson transitions driven by non-Hermitian disorders for three dimensional (3D)…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…
Non-Hermitian dynamics, as observed in photonic, atomic, electrical, and optomechanical platforms, holds great potential for sensing applications and signal processing. Recently, fully tunable nonreciprocal optical interaction has been…
Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…