Related papers: Semi-Poisson statistics in quantum chaos
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
The classical trajectories of a particle governed by the PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in depth. It is known that almost all trajectories that begin at a classical turning point…
We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield…
We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
With many Hamiltonians one can naturally associate a |Psi|^2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
We present a trajectory-based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities, in the regime of many open channels. Our method to obtain the $m$th moment of the density of transmission…
We establish a new spin-statistics theorem for a class of free pseudo-Hermitian quantum field theories whose particles furnish unitary irreducible representations of the Poincar\'{e} group. In this framework, free pseudo-Hermitian fields…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
For Hamiltonian systems, level statistics provide a faithful diagnostic of quantum chaos. By analogy, the statistics of the Lindbladian spectrum are often used in open quantum systems, and the Grobe-Haake-Sommers conjecture proposes that…
We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine the classical partition function thereof, we…
We present a statistical analysis on the performance of a protocol for the faithful transfer of a quantum state in finite qubit or spin chains, in the presence of diagonal and off-diagonal disorder. It is shown that the average-state…
We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…