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Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…
We report the first analytical calculation of the distribution of the time headways in some special cases of a particle-hopping model of vehicular traffic on idealized single-lane highways and compare with the corresponding results of our…
It is known that the origin of the deviations from standard thermodynamics proceed from the strong coupling to the bath. Here, it is shown that these deviations are related to the power spectrum of the bath. Specifically, it is shown that…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different…
Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is…
The Curie-Weiss model is used to study phase transitions in statistical mechanics and has been the object of rigorous analysis in mathematical physics. We analyse the problem of reconstructing the probability measure of a multi-group…
We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy $V_\mathcal{SE}$ as a stochastic variable. Using a reference-particle decomposition, we derive exact, closed-form…
Based on the relationship that the interaction energy between any two subsystems is equal to their internal energy multiplied by the interaction coefficient, we have derived a series correlated expressions of statistical physical…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through…
Many technologies emerging from quantum information science heavily rely upon the generation and manipulation of entangled quantum states. Here, we propose and demonstrate a new class of quantum interference phenomena that arise when states…
Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…
We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM). The COE is defined as the…
We introduce the concept of fidelity for dynamical maps in an open quantum system scenario. We derive an inequality linking this quantity to the distinguishability of the inducing environmental states. Our inequality imposes constraints on…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional spin glasses and hard spheres we point…
We consider physical Hamiltonians that can be represented by the multiparametric Gaussian ensembles, theoretically derive the state ensembles for its eigenstates and analyze the effect of varying system conditions on its bipartite…
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with…
The eigenstates and the scattering transmission for two interacting electrons are found exactly for I quantum dots, including the hybridization with the states on the leads. The results imply limitations on the validity of the Coulomb…