Related papers: Direct derivation of microcanonical ensemble avera…
Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical…
A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68}, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly…
We present a derivation of power law canonical distributions from first principle statistical mechanics, including the exponential distribution as a It is presented a derivation of power law canonical distributions from first principle…
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can…
We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single…
We propose a method to calculate finite-temperature properties of a quantum many-body system for a microcanonical ensemble by introducing a pure quantum state named here an energy-filtered random-phase state, which is also a potentially…
We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas in a quantum-mechanical framework which is appropriate for the statistical model of hadronization. By using a suitable transition operator for…
A theoretical approach is proposed to calculate an effective dielectric constant of a matrix disperse system (MDS) of metallic particles (spheres) randomly distributed and embedded in a uniform dielectric medium. Deviations from the…
We introduce a simple but efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations. By evaluating the thermodynamic grand potential instead of the ground state total energy, we greatly reduce the sampling…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
Quantum relativistic probability description of continuous world is re-examined. The new conception of physical world is offered. It is based on deterministic description of elementary particles, on conception The standard probability…
Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
We solve the mean-field $\phi^4$ model in an external magnetic field in the microcanonical ensemble using two different methods. The first one is based on Rugh's microcanonical formalism and leads to express macroscopic observables, such as…