Related papers: Squeezed ensemble for systems with first-order pha…
The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic…
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows…
I present a theoretical model of a quantum statistical ensemble for which, unlike in conventional physics, the total number of particles is extremely small. The thermodynamical quantities are calculated by taking a small $N$ by virtue of…
Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example in ultrafast coherent…
A new master equation performing isotropic phase-number squeezing is suggested. The phase properties of coherent superpositions are analyzed when the state evolves in presence of a bath with fluctuations squeezed in this isotropic way. We…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing…
In this paper we develop a statistical mechanical interpretation of the noiseless source coding scheme based on an absolutely optimal instantaneous code. The notions in statistical mechanics such as statistical mechanical entropy,…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Spin squeezing is a form of entanglement that reshapes the quantum projection noise to improve measurement precision. Here, we provide numerical and analytic evidence for the following conjecture: any Hamiltonian exhibiting finite…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration. Here we discuss how extended ensemble Monte Carlo simulations can be used to study the…
In many medical and business applications, researchers are interested in estimating individualized treatment effects using data from a randomized experiment. For example in medical applications, doctors learn the treatment effects from…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits…
We investigate a quasi-adiabatic thermal process for preparing finite-temperature ensembles in the thermodynamic limit. The process gradually transforms a thermal ensemble of a noninteracting system into that of an interacting system of…
Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model…