Related papers: Random Partitions and the Quantum Benjamin-Ono Hie…
We study random partitions $\lambda=(\lambda_1,\lambda_2,...,\lambda_d)$ of $n$ whose length is not bigger than a fixed number $d$. Suppose a random partition $\lambda$ is distributed according to the Jack measure, which is a deformation of…
Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a…
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect,…
While run-and-tumble particles are a foundational model for self-propelled particles as bacteria or Janus particles, the analytical derivation of their steady state from the microscopic details is still an open problem. By directly modeling…
A new quantum mechanical distribution function $n^I(\varepsilon)$, is derived for the condition $n \ge g$, where in contrast to the exclusion principle $n \le g$ for fermions, each energy state must be populated by at least one particle.…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
The primary focus of this work is to investigate how the most emblematic classical probability density, namely a Gaussian, can be mapped to a valid quantum states. To explore this issue, we consider a Gaussian whose squared variance depends…
We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to…
We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical…
This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting of the…
We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…
Core partitions have attracted much attention since Anderson's work (2002) on the number of $(s,t)$-core partitions for coprime $s,t$. Recently, there has been a growing interest in studying the limiting distributions of the sizes of random…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
The equilibrium properties of a system of passive diffusing particles in an external magnetic field are unaffected by the Lorentz force. In contrast, active Brownian particles exhibit steady-state phenomena that depend on both the strength…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
The Benjamin-Ono equation describes the propagation of internal waves in a stratified fluid. In the present work, we study large time dynamics of its regular solutions via some probabilistic point of view. We prove the existence of an…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…