Related papers: CLT for NESS of a reaction-diffusion model
We derive a Central Limit Theorem (CLT) for $\log \left\vert\det \left( W_{N}-E_{N}\right)\right\vert,$ where $W_{N}$ is a Wigner matrix, and $E_{N}$ is local to the edge of the semi-circle law. Precisely, $E_N=2+N^{-2/3}\sigma_N$ with…
A parabolic-parabolic (Patlak-) Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a…
In the setting of the principle of local equilibrium which asserts that the temperature is a function of the energy levels of the system, we exhibit plenty of steady states describing the condensation of free Bosons which are not in thermal…
The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron…
We study a system of $N$ particles interacting through the Kac collision, with $m$ of them interacting, in addition, with a Maxwellian thermostat at temperature $\frac{1}{\beta}$. We use two indicators to understand the approach to the…
We study a two state ``jumping diffusivity'' model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of…
We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the…
A beam's density matrix that is described by the superposition of excitation on coherent states with thermal noise (SECST) is presented, and its matrix elements in Fock space are calculated. The maximum information transmitted by the SECST…
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…
Through exact numerical solutions we show Bose-Einstein condensation (BEC) for the one-dimensional (1D) bosons with repulsive short-range interactions at zero temperature by taking a particular large size limit. Following the…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
We study a model of random colliding particles interacting with an infinite reservoir at fixed temperature and chemical potential. Interaction between the particles is modeled via a Kac master equation \cite{kac}. Moreover, particles can…
We study the mass density distribution of Newtonian self-gravitating systems. Modeling the system as a fluid in hydrostatical equilibrium, we obtain from first principle the field equation and its solution of correlation function $\xi(r)$…
It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of $L^2$…
We investigate sub-AdS scale locality in a weakly coupled toy model of the AdS$_3$/CFT$_2$ correspondence. We find that this simple model has the correct density of states at low and high energies to be dual to Einstein gravity coupled to…
Linear response theory is ubiquitous throughout physics and plays a central role in the theoretical description of warm dense matter -- an extreme state that occurs within compact astrophysical objects and that is traversed on the…
We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down…