Related papers: Electrostatics on Branching Processes
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
We introduce ensembles of repelling charged particles restricted to a ball in a non-archimedean field (such as the $p$-adic numbers) with interaction energy between pairs of particles proportional to the logarithm of the ($p$-adic) distance…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to…
The Brown-Resnick max-stable process has proven to be well-suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is intractable and inference must be based on a composite…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
The partition function and specific heat of a system consisting of a finite number of bosons confined in an external potential are calculated in canonical ensemble. Using the grand partition function as the generating function of the…
The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…
Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
The partition function of a bosonic Riemann gas is given by the Riemann zeta function. We assume that the hamiltonian of this gas at a given temperature $\beta^{-1}$ has a random variable $\omega$ with a given probability distribution over…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
We open a new discussion of generalized canonical partition function in standard statistical mechanics and apply it for the study of Bose-Einstein condensation. We discuss the possible cases for the generalized canonical partition function…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…