Related papers: Spatial random permutations and infinite cycles
It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the…
We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group $S_n$ and are consistent as $n$ varies. The extreme infinitely spherically symmetric permutation-valued processes are identified…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
In this paper we study the relation between long cycles and Bose-Condensation in the Infinite range Bose-Hubbard Model with a hard core interaction. We calculate the density of particles on long cycles in the thermodynamic limit and find…
An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
We study spatial correlations of vortices in different quantum states or with Bose or Fermi statistics. This is relevant for both optical vortices and condensed-matter ones such as microcavity polaritons, or any platform that can prepare…
The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different…
In this paper we study the state determination for composite systems of two spatial qubits. We show, theoretically, that one can use the technique of quantum tomography to reconstruct the density matrixes of these systems. This tomographic…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
Recently, a novel algorithm for computing the density of states in statistical systems and quantum field theories has been proposed. The same method can be applied to theories at finite density affected by the notorious sign problem,…
We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as…
We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…
A finite one-dimensional microscopic model of a superfulid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal…
Based on the paper "Fourier formula for quantum partition functions", arXiv:2106.10032 [math-ph], we show that in an infinite system of identical bosons interacting via a positive-type pair potential there is off-diagonal long-range order…
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
The measured values of the matter energy density and the vacuum energy density are obtained using an adiabatic black hole percolating model at the critical point. The percolation of black holes is related with an expanding isotropic…
Non-equilibrium conditions give rise to classes of universally evolving configurations of quantum-many body systems at non-thermal fixed points. While the fixed point and thus full scaling in space and time is generically reached at very…