Related papers: Long Cycles in the Infinite-Range-Hopping Bose-Hub…
In this paper we study the relation between long cycles and Bose-Einstein condensation in the Infinite-Range Bose-Hubbard Model. We obtain an expression for the cycle density involving the partition function for a Bose-Hubbard Hamiltonian…
We study the relationship between long cycles and Bose-Einstein condensation (BEC) in the case of several models. A convenient expression for the density of particles on cycles of length $q$ is obtained, in terms of $q$ unsymmetrised…
In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density $\rho=\rho_{{\rm…
In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the…
The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated. For the purpose of considering the non-ergodicity, a…
We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose--Einstein condensation. Starting from the Landsberg recursion relation for the…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
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…
We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the…
In this study, we reveal nontrivial quantum physics in an infinite-temperature system. By performing an unbiased quantum Monte Carlo simulation, we study a hybrid model composed of hard-core bosons, whose hopping amplitude is mediated by…
The usual order parameter for the Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order…
We study the lengths of the cycles formed by trajectories in the Feynman-Kac representation of the Bose gas. We discuss the occurrence of infinite cycles and their relation to Bose-Einstein condensation.
This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…
We study correlations of atomic density in a weakly interacting Bose-Einstein condensate, expanding diffusively in a random potential. We show that these correlations are long-range and that they are strongly enhanced at long times. Density…
In this paper we investigate the Bose-Einstein condensation of massive spin-1 particles in an Einstein universe. The system is considered under relativistic conditions taking into consideration the possibility of particle-antiparticle pair…
We study the dynamics in a one dimensional hard-core Bose gas with power-law hopping after an abrupt reduction of the hopping range using the time-dependent density-matrix renormalization group (t-DMRG) and bosonization techniques. In…
We consider a massive complex scalar field with contact interactions with a source and show that, upon Bose-Einstein condensation, there is an emergent long-range interaction between sources. This interaction becomes long-range in the limit…
This paper studies probabilistic mean-field models for interacting bosons at a positive temperature in the thermodynamic limit with random particle density. In particular, we prove large deviation principles for empirical cycle counts in…
We study two-body correlations in a many-boson system with a hyperspherical approach, where we can use arbitrary scattering length and include two-body bound states. As a special application we look on Bose-Einstein condensation and…
We study theoretically the collective dynamics of rotational excitations of polar molecules loaded into an optical lattice in two dimensions. These excitations behave as hard-core bosons with a relativistic energy dispersion arising from…