We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number $k\geq 2$ . The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper bound on the ground state energy per site. For a density $ρ$ a trivial upper bound is known to be $-kρ(1-ρ)$ . We obtain a smaller variational bound within a reasonably large family of trial functions. The estimates make use of a large deviation principle for the energy of the Ising model on the same lattice.We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number $k\geq 2$. The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper bound on the ground state energy per site. For a density $ρ$ a trivial upper bound is known to be $-kρ(1-ρ)$. We obtain a smaller variational bound within a reasonably large family of trial functions. The estimates make use of a large deviation principle for the energy of the Ising model on the same lattice.

arXiv:cond-mat/9905421May 28, 19990 citations

On the low density limit of Boson models

Luigi Accardi, Yun Gang Lu

Lecture notes in mathematicsJan 1, 19902 citations

On the microscopic theory of interacting bosons

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Progress in Particle and Nuclear PhysicsJan 1, 19831 citation

Large deviation analysis for classes of interacting Bosonic cycle counts

Stefan Adams, Matthew Dickson

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 all our models, and as such generalise recent work in \cite{ACK} where upper and lower large deviation bounds do not match. Namely, on the one hand we generalise to the so-called grand canonical ensemble, and on the other hand, we consider classes of interaction potentials depending on the cycle counts which are not restricted to be positive. Our large deviation results provide representation formulae for the thermodynamic limit of the pressure which in turn leads to proving Bose-Einstein-condensation (BEC) in all our models. A primary focus and novelty is the pressure representation via extended large deviation analysis for the so-called hard-sphere, or HYL-model (Huang-Yang-Luttinger) studied in \cite{Lew86}. This model has negative counter terms in the Hamiltonian and shows BEC depending on the coupling constants.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 all our models, and as such generalise recent work in \cite{ACK} where upper and lower large deviation bounds do not match. Namely, on the one hand we generalise to the so-called grand canonical ensemble, and on the other hand, we consider classes of interaction potentials depending on the cycle counts which are not restricted to be positive. Our large deviation results provide representation formulae for the thermodynamic limit of the pressure which in turn leads to proving Bose-Einstein-condensation (BEC) in all our models. A primary focus and novelty is the pressure representation via extended large deviation analysis for the so-called hard-sphere, or HYL-model (Huang-Yang-Luttinger) studied in \cite{Lew86}. This model has negative counter terms in the Hamiltonian and shows BEC depending on the coupling constants.

arXiv:1809.03387Sep 10, 20184 citations

Statistical mechanics of a system of interacting bosons

K. K. Singh

PhysicaJan 1, 196723 citations

We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number

k\geq 2

. The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper bound on the ground state energy per site. For a density

ρ

a trivial upper bound is known to be

-kρ(1-ρ)

. We obtain a smaller variational bound within a reasonably large family of trial functions. The estimates make use of a large deviation principle for the energy of the Ising model on the same lattice.