aqora

Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model

J.-B. Bru, T. C. Dorlas

Journal of Statistical PhysicsOct 1, 200326 citations

Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores

G. Boland, J. V. Pulé

arXiv:0806.0791Journal of Statistical PhysicsJul 2, 20085 citations

Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores

G. Boland, Joseph V. Pulé

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 that the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation but this density is not equal to that of the Bose condensate.

Jan 1, 20086 citations

On the Nature of Bose-Einstein Condensation in Disordered Systems

Thomas Jaeck, Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

arXiv:0905.4790Journal of Statistical PhysicsSep 28, 20098 citations

Long cycles in the infinite-range-hopping Bose–Hubbard model

G. Boland

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 with a single-site correction. Inspired by the approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long cycle density vanishes. In the presence of condensation we can justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long cycle density with the condensate and find that although they coexist, in general, they are not equal.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 with a single-site correction. Inspired by the approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long cycle density vanishes. In the presence of condensation we can justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long cycle density with the condensate and find that although they coexist, in general, they are not equal.

arXiv:1002.3079Journal of Mathematical PhysicsJul 1, 20092 citations

Bose-Einstein condensation in an exactly solvable model of strongly interacting bosons

Michael W. Kirson

An exact algebraic solution is presented for the spectrum of the Bose-Hubbard model for pure systems in the limit of infinite-range hopping and infinite on-site repulsion. This strongly interacting boson system is shown to exhibit Bose-Einstein condensation into the lowest unperturbed single-particle state, with a transition temperature which, for any density of bosons, is always lower than that in the absence of interactions.

Journal of Physics A Mathematical and GeneralJan 24, 20006 citations

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

Related papers

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

Related papers