Studies of bosons in optical lattices in a harmonic potential

TL;DR

This paper provides a theoretical analysis of Bose condensation and specific heat in finite optical lattice systems with harmonic trapping, exploring how these properties vary with temperature, dimensionality, and system size.

Contribution

It introduces a numerical approach to diagonalize the Hamiltonian for non-interacting bosons in finite lattices, analyzing their thermodynamic properties across different dimensions.

Findings

Condensate fraction depends on temperature, dimensionality, and lattice size.

Specific heat shows characteristic behavior related to dimensionality and finite size effects.

Preliminary results on fermionic specific heat are also discussed.

Abstract

We present a theoretical study of bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.