Using the Liouville space framework developed in nonlinear optics, we calculate the linear response functions and susceptibilities of Bose-Einstein condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures of the dynamics of finite-temperature BEC are obtained by solving the Hartree-Fock-Bogoliubov theory. Numerical simulations of the position-dependent linear response functions of one-dimensional trapped BEC in the time and the frequency domains are presented.

arXiv:cond-mat/0301108Physical Review AApr 7, 20032 citations

arXiv:1501.04694 · The European Physical Journal D

Space-time curvature signatures in Bose-Einstein condensates

Tonatiuh Matos, E. Gómez

Published May 1, 2015• 6 citations

arXiv HTML PDF

DOI: 10.1140/epjd/e2015-60062-3

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α< 0

. Inspired by Haldane's exclusion statistics, this formulation introduces a modified occupation weight function that encodes effective statistical interactions via the parameter

α

. Using thermodynamic geometry, we analyze the sign and singular behavior of the thermodynamic curvature as a diagnostic of underlying interactions and phase structures. A crossover temperature

T^{*}

, at which the curvature changes sign, marks the transition between effectively attractive (Bose-like) and repulsive (Fermi-like) statistical regimes. When expressed relative to the Bose--Einstein condensation temperature

T_{c}

, the ratio

T^{*}/T_{c}

depends universally on

α

. For negative

α

, corresponding to hyperbosonic statistics, we find curvature singularities at specific fugacities, indicating modified condensation phenomena distinct from conventional Bose condensation. These results highlight the geometric and thermodynamic consequences of alpha statistics and establish a link between fractional exclusion principles and curvature-induced interaction signatures in statistical thermodynamics.