BoseEinstein condensation on a manifold with nonnegative Ricci curvature
Abstract
The BoseEinstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the cnumber substitution on a manifold is given.
 Authors:
 Department of Physics, Boğaziçi University, 34342 Bebek, Istanbul (Turkey)
 Publication Date:
 OSTI Identifier:
 22403091
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSEEINSTEIN CONDENSATION; BOSEEINSTEIN GAS; EIGENVALUES; GROUND STATES; HEAT; KERNELS; LAPLACIAN
Citation Formats
Akant, Levent, Email: levent.akant@boun.edu.tr, Ertuğrul, Emine, Email: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, Email: waskhez@gmail.com, and Turgut, O. Teoman, Email: turgutte@boun.edu.tr. BoseEinstein condensation on a manifold with nonnegative Ricci curvature. United States: N. p., 2015.
Web. doi:10.1063/1.4906135.
Akant, Levent, Email: levent.akant@boun.edu.tr, Ertuğrul, Emine, Email: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, Email: waskhez@gmail.com, & Turgut, O. Teoman, Email: turgutte@boun.edu.tr. BoseEinstein condensation on a manifold with nonnegative Ricci curvature. United States. doi:10.1063/1.4906135.
Akant, Levent, Email: levent.akant@boun.edu.tr, Ertuğrul, Emine, Email: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, Email: waskhez@gmail.com, and Turgut, O. Teoman, Email: turgutte@boun.edu.tr. 2015.
"BoseEinstein condensation on a manifold with nonnegative Ricci curvature". United States.
doi:10.1063/1.4906135.
@article{osti_22403091,
title = {BoseEinstein condensation on a manifold with nonnegative Ricci curvature},
author = {Akant, Levent, Email: levent.akant@boun.edu.tr and Ertuğrul, Emine, Email: emine.ertugrul@boun.edu.tr and Tapramaz, Ferzan, Email: waskhez@gmail.com and Turgut, O. Teoman, Email: turgutte@boun.edu.tr},
abstractNote = {The BoseEinstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the cnumber substitution on a manifold is given.},
doi = {10.1063/1.4906135},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 56,
place = {United States},
year = 2015,
month = 1
}

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