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dc.contributor.authorBordag, Michael
dc.contributor.authorMuñoz Castañeda, José María
dc.contributor.authorSantamaría Sanz, Lucía 
dc.date.accessioned2025-01-23T08:22:12Z
dc.date.available2025-01-23T08:22:12Z
dc.date.issued2020-03
dc.identifier.issn1434-6044
dc.identifier.urihttp://hdl.handle.net/10259/10005
dc.description.abstractThe basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac δ − δ' functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case T → 0 we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.en
dc.description.sponsorshipThe authors are grateful to the Spanish GovernmentMINECO (MTM2014- 57129-C2-1-P) for the financial support received. JMMC and LSS are grateful to the Junta de Castilla y León (BU229P18, VA137G18 and VA057U16) for the financial support. LSS is grateful to the Spanish Government-MINECO for the FPU-fellowships programme (FPU18/00957).es
dc.format.mimetypeapplication/pdf
dc.language.isoenges
dc.publisherSpringeres
dc.relation.ispartofThe European Physical Journal C. 2020, V. 80, n. 3es
dc.rightsAtribución 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subject.otherFísicaes
dc.subject.otherPhysicsen
dc.titleFree energy and entropy for finite temperature quantum field theory under the influence of periodic backgroundsen
dc.typeinfo:eu-repo/semantics/articlees
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.relation.publisherversionhttps://doi.org/10.1140/epjc/s10052-020-7783-3es
dc.identifier.doi10.1140/epjc/s10052-020-7783-3
dc.identifier.essn1434-6052
dc.journal.titleThe European Physical Journal Ces
dc.volume.number80es
dc.issue.number3es
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersiones


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