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Santamaría Sanz, Lucía 2025-03-13T08:33:35Z 2025-03-13T08:33:35Z 2024-05 1751-8113 http://hdl.handle.net/10259/10319 10.1088/1751-8121/ad4754 1751-8121 The one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised in terms of the scattering data, allowing to compute the quantum vacuum interaction energy between nodes at zero temperature, as well as the total Helmholtz free energy, the entropy, and the Casimir pressure between nodes at finite non-zero temperature. Some examples of periodic potentials built from the repetition in one of the three spatial dimensions of the same punctual or compact supported potential are addressed: a stack of parallel plates constructed by positioning -functions at the lattice nodes, and an 'upside-down tiled roof' of parallel two-dimensional Pöschl–Teller wells centred at the nodes. They will be called generalised Dirac comb and Pöschl–Teller comb, respectively. Positive one-loop quantum corrections to the entropy appear for both combs at non-zero temperatures. Moreover, the Casimir force between the lattice nodes is always repulsive for both chains when non-trivial temperatures are considered, implying that the primitive cell increases its size due to the quantum interaction of the phonon field. This research was supported by the Spanish Ministry of Science and Innovation MICIN with funding from European Union NextGenerationEU (PRTRC17.I1) and by the Regional Government of Castilla y Le´on (Junta de Castilla y Le´on, Spain) through QCAYLE project. application/pdf eng IOP Publishing Journal of Physics A: Mathematical and Theoretical. 2024, V. 57, n. 22, p. 225402 https://doi.org/10.1088/1751-8121/ad4754 Thermal field theory Scattering amplitudes Topological solitons Quantum vacuum Física Matemáticas Physics Mathematics Quantum field theory at finite temperature for 3D periodic backgrounds info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion info:eu-repo/semantics/openAccess Journal of Physics A: Mathematical and Theoretical 57 22 225402