Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction

Deuchert, Andreas; Geisinger, Alissa; Hainzl, Christian; Loss, Michael

doi:10.1007/s00023-018-0665-7

Cited by 11 publications

(12 citation statements)

References 25 publications

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“…The correct value (33) of the energy E 0 of the vacuum of the quasi-particles is a fundamental ingredient in the following discussions in Sections 4 and 5. Group properties of the quasi-particles vacuum and features of the solution of the gap equation have been discussed, for instance, in [29][30][31][32].…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Quasi-Particles, Thermodynamic Consistency, and the Gap Equation

Guadagnini

2017

Advances in Mathematical Physics

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The thermodynamic potentials of superconducting electrons are derived by means of the Bogoliubov-Valatin formalism. The thermodynamic potentials can be obtained by computing the free energy of a gas of quasi-particles, whose energy spectrum is conditional on the gap function. However, the nontrivial dependence of the gap on the temperature jeopardises the validity of the standard thermodynamic relations. In this article, it is shown how the thermodynamic consistency (i.e., the validity of the Maxwell relations) is recovered, and the correction terms to the quasi-particles potentials are computed. It is shown that the Bogoliubov-Valatin transformation avoids the problem of the thermodynamic consistency of the quasi-particle approach; in fact, the correct identification of the variables, which are associated with the quasi-particles, leads to a precise calculation of the quasiparticles vacuum energy and of the dependence of the chemical potential on the electron density. The stationarity condition for the grand potential coincides with the gap equation, which guarantees the thermodynamic consistency. The expressions of various thermodynamic potentials, as functions of the ( , , ) variables, are produced in the low temperature limit; as a final check, a rederivation of the condensation energy is presented.

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Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Quasi-Particles, Thermodynamic Consistency, and the Gap Equation

Guadagnini

2017

Advances in Mathematical Physics

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“…From a mathematical point of view, the gap equation has been studied for interaction kernels suitable to describe the physics of conduction electrons in solids in [42,3,48,50,40,51]. We refer to [28,16,31,32,22,4,19,13] for works that investigate the translation-invariant BCS functional with a local pair interaction. BCS theory in the presence of external fields has been studied in [33,5,20,12,6].…”

Section: Introductionmentioning

confidence: 99%

Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

Deuchert¹,

Hainzl²,

Maier³

2021

Preprint

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Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional for the case of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works [17,18] of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell.

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“…For a fixed temperature T , the existence and uniqueness of the solution were established and studied in [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2]. See also Kuzemsky [22,Chapters 26 and 29] and [23,24].…”

Section: Introductionmentioning

confidence: 99%

An Operator-theoretical Study on the BCS-Bogoliubov Model of Superconductivity Near Absolute Zero Temperature

Watanabe

2021

Preprint

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In the BCS-Bogoliubov model of superconductivity, no one gave a proof of the statement that the solution to the BCS-Bogoliubov gap equation is differentiable with respect to the temperature. But, without such a proof, one differentiates the solution and the thermodynamic potential with respect to the temperature twice, and one obtains the entropy and the specific heat at constant volume of a superconductor. In the preceding papers, the present author showed that the solution is indeed differentiable with respect to the temperature twice. Thanks to these results, we in this paper differentiate the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume from the viewpoint of operator theory. Here, the potential in the BCS-Bogoliubov gap equation is a function and need not be a constant. We then show the behavior near absolute zero temperature of the entropy, the specific heat, the solution and the critical magnetic field. Mathematics Subject Classification 2020. 45G10, 47H10, 47N50, 82D55.

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Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction

Cited by 11 publications

References 25 publications

Quasi-Particles, Thermodynamic Consistency, and the Gap Equation

Quasi-Particles, Thermodynamic Consistency, and the Gap Equation

Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

An Operator-theoretical Study on the BCS-Bogoliubov Model of Superconductivity Near Absolute Zero Temperature

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