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

2021 ◽  
Author(s):  
Shuji Watanabe
Keyword(s):  
Specific Heat ◽  
Operator Theory ◽  
Present Author ◽  
Thermodynamic Potential ◽  
Theoretical Study ◽  
Critical Magnetic Field ◽  
Constant Volume ◽  
Absolute Zero ◽  
Zero Temperature ◽  
Gap Equation

Abstract 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.

scholarly journals An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shuji Watanabe
Keyword(s):  
Specific Heat ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Theoretical Study ◽  
Critical Magnetic Field ◽  
Absolute Zero ◽  
Zero Temperature ◽  
Positive Continuous Function ◽  
Gap Equation ◽  
Uniqueness Of The Solution

AbstractIn the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the viewpoint of operator theory, and showed that the solution is partially differentiable with respect to the temperature twice. Thanks to these results, we can indeed partially differentiate the solution and the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume of a superconductor. In this paper we show the behavior near absolute zero temperature of the thus-obtained entropy, the specific heat, the solution and the critical magnetic field from the viewpoint of operator theory since we did not study it in the preceding papers. Here, the potential in the BCS-Bogoliubov gap equation is an arbitrary, positive continuous function and need not be a constant.

THE SPECIFIC HEAT OF A FERMI GAS AT LOW TEMPERATURE: A CLOSER LOOK AT THE lnT BEHAVIOR

1999 ◽  
Vol 13 (28) ◽  
pp. 3357-3367 ◽  
Author(s):  
A. REBEI ◽  
W. N. G. HITCHON
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Finite Temperature ◽  
Thermodynamic Potential ◽  
Fermi Gas ◽  
Zero Temperature

At finite temperature, a Fermi gas can have states that simultaneously hold a particle and a hole with a finite probability. This gives rise to a new set of diagrams that are absent at zero temperature. The so called "anomalous" diagram is just one of the new diagrams. We have already studied the contribution of these new diagrams to the thermodynamic potential (Phys. Lett.A224, 127 (1996)). Here we continue that work and calculate their effect on the specific heat. We will also calculate the finite temperature contribution of the ring diagrams. We conclude that the ln T behavior of the specific heat due to exchange gets canceled by the new contribution of the new diagrams, and that screening is not essential to resolve this anomaly.

THEORETICAL STUDY OF LATTICE DYNAMICAL PROPERTIES IN FERROELECTRIC LiTaO3

1992 ◽  
Vol 06 (20) ◽  
pp. 3279-3293 ◽  
Author(s):  
YIMIN JIANG ◽  
CHENG GOU
Keyword(s):  
Specific Heat ◽  
Theoretical Study ◽  
Phonon Dispersion ◽  
Dispersion Curves ◽  
Optical Data ◽  
General Function ◽  
Zero Temperature ◽  
Phonon Dispersion Curves ◽  
Maximum Value ◽  
The One

We present the phonon-dispersion curves, the one-phonon density of states, the lattice specific heat cv(T) and the Debye temperature Θ(T) of the ferroelectric LiTaO 3, based on full lattice dynamical model whose parametèrs are fitted to the optical data and neutron measured dispersion curves. A model theory is developed to describe the transition from Debye to non-Debye behaviors observed in the low temperature part of the cv/T3 curve. The cv/T3 function, when is properly scaled, can be fitted by a general function derived from the model. It can be characterized by the temperature T max at which it has maximum, its maximum value (cv/T3)T=T max and its value at zero temperature (cv/T3)T=0. These results are considered useful in searching possibly anomalous phonon behavior from the specific heat cv(T).

scholarly journals Trapped individual ion at absolute zero temperature

1989 ◽  
Vol 86 (15) ◽  
pp. 5671-5671 ◽  
Author(s):  
N. Yu ◽  
H. Dehmelt ◽  
W. Nagourney
Keyword(s):  
Absolute Zero ◽  
Zero Temperature ◽  
Individual Ion

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

Superconductors with spin–orbit interactions

2016 ◽  
Vol 30 (25) ◽  
pp. 1650183 ◽  
Author(s):  
Yu. N. Ovchinnikov
Keyword(s):  
Magnetic Field ◽  
Superconducting Films ◽  
Critical Magnetic Field ◽  
Spin Orbit ◽  
Zero Temperature ◽  
Interband Pairing ◽  
Two Parameters ◽  
Spin Orbit Interactions ◽  
Parameter Values ◽  
Thin Superconducting Films

The effect of spin-orbit (SO) interaction on the formation of the critical states in thin superconducting films in magnetic field oriented along the film is investigated. Hereby, the case of interband pairing is considered. It was found that eight branches exist in the plane of two parameters [Formula: see text] determined by the value of magnetic field and SO interaction. Six modes leads to inhomogeneous states with different values of the impulse [Formula: see text]. Each state is doubly degenerate over direction of impulse [Formula: see text]. The parameter values at critical point are found for all eight branches in explicit form for zero temperature. The optimal two branches are estimated, corresponding to largest critical magnetic field value for given SO interaction.

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