Contribution to the Theory of Weak Coupling Superconductors

1971 ◽  
Vol 49 (6) ◽  
pp. 724-746 ◽  
Author(s):  
C. R. Leavens ◽  
J. P. Carbotte
Keyword(s):  
Critical Temperature ◽  
Isotope Effect ◽  
Normal State ◽  
Weak Coupling ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Approximate Analytic Solution ◽  
Zero Temperature ◽  
Eliashberg Equations ◽  
Normal State Properties

We have managed to simplify the Eliashberg equations for the case of weak coupling superconductors. Further, an explicit approximate analytic solution of the simplified equations has been obtained for the zero temperature gap edge. An expression for the critical temperature is also given. It is found to be of the BCS form and allows the BCS parameter N(0)V to be identified with a simple function of the normal state properties. The validity of our simplified integral equations and of our analytic solution is established by comparison with numerical solutions of the complete Eliashberg equations. The equations are used to discuss the effect of pressure on the gap, the isotope effect, as well as other properties.

EFFECTIVE THEORY OF BOSONIC SUPERFLUIDS

1994 ◽  
Vol 08 (15) ◽  
pp. 2021-2039 ◽  
Author(s):  
ADRIAAN M.J. SCHAKEL
Keyword(s):  
Critical Temperature ◽  
Weak Coupling ◽  
Particle Number ◽  
Landau Theory ◽  
Effective Theory ◽  
Bcs Theory ◽  
Goldstone Mode ◽  
Zero Temperature ◽  
Temperature Expansion ◽  
High Temperature Expansion

We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.

Effects of energy dependence in the electronic density of states on some normal state properties

1983 ◽  
Vol 61 (5) ◽  
pp. 758-783 ◽  
Author(s):  
B. Mitrović ◽  
J. P. Carbotte
Keyword(s):  
Energy Dependence ◽  
Density Of States ◽  
Normal State ◽  
Impurity Scattering ◽  
Eliashberg Equations ◽  
Electronic Density ◽  
Electronic Density Of States ◽  
Electron Phonon Interaction ◽  
Normal State Properties ◽  
Energy Equations

We study the effects of energy dependence in the electronic density of states (EDOS) on the electron quasiparticle properties in the normal state. The Migdal–Eliashberg equations generalized to include a nonconstant EDOS are derived in the isotropic approximation. By numerical solution of the electron self-energy equations in the normal state, we assess the effect of the interplay of the energy dependence in the EDOS, the electron–phonon interaction, and/or elastic impurity scattering on the electron quasiparticle properties. Self-consistency requirements are fully discussed.

scholarly journals The Study on Hybridized Two-Band Superconductor

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
T. Chanpoom ◽  
J. Seechumsang ◽  
S. Chantrapakajee ◽  
P. Udomsamuthirun
Keyword(s):  
Critical Temperature ◽  
Isotope Effect ◽  
Conduction Electron ◽  
Lower Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Zero Temperature ◽  
Electron Band ◽  
Conduction Electron Band

The two-band hybridized superconductor which the pairing occurred by conduction electron band and other-electron band are considered within a mean-field approximation. The critical temperature, zero-temperature order parameter, gap-to-Tcratio, and isotope effect coefficient are derived. We find that the hybridization coefficient shows a little effect on the superconductor that conduction electron band has the same energy as other-electron band but shows more effect on the superconductor that conduction electron band coexists with lower-energy other-electron band. The critical temperature is decreased as the hybridization coefficient increases. The higher value of hybridization coefficient, lower value of gap-to-Tcratio, and higher value of isotope effect coefficient are found.

scholarly journals A Reliable Iterative Transform Method for Solving an Epidemic Model

2021 ◽  
pp. 4839-4846
Author(s):  
Reem Waleed Huisen ◽  
Sinan H. Abd Almjeed ◽  
Areej Salah Mohammed
Keyword(s):  
Epidemic Model ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Absolute Error ◽  
Maximum Error ◽  
Disease Spread ◽  
Approximate Analytic Solution ◽  
Transform Method ◽  
Epidemic Period ◽  
The Laplace Transform

    The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

On different formulas for the Tc of an impure anisotropic superconductor

1985 ◽  
Vol 63 (5) ◽  
pp. 574-585 ◽  
Author(s):  
M. Ashraf ◽  
J. P. Carbotte
Keyword(s):  
Critical Temperature ◽  
Numerical Solutions ◽  
Analytic Formula ◽  
Exact Results ◽  
Eliashberg Equations ◽  
Anisotropic Superconductor ◽  
Pure Metals

Exact numerical solutions of the Eliashberg equations are obtained for several representative metals, from which the impurity dependence of the critical temperature of an anisotropic superconductor is determined. The exact results are used to assess the accuracy of some of the simple, approximate, but analytic, formulas now available in the literature. All are found to be, at best, semiquantitative. An attempt is made to improve on the available formulas by deriving a new one based on the original quantitative work of Leavens and Carbotte for pure metals. While our final analytic formula should be useful for many purposes, it is still found that for accurate quantitative work the full equations are preferable.

Normal state properties and oxygen isotope effect of (Ba,K)BiO3

1989 ◽  
Vol 157 (3) ◽  
pp. 469-477 ◽  
Author(s):  
S. Kondoh ◽  
M. Sera ◽  
Y. Ando ◽  
M. Sato
Keyword(s):  
Oxygen Isotope ◽  
Isotope Effect ◽  
Normal State ◽  
Normal State Properties

TRANSPORT PROPERTIES OF ANYONS

1992 ◽  
Vol 06 (17) ◽  
pp. 2837-2854
Author(s):  
D. V. KHVESHCHENKO
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Transport Properties ◽  
Stress Tensor ◽  
Electric Current ◽  
Normal State ◽  
Correlation Functions ◽  
Electromagnetic Response ◽  
Zero Temperature ◽  
Tensor Correlation

We consider electromagnetic response as well as electrical and thermal transport in a normal state of anyon system at finite temperatures. We find the frequency and momentum dependences of electrical and thermal conductivities in the longwavelength limit. It is also shown that a pole of electric current and stress tensor correlation functions identified at zero temperature with a gapless sound-like mode becomes a diffusion above the critical temperature of the hypothetical superfluid anyon phase transition.

Some Effects of Pressure on Superconductivity

1971 ◽  
Vol 49 (11) ◽  
pp. 1493-1506 ◽  
Author(s):  
J. P. Carbotte ◽  
P. Vashishta
Keyword(s):  
Critical Temperature ◽  
Hydrostatic Pressure ◽  
Simple Model ◽  
Specific Heat ◽  
Normal State ◽  
Zero Temperature ◽  
Condensation Energy ◽  
Quasi Particle ◽  
Effect Of Hydrostatic Pressure

We have calculated the effect of hydrostatic pressure on select properties of a number of simple superconducting metals. We discuss the changes with decreasing volume in the critical temperature, the zero temperature gap, the condensation energy, and the normal state specific heat. Semiquantitative agreement with experiment is obtained in all cases. Throughout, the Eliashberg formulation is employed. Information on the kernels entering into these equations is taken from quasi particle tunneling data at zero pressure. At finite pressure the kernels are rescaled according to a simple model.

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