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Related Concept Videos

Phase Diagram01:19

Phase Diagram

6.2K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
6.2K
pV-Diagrams01:18

pV-Diagrams

4.6K
The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
4.6K
Phase Diagrams02:39

Phase Diagrams

44.8K
A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
44.8K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

19.8K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
19.8K
Density00:56

Density

16.3K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
16.3K
Equation of State01:07

Equation of State

2.0K
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
2.0K

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Measuring the Densities of Aqueous Glasses at Cryogenic Temperatures
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Measuring the Densities of Aqueous Glasses at Cryogenic Temperatures

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The BCS Critical Temperature at High Density.

Joscha Henheik1

  • 1IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.

Mathematical Physics, Analysis, and Geometry
|February 7, 2022
PubMed
Summary
This summary is machine-generated.

We derived a formula for BCS critical temperature in high-density systems, confirming previous findings and identifying conditions for superconducting domes. This research advances understanding of superconductivity in dense matter.

Keywords:
BCS theoryCritical temperatureSuperconducting domes

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics

Background:

  • The Bardeen-Cooper-Schrieffer (BCS) theory describes conventional superconductivity.
  • Understanding critical temperature () in high-density systems is crucial for materials science.

Purpose of the Study:

  • To derive an asymptotic formula for BCS critical temperature () in the high-density limit.
  • To rigorously confirm the behavior of at high densities.
  • To identify conditions leading to superconducting domes.

Main Methods:

  • Asymptotic analysis of the BCS critical temperature formula.
  • Investigation of the interaction potential's behavior on the Fermi surface.

Main Results:

  • An asymptotic formula for was derived, dependent on the interaction potential near the Fermi surface.
  • Rigorous confirmation of previously proposed high-density behavior of .
  • Precise conditions for the emergence of superconducting domes were identified.

Conclusions:

  • The derived formula provides new insights into superconductivity in high-density systems.
  • The study confirms theoretical predictions and clarifies conditions for superconducting dome formation.
  • This work contributes to the fundamental understanding of BCS superconductivity.