BCS-TYPE THEORY IN CANONICAL ENSEMBLES

2006 ◽  
Vol 15 (08) ◽  
pp. 1761-1768 ◽  
Author(s):  
H. NAKADA ◽  
K. TANABE
Keyword(s):  
Phase Transition ◽  
Type Theory ◽  
Particle Number ◽  
Temperature Limit ◽  
Zero Temperature ◽  
Pauli Blocking ◽  
Finite Systems ◽  
Particle Number Conservation ◽  
New Interpretation ◽  
Canonical Ensembles

To investigate the pairing phase transition in finite systems with the particle-number conservation, we formulate a new BCS-type theory at finite temperature, by deriving a set of variational equations of the free energy after the particle-number projection. This theory enables us to distinguish the symmetry-restoring fluctuation (SRF) from additional quantum fluctuations. By numerical calculations, it is found that the phase transition is compatible with the conservation law in this theory, and that the SRF shifts up the critical temperature. Having correct zero-temperature limit, this theory also gives new interpretation on the Pauli blocking effect in systems with odd particle number.

scholarly journals Electromagnetic instability and Schwinger effect in the Witten–Sakai–Sugimoto model with D0–D4 background

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Wenhe Cai ◽  
Kang-le Li ◽  
Si-wen Li
Keyword(s):  
Phase Transition ◽  
Decay Rate ◽  
Temperature Limit ◽  
Zero Temperature ◽  
Vacuum Decay ◽  
Constant Electromagnetic Field ◽  
Schwinger Effect ◽  
Electromagnetic Instability ◽  
Probe Brane ◽  
Chiral Potential

Abstract Using the Witten–Sakai–Sugimoto model in the D0–D4 background, we holographically compute the vacuum decay rate of the Schwinger effect in this model. Our calculation contains the influence of the D0-brane density which could be identified as the $$\theta $$θ angle or chiral potential in QCD. Under the strong electromagnetic fields, the instability appears due to the creation of quark–antiquark pairs and the associated decay rate can be obtained by evaluating the imaginary part of the effective Euler–Heisenberg action which is identified as the action of the probe brane with a constant electromagnetic field. In the bubble D0–D4 configuration, we find the decay rate decreases when the $$\theta $$θ angle increases since the vacuum becomes heavier in the present of the glue condensate in this system. And the decay rate matches to the result in the black D0–D4 configuration at zero temperature limit according to our calculations. In this sense, the Hawking–Page transition of this model could be consistently interpreted as the confined/deconfined phase transition. Additionally there is another instability from the D0-brane itself in this system and we suggest that this instability reflects to the vacuum decay triggered by the $$\theta $$θ angle as it is known in the $$\theta $$θ-dependent QCD.

Macroscopic Squeezing in Bose–Einstein Condensate

1998 ◽  
Vol 12 (18) ◽  
pp. 705-713 ◽  
Author(s):  
Patric Navez
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Einstein Condensate ◽  
Condensed State ◽  
Zero Temperature ◽  
Hartree Fock ◽  
Bose Einstein Condensate ◽  
Normal Behavior ◽  
Particle Number Conservation ◽  
Bose Einstein

We study the ground state of a uniform Bose gas at zero temperature in the Hartree–Fock–Bogoliubov (HFB) approximation. We find a solution of the HFB equations which obeys the Hugenholtz–Pines theorem. This solution imposes a macroscopic squeezing to the condensed state and as a consequence displays large particle number fluctuations. Particle number conservation is restored by building the appropriate U(1) invariant ground state via the superposition of the squeezed states. The condensed particle number distribution of this new ground state is calculated as well as its fluctuations which present a normal behavior.

scholarly journals Size dependent nature of the magnetic-field driven superconductor-to-insulator quantum-phase transitions

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Xiaofu Zhang ◽  
Adriana E. Lita ◽  
Huanlong Liu ◽  
Varun B. Verma ◽  
Qiang Zhou ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Phase Transitions ◽  
Temperature Limit ◽  
Quantum Phase ◽  
Zero Temperature ◽  
Size Dependent ◽  
Open Question ◽  
The Magnetic Field

AbstractThe nature of the magnetic-field driven superconductor-to-insulator quantum-phase transition in two-dimensional systems at zero temperature has been under debate since the 1980s, and became even more controversial after the observation of a quantum-Griffiths singularity. Whether it is induced by quantum fluctuations of the superconducting phase and the localization of Cooper pairs, or is directly driven by depairing of these pairs, remains an open question. We herein experimentally demonstrate that in weakly-pinning systems and in the limit of infinitely wide films, a sequential superconductor-to-Bose insulator-to-Fermi insulator quantum-phase transition takes place. By limiting their size to smaller than the effective penetration depth, however, the vortex interaction alters, and the superconducting state re-enters the Bose-insulating state. As a consequence, one observes a direct superconductor-to-Fermi insulator in the zero-temperature limit. In narrow films, the associated critical-exponent products diverge along the corresponding phase boundaries with increasing magnetic field, which is a hallmark of the quantum-Griffiths singularity.

scholarly journals Dissipation of Quantum Turbulence in the Zero Temperature Limit

2007 ◽  
Vol 99 (26) ◽  
Author(s):  
P. M. Walmsley ◽  
A. I. Golov ◽  
H. E. Hall ◽  
A. A. Levchenko ◽  
W. F. Vinen
Keyword(s):  
Quantum Turbulence ◽  
Temperature Limit ◽  
Zero Temperature

The thermodynamics of the divalent metal fluorides. I. Heat capacity of lead tetrafluorostannate, PbSnF4, from 10.3 to 352 K

1988 ◽  
Vol 66 (4) ◽  
pp. 549-552 ◽  
Author(s):  
Jane E. Callanan ◽  
Ron D. Weir ◽  
Edgar F. Westrum Jr.
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Thermodynamic Functions ◽  
Adiabatic Calorimetry ◽  
Temperature Limit ◽  
Divalent Metal ◽  
Ion Conductor ◽  
Metal Fluorides ◽  
Fast Ion Conductor ◽  
Fast Ion

We have measured the heat capacity of the fast ion conductor PbSnF4 at 10.3 < T < 352 K by adiabatic calorimetry. Our results show anomalous values in the Cp,m in the region 300 < T < 352 K. These are associated with the α–β crystallographic transition reported at 353 K. Because the upper temperature limit of our cryostat is around 354 K, it was impossible to follow the phase transition to completion. A more subtle anomaly in the Cp,m was detected between 130 and 160 K. Standard molar thermodynamic functions are presented at selected temperatures from 5 to 350 K.

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