SUPERCONDUCTIVITY ENHANCEMENTS IN SMALL METALLIC GRAINS

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2369-2374
Author(s):  
RENRONG ZHENG ◽  
ZHI QIAN CHEN ◽  
SHUN QUAN ZHU
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Pairing Correlation ◽  
Gap Equation ◽  
Gaussian Unitary Ensemble ◽  
Level Statistics ◽  
Gaussian Orthogonal Ensemble ◽  
Metallic Grains ◽  
Unitary Ensemble ◽  
Small Metallic Grains

The reasons for superconductivity enhancement in small metallic grains including hundreds of thousand electrons are investigated by solving the generalized gap equation based on BCS mean field theory. The analysis suggests that the superconductivity enhancement in small metallic grains are the results caused by the pairing correlation and the level statistics in the Gaussian orthogonal ensemble (GOE) and the Gaussian unitary ensemble (GUE).

Generalization of Brody distribution for statistical investigation

2014 ◽  
Vol 03 (04) ◽  
pp. 1450017 ◽  
Author(s):  
H. Sabri ◽  
Sh. S. Hashemi ◽  
B. R. Maleki ◽  
M. A. Jafarizadeh
Keyword(s):  
Nearest Neighbor ◽  
Matrix Theory ◽  
Likelihood Estimation ◽  
Statistical Investigation ◽  
Distribution Functions ◽  
Estimation Methods ◽  
General Distribution ◽  
Gaussian Unitary Ensemble ◽  
Gaussian Orthogonal Ensemble ◽  
Unitary Ensemble

In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ensemble and Gaussian Unitary Ensemble limits of Random Matrix Theory in the nearest neighbor spacing statistic framework. Parameters of new distribution are extracted via Maximum Likelihood Estimation technique for different sequences. This general distribution suggests more exact results in comparison with the results of other estimation methods and distribution functions.

scholarly journals Onset of universality in the dynamical mixing of a pure state

2021 ◽  
Author(s):  
M. Carrera-Núñez ◽  
A. M. Martínez-Argüello ◽  
J. M. Torres ◽  
E. J. Torres-Herrera
Keyword(s):  
Pure State ◽  
Matrix Theory ◽  
Chaotic Regime ◽  
Many Body ◽  
Analytical Treatment ◽  
Gaussian Unitary Ensemble ◽  
Time Dynamics ◽  
Spectral Statistics ◽  
Gaussian Orthogonal Ensemble ◽  
Unitary Ensemble

Abstract We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the Gaussian orthogonal ensemble to the Gaussian unitary ensemble (GUE) for short and large times, respectively. Using a semi-analytical treatment relying on a power series of the density matrix as a function of time, we find that the crossover occurs in a characteristic time that scales as the inverse of the dimension. The RMT results are contrasted with a paradigmatic model of many-body localization in the chaotic regime, where the GUE statistics is reached at large times, while for short times the statistics strongly depends on the peculiarity of the considered subspace.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Swarm shedding in networks of self-propelled agents

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jason Hindes ◽  
Victoria Edwards ◽  
Klimka Szwaykowska Kasraie ◽  
George Stantchev ◽  
Ira B. Schwartz
Keyword(s):  
Network Topology ◽  
Collective Motion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Interaction Strength ◽  
Central Question ◽  
Agent Interaction ◽  
Sparse Networks ◽  
Swarm Pattern ◽  
Limited Sensing

AbstractUnderstanding swarm pattern formation is of great interest because it occurs naturally in many physical and biological systems, and has artificial applications in robotics. In both natural and engineered swarms, agent communication is typically local and sparse. This is because, over a limited sensing or communication range, the number of interactions an agent has is much smaller than the total possible number. A central question for self-organizing swarms interacting through sparse networks is whether or not collective motion states can emerge where all agents have coherent and stable dynamics. In this work we introduce the phenomenon of swarm shedding in which weakly-connected agents are ejected from stable milling patterns in self-propelled swarming networks with finite-range interactions. We show that swarm shedding can be localized around a few agents, or delocalized, and entail a simultaneous ejection of all agents in a network. Despite the complexity of milling motion in complex networks, we successfully build mean-field theory that accurately predicts both milling state dynamics and shedding transitions. The latter are described in terms of saddle-node bifurcations that depend on the range of communication, the inter-agent interaction strength, and the network topology.

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