Ultra-small metallic grains: effect of statistical fluctuations of the chemical potential on superconducting correlations and vice versa

The odd-even staggering (OES) in nuclear binding energies is a well-known fact. A rather similar effect can be found in other finite fermion systems. For instance, ultra small metallic grains and metal clusters. The staggering in nuclei and grains is attributed primarily to pairing correlations. In clusters, it is originated by the Jahn–Teller effect [Phys. Rev. Lett. 81, 3599 (1998)]. Here, we work with a simple, Lipkin-like, exactly solvable two-level fermion model. A statistical mechanics’ treatment of it shows that OES effects also emerge here, as revealed by theoretical tools connected with the so-called statistical complexity.

Download Full-text

Constructing the State

10.1093/oso/9780199595068.003.0003 ◽

2017 ◽

Author(s):

Jochen Rau

Keyword(s):

Maximum Entropy ◽

Chemical Potential ◽

Gibbs State ◽

Maximum Entropy Principle ◽

The State ◽

Generic Properties ◽

Expectation Values ◽

Macroscopic System ◽

Statistical Fluctuations ◽

Entropy Principle

The limited data available about a macroscopic system may come in various forms: sharp constraints, expectation values, or control parameters. While these data impose constraints on the state, they do not specify it uniquely; a further principle—the maximum entropy principle—must be invoked to construct it. This chapter discusses basic notions of information theory and why entropy may be regarded as a measure of ignorance. It shows how the state—called a Gibbs state—is constructed using the maximum entropy principle, and elucidates its generic properties, which are conveniently summarized in a thermodynamic square. The chapter further discusses the second law and how it is linked to the reproducibility of macroscopic processes. It introduces the concepts of equilibrium and temperature, as well as pressure and chemical potential. Finally, this chapter considers statistical fluctuations of the energy and of other observables in case these are given as expectation values.

Download Full-text

Mesoscopic Interplay of Superconductivity and Ferromagnetismin Ultra-Small Metallic Grains

NATO Science for Peace and Security Series B: Physics and Biophysics - Complex Phenomena in Nanoscale Systems ◽

10.1007/978-90-481-3120-4_3 ◽

2009 ◽

pp. 25-35

Author(s):

S. Schmidt ◽

Y. Alhassid

Keyword(s):

Metallic Grains ◽

Small Metallic Grains

Download Full-text

Breakdown of Superconductivity in Small Metallic Grains

Chinese Physics Letters ◽

10.1088/0256-307x/17/10/022 ◽

2000 ◽

Vol 17 (10) ◽

pp. 762-764 ◽

Cited By ~ 3

Author(s):

Chen Zhi-Qian ◽

Zheng Ren-Rong

Keyword(s):

Metallic Grains ◽

Small Metallic Grains

Download Full-text

Spectral Explanation for Statistical Odd-Even Staggering in Few Fermions Systems

Quantum Reports ◽

10.3390/quantum3010010 ◽

2021 ◽

Vol 3 (1) ◽

pp. 166-172 ◽

Cited By ~ 1

Author(s):

Angelo Plastino ◽

Gustavo Luis Ferri ◽

Angel Ricardo Plastino

Keyword(s):

Metal Clusters ◽

Binding Energies ◽

Energy Spectra ◽

Fermion Model ◽

Nuclear Binding ◽

Fermion Systems ◽

Established Fact ◽

Metallic Grains ◽

Small Metallic Grains

Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as for example, ultra small metallic grains and metal clusters. We work in this effort with the above-mentioned Lipkin-like, two-level fermion model and show that statistical staggering effects can be detailedly explained by recourse to a straightforward analysis of the associated energy-spectra.

Download Full-text

SUPERCONDUCTIVITY ENHANCEMENTS IN SMALL METALLIC GRAINS

International Journal of Modern Physics B ◽

10.1142/s0217979205030992 ◽

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).

Download Full-text