scholarly journals Spectral Gap in Mean-Field $${\mathcal {O}}(n)$$-Model

2020 ◽  
Vol 380 (3) ◽  
pp. 1361-1400
Author(s):  
Simon Becker ◽  
Angeliki Menegaki
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Gibbs Measure ◽  
Spectral Gap ◽  
Mean Field ◽  
Field Interaction ◽  
Ginzburg Landau ◽  
Semiclassical Methods ◽  
One Step ◽  
Renormalization Approach

AbstractWe study the dependence of the spectral gap for the generator of the Ginzburg–Landau dynamics for all $$\mathcal O(n)$$ O ( n ) -models with mean-field interaction and magnetic field, below and at the critical temperature on the number N of particles. For our analysis of the Gibbs measure, we use a one-step renormalization approach and semiclassical methods to study the eigenvalue-spacing of an auxiliary Schrödinger operator.

scholarly journals Persistence of superconductivity in thin shells beyond Hc1

2016 ◽  
Vol 18 (04) ◽  
pp. 1550047 ◽  
Author(s):  
Andres Contreras ◽  
Xavier Lamy
Keyword(s):  
Magnetic Field ◽  
Model Problem ◽  
Landau Theory ◽  
Normal Component ◽  
Mean Field ◽  
Compact Surface ◽  
Thin Shells ◽  
Symmetric Model ◽  
Ginzburg Landau ◽  
Zero Locus

In Ginzburg–Landau theory, a strong magnetic field is responsible for the breakdown of superconductivity. This work is concerned with the identification of the region where superconductivity persists, in a thin shell superconductor modeled by a compact surface [Formula: see text], as the intensity [Formula: see text] of the external magnetic field is raised above [Formula: see text]. Using a mean field reduction approach devised by Sandier and Serfaty as the Ginzburg–Landau parameter [Formula: see text] goes to infinity, we are led to studying a two-sided obstacle problem. We show that superconductivity survives in a neighborhood of size [Formula: see text] of the zero locus of the normal component [Formula: see text] of the field. We also describe intermediate regimes, focusing first on a symmetric model problem. In the general case, we prove that a striking phenomenon we call freezing of the boundary takes place: one component of the superconductivity region is insensitive to small changes in the field.

THERMAL ENTANGLEMENT IN SPIN SYSTEMS

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5117-5121 ◽  
Author(s):  
N. CANOSA ◽  
R. ROSSIGNOLI
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Applied Magnetic Field ◽  
Uniform Magnetic Field ◽  
Mean Field ◽  
Spin Systems ◽  
Thermal Entanglement ◽  
Global Entanglement ◽  
Thermal States

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

Fluctuation diamagnetic susceptibility in type-II superconductors under magnetic field

2019 ◽  
Vol 34 (04) ◽  
pp. 2050007
Author(s):  
Le Thi Cam Tuyen ◽  
Bui Duc Tinh ◽  
Le Minh Thu ◽  
Nguyen Quang Hoc ◽  
Nguyen Khac Man
Keyword(s):  
Magnetic Field ◽  
Diamagnetic Susceptibility ◽  
High Temperature Superconductors ◽  
Mean Field ◽  
Nonlinear Behavior ◽  
Ginzburg Landau ◽  
Susceptibility Data ◽  
Low Field ◽  
Lowest Landau Level ◽  
Field Transition

Strong fluctuation effects were found in both low- and high-field regimes by recent measurements of magnetization on [Formula: see text] (LCCO) single crystals. The low-field fluctuation diamagnetic susceptibility data could not be fitted by simple Gaussian fluctuation theory using the lowest Landau level (LLL) approximation because of the slightly nonlinear behavior around the mean-field transition temperature [Formula: see text]. Self-consistent calculation of fluctuation diamagnetic susceptibility in high-temperature superconductors, based on the Ginzburg–Landau (GL) two-dimensional model and including all Landau levels, is presented. Our results are valid for arbitrary values of the magnetic field not too close to [Formula: see text]. The results agree well with the experimental data in a wide region around [Formula: see text], including both below and above [Formula: see text].

scholarly journals Quantum Mechanics and Superconductivity in a Magnetic Field

1993 ◽  
Vol 46 (3) ◽  
pp. 333 ◽  
Author(s):  
AH MacDonald ◽  
Hiroshi Akera ◽  
MR Norman
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Landau Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Point Of View ◽  
Ginzburg Landau ◽  
Accurate Picture ◽  
The Individual

The influence of a magnetic field on superconductivity is usually described either phenomenologically, using Ginzburg-Landau theory, or semiclassically, using Gor'kov theory. In this article we discuss the influence of magnetic fields on the mean-field theory of the superconducting instability from a completely quantum-mechanical point of view. The suppression of superconductivity by an external magnetic field is seen in this more physically accurate picture to be due to the impossibility, in quantum mechanics, of precisely specifying both the centre-of-mass state of a pair and the individual electron kinetic energies. We also discuss the possibility of novel aspects of superconductivity at extremely strong magnetic fields, where recent work has shown that the transition temperature may be enhanced rather than suppressed by a magnetic field and where a quantum treatment is essential.

Magnetic field, chiral transition and Pauli interaction

2014 ◽  
Vol 29 (11) ◽  
pp. 1450058 ◽  
Author(s):  
Tomasz L. Partyka
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Mean Field ◽  
Chiral Transition ◽  
Field Level ◽  
The Mean

The possibility that the Pauli interaction could influence the critical temperature of chiral transition is investigated. We work within the Nambu-Jona–Lasinio model at the mean field level, with quark anomalous magnetic moment as a parameter.

scholarly journals On the dynamical interaction between overshooting convection and an underlying dipole magnetic field – I. The non-dynamo regime

2021 ◽  
Vol 503 (1) ◽  
pp. 362-375
Author(s):  
L Korre ◽  
NH Brummell ◽  
P Garaud ◽  
C Guervilly
Keyword(s):  
Magnetic Field ◽  
Turbulent Diffusion ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Mean Field ◽  
Stable Region ◽  
Turbulent Regime ◽  
Poloidal Magnetic Field ◽  
Dynamical Interaction ◽  
Large Scale Field

ABSTRACT Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modelled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.

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