Incompressibility Estimates for the Laughlin Phase

Autor: Nicolas Rougerie, Jakob Yngvason
Přispěvatelé: Laboratoire de physique et modélisation des milieux condensés (LPM2C), Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS), Erwin Schrödinger Institute for Mathematical Physics, ESIMP, ANR-13-JS01-0005,MaThoStaQ,Méthodes mathématiques pour le problème à N corps en mécanique statistique et quantique(2013)
Rok vydání: 2014
Předmět:
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas]
Complex system
FOS: Physical sciences
01 natural sciences
Rigidity (electromagnetism)
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Quantum mechanics
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
0103 physical sciences
Perpendicular magnetic field
0101 mathematics
010306 general physics
Wave function
Quantum
[PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall]
Mathematical Physics
Physics
Large particle
Condensed Matter - Mesoscale and Nanoscale Physics
010102 general mathematics
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Landau quantization
Quantum Gases (cond-mat.quant-gas)
Fractional quantum Hall effect
[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el]
Condensed Matter - Quantum Gases
Zdroj: Communications in Mathematical Physics. 336:1109-1140
ISSN: 1432-0916
0010-3616
DOI: 10.1007/s00220-014-2232-5
Popis: This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin’s famous wave function. We investigate a model for the response of such strongly correlated ground states to variations of an external potential. This leads to a family of variational problems of a new type. Our main results are rigorous energy estimates demonstrating a strong rigidity of the response of strongly correlated states to the external potential. In particular, we obtain estimates indicating that there is a universal bound on the maximum local density of these states in the limit of large particle number. We refer to these as incompressibility estimates.
Databáze: OpenAIRE
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