Exercises for a Book on Random Potentials

1987 ◽  
pp. 45-65
Author(s):  
René Carmona
Keyword(s):  
Random Potentials

Towards localisation by Gaussian random potentials in multi-dimensional continuous space

1996 ◽  
Vol 38 (4) ◽  
pp. 343-348
Author(s):  
Werner Fischer ◽  
Hajo Leschke ◽  
Peter Müller
Keyword(s):  
Random Potentials ◽  
Continuous Space

Polymer Transport in Random Potentials and the Genetic Code: The Waltz of Life

2003 ◽  
pp. 459-474
Author(s):  
M. Aldana-González ◽  
G Cocho ◽  
H. Larralde ◽  
G. Martínez-Mekler
Keyword(s):  
Genetic Code ◽  
Random Potentials ◽  
Polymer Transport

MODULATION OF ORDER PARAMETER OF EXCITON BOSE-EINSTEIN CONDENSATE IN A RING

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3797-3802 ◽  
Author(s):  
S.-R. ERIC YANG ◽  
Q-HAN PARK ◽  
J. YEO
Keyword(s):  
Ground State ◽  
Order Parameter ◽  
Weak Magnetic Field ◽  
Random Potential ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Random Potentials ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with a random variation of the effective exciton potential along the circumference. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate, which is valid even in the presence of a weak magnetic field. For several types of the random potentials our numerical solution of the ground state of the GPE displays a necklace-like structure. This is a consequence of the interplay between the random potential and a strong nonlinear repulsive term of the GPE. We have investigated how the mean distance between modulation peaks depends on properties of the random potentials.

scholarly journals Wegner estimate for discrete Schrödinger operators with Gaussian random potentials

2019 ◽  
Vol 27 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Martin Tautenhahn
Keyword(s):  
Conditional Distribution ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Gaussian Random Process ◽  
Random Potentials ◽  
Wegner Estimate ◽  
Compactly Supported ◽  
Covariance Functions ◽  
Monotonicity Assumption ◽  
Discrete Schrödinger Operators

Abstract We prove a Wegner estimate for discrete Schrödinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially; no monotonicity assumption is required. This improves earlier results where abstract conditions on the conditional distribution, compactly supported and non-negative, or compactly supported covariance functions with positive mean are considered.

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