scholarly journals Classical motion in random potentials

2012 ◽  
Vol 34 (2) ◽  
pp. 557-593
Author(s):  
ANDREAS KNAUF ◽  
CHRISTOPH SCHUMACHER
Keyword(s):  
Time Evolution ◽  
Random Potential ◽  
Classical Particle ◽  
Random Potentials ◽  
Classical Motion

AbstractWe consider the motion of a classical particle under the influence of a random potential on ℝd, in particular the distribution of asymptotic velocities and the question of ergodicity of time evolution.

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 Binary Bose-Einstein condensates in a disordered time-dependent potential

2021 ◽  
Author(s):  
Karima Abbas ◽  
Abdelaali Boudjemaa
Keyword(s):  
Time Evolution ◽  
Random Potential ◽  
Time Dependent ◽  
Interspecies Interactions ◽  
Closed Set ◽  
System Parameters ◽  
Dependent Potential ◽  
Time Propagation ◽  
Bose Einstein

Abstract We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.

scholarly journals Ordering of binary colloidal crystals by random potentials

Soft Matter ◽  
2020 ◽  
Vol 16 (17) ◽  
pp. 4267-4273 ◽  
Author(s):  
André S. Nunes ◽  
Sabareesh K. P. Velu ◽  
Iryna Kasianiuk ◽  
Denis Kasyanyuk ◽  
Agnese Callegari ◽  
...  
Keyword(s):  
Random Potential ◽  
Colloidal Crystal ◽  
Colloidal Crystals ◽  
Random Potentials

A random potential can control the number of defects in a binary colloidal crystal.

LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS

1994 ◽  
Vol 06 (05a) ◽  
pp. 1163-1182 ◽  
Author(s):  
MICHAEL AIZENMAN
Keyword(s):  
Time Evolution ◽  
Elementary Proof ◽  
Random Potential ◽  
Linear Operators ◽  
Matrix Elements ◽  
Weak Disorder ◽  
Evolution Operators ◽  
Translation Invariant ◽  
The Matrix ◽  
Relevant Range

An elementary proof is given of localization for linear operators H = Ho + λV, with Ho translation invariant, or periodic, and V (·) a random potential, in energy regimes which for weak disorder (λ → 0) are close to the unperturbed spectrum σ (Ho). The analysis is within the approach introduced in the recent study of localization at high disorder by Aizenman and Molchanov [4]; the localization regimes discussed in the two works being supplementary. Included also are some general auxiliary results enhancing the method, which now yields uniform exponential decay for the matrix elements <0|P[a,b] exp (−itH)|x> of the spectrally filtered unitary time evolution operators, with [a, b] in the relevant range.

The Impact of a Long-Ranged Random Potential on the Transport Properties of Amorphous Semiconductors

1992 ◽  
Vol 258 ◽  
Author(s):  
Harald Overhof
Keyword(s):  
Activation Energy ◽  
Transport Properties ◽  
Random Potential ◽  
Amorphous Semiconductors ◽  
Random Potentials ◽  
Detailed Model ◽  
Model Calculations ◽  
Undoped Material ◽  
Dc Current ◽  
The Impact

ABSTRACTWe discuss electrostatic random potentials in doped and in compensated amorphous semiconductors. These potentials are caused by the residual inhomogeneity of a random distribution of charged dopants and their compensating charges. Random potentials are also present in undoped material with negative-U defects. A high density of positive-U defects can also give rise to a random potential in undoped material.We demonstrate with the help of detailed model calculations the effect of such random electrostatic potentials on the transport properties. For transport in extended states the random potential does not give rise to a mere shift of the mobility edge. Instead several new features are observed: the activation energy of the resulting Ohmie dc conductivity is virtually unaffected by the random potential in contrast to the activation energy of the thermoelectric power and that of the Hall effect, respectively. The Ohmie dc current changes at high fields into a superlinear current. The random potential contributes to the dispersion of the transients in time-of-flight experiments but leaves the field dependence of the TOF mobility unaltered. Comparing our results with experimental data we discuss under which circumstances the effect of random potentials can be identified.

scholarly journals A NOTE ON THE TIME EVOLUTION OF GENERALIZED COHERENT STATES

2001 ◽  
Vol 15 (15) ◽  
pp. 2107-2113 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Time Evolution ◽  
Path Integral ◽  
Coherent States ◽  
Integral Representations ◽  
Quantum Evolution ◽  
Restricted Class ◽  
Classical Motion ◽  
Generalized Coherent States

I consider the time evolution of generalized coherent states based on non-standard fiducial vectors, and show that only for a restricted class of such vectors does the associated classical motion determine the quantum evolution of the states. I discuss some consequences of this for path integral representations.

scholarly journals ABSOLUTELY CONTINUOUS SPECTRUM FOR A RANDOM POTENTIAL ON A TREE WITH STRONG TRANSVERSE CORRELATIONS AND LARGE WEIGHTED LOOPS

2009 ◽  
Vol 21 (06) ◽  
pp. 709-733 ◽  
Author(s):  
RICHARD FROESE ◽  
DAVID HASLER ◽  
WOLFGANG SPITZER
Keyword(s):  
Continuous Spectrum ◽  
Binary Tree ◽  
Random Potential ◽  
Random Schrödinger Operators ◽  
Strongly Correlated ◽  
Tree Graph ◽  
Absolutely Continuous Spectrum ◽  
Random Potentials ◽  
Absolutely Continuous ◽  
Tree Graphs

We consider random Schrödinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model, we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.

scholarly journals EXISTENCE AND UNIQUENESS OF THE INTEGRATED DENSITY OF STATES FOR SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS AND UNBOUNDED RANDOM POTENTIALS

2001 ◽  
Vol 13 (12) ◽  
pp. 1547-1581 ◽  
Author(s):  
THOMAS HUPFER ◽  
HAJO LESCHKE ◽  
PETER MÜLLER ◽  
SIMONE WARZEL
Keyword(s):  
Boundary Condition ◽  
Density Of States ◽  
Random Potential ◽  
Dimensional Euclidean Space ◽  
Integrated Density Of States ◽  
Moment Condition ◽  
Infinite Volume ◽  
Random Potentials ◽  
Volume Operator ◽  
Funct Anal

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results obtained by S. Doi, A. Iwatsuka and T. Mine (Math. Z. 237 (2001) 335) and S. Nakamura (J. Funct. Anal. 173 (2001) 136).

scholarly journals Diffusion of a classical particle in a static random potential

1984 ◽  
Vol 5 (4) ◽  
pp. 489-499
Author(s):  
Pierre Bertrand ◽  
Bernard Gaveau
Keyword(s):  
Random Potential ◽  
Classical Particle
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