scholarly journals Mobility edge of two interacting particles in three-dimensional random potentials

2019 ◽  
Vol 99 (22) ◽  
Author(s):  
Filippo Stellin ◽  
Giuliano Orso
Keyword(s):  
Three Dimensional ◽  
Interacting Particles ◽  
Mobility Edge ◽  
Random Potentials

LOW ENERGY EXCITATIONS AND NON-ERGODICITY IN THE COULOMB GLASS

1994 ◽  
Vol 08 (07) ◽  
pp. 923-933 ◽  
Author(s):  
M. Ortuño ◽  
M. Pollak ◽  
J. Talamantes
Keyword(s):  
Relaxation Time ◽  
Low Temperatures ◽  
Random Media ◽  
Three Dimensional ◽  
Low Energy ◽  
Zero Temperature ◽  
Correlation Effects ◽  
Interacting Particles ◽  
Coulomb Glass

Recent computational methods permit the determination of the low energy states of fair sized systems of localized interacting particles in random media. Making use of such methods, this paper evaluates the nature of the low-energy excitations of the system, and it’s implications on conductivity and on ergodicity. Two- and three-dimensional systems are examined. It is found that the low energy excitations exhibit strong correlation effects, indicating that one-particle theories for equilibrium and non-equilibrium properties are not justified. Ergodicity is tested by relaxation at zero temperature. It is found that relaxation time can be extremely long, indicating that the system is not ergodic at low temperatures.

scholarly journals DECONFINEMENT AND COLD ATOMS IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5169-5178
Author(s):  
M. A CAZALILLA ◽  
A. F. HO ◽  
T. GIAMARCHI
Keyword(s):  
Optical Lattices ◽  
Cold Atoms ◽  
Three Dimensional ◽  
Optical Traps ◽  
High Dimensional ◽  
Interacting Particles ◽  
Controllable System ◽  
One Dimensional ◽  
Physical Systems ◽  
The One

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

Stochastic resonances and the mobility edge in a three-dimensional tight-binding Anderson model

1994 ◽  
Vol 50 (7) ◽  
pp. 4867-4870 ◽  
Author(s):  
Indra Dasgupta ◽  
Tanusri Saha ◽  
Abhijit Mookerjee
Keyword(s):  
Anderson Model ◽  
Tight Binding ◽  
Three Dimensional ◽  
Mobility Edge

Mobility edge in the three dimensional Anderson model

1985 ◽  
Vol 60 (1) ◽  
pp. 13-17 ◽  
Author(s):  
B. R. Buŀka ◽  
B. Kramer ◽  
A. MacKinnon
Keyword(s):  
Anderson Model ◽  
Three Dimensional ◽  
Mobility Edge

LOCALIZATION LENGTH IN THE COOPER PROBLEM WITH DISORDER

2001 ◽  
Vol 15 (04) ◽  
pp. 409-424 ◽  
Author(s):  
M. A. N. ARAÚJO
Keyword(s):  
Dispersion Relation ◽  
Single Particle ◽  
Three Dimensional ◽  
Localization Length ◽  
Bound State ◽  
Single Electron ◽  
S Wave ◽  
Mobility Edge ◽  
Spatial Dimensions ◽  
Particle Localization

We study the localization properties of a bound state of two electrons in the presence of a Fermi sea of normal electrons which are Anderson localized due to disorder. We describe the bound state as in the s-wave Cooper problem. The localization length of the pair depends on its dispersion relation for small momenta relative to the Fermi surface. Expressions for the pair localization length are derived, for both one and two spatial dimensions, in the limit of large single-particle localization length. In one dimensional we find that there is no considerable enhancement of the pair localization length (L c2 ) over that of a single electron (L c ). In two dimensional there is a large enhancement in the limit of large L c . In three dimensional the pair dispersion relation is obtained in both diffusive and (single-particle) localized regimes and the implications on localization are discussed. In this case the mobility edge of the pair is located below the single-electron mobility edge.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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