scholarly journals Comment on “No Enhancement of the Localization Length for Two Interacting Particles in a Random Potential”

1997 ◽  
Vol 78 (25) ◽  
pp. 4889-4889 ◽  
Author(s):  
Klaus Frahm ◽  
Axel Müller-Groeling ◽  
Jean-Louis Pichard ◽  
Dietmar Weinmann
Keyword(s):  
Random Potential ◽  
Localization Length ◽  
Interacting Particles

scholarly journals Effect of noise for two interacting particles in a random potential

1996 ◽  
Vol 35 (7) ◽  
pp. 517-522 ◽  
Author(s):  
F Borgonovi ◽  
D. L Shepelyansky
Keyword(s):  
Random Potential ◽  
Interacting Particles

scholarly journals Anomalous Anderson localization behaviors in disordered pseudospin systems

2017 ◽  
Vol 114 (16) ◽  
pp. 4087-4092 ◽  
Author(s):  
A. Fang ◽  
Z. Q. Zhang ◽  
Steven G. Louie ◽  
C. T. Chan
Keyword(s):  
Disordered Systems ◽  
Anderson Localization ◽  
Random Potential ◽  
Incident Angle ◽  
Localization Length ◽  
Normal Incidence ◽  
Wave Localization ◽  
Sharp Transition ◽  
Angle Dependence ◽  
Localization Behavior

We discovered unique Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the wave localization behaviors are entirely different from those of conventional disordered systems. We show that there exists a critical strength of random potential (Wc), which is equal to the incident energy (E), below which the localization length ξ decreases with the random strength W for a fixed incident angle θ. But the localization length drops abruptly to a minimum at W=Wc and rises immediately afterward. The incident angle dependence of the localization length has different asymptotic behaviors in the two regions of random strength, with ξ∝sin−4θ when W<Wc and ξ∝sin−2θ when W>Wc. The existence of a sharp transition at W=Wc is due to the emergence of evanescent waves in the systems when W>Wc. Such localization behavior is unique to pseudospin-1 systems. For pseudospin-1/2 systems, there is also a minimum localization length as randomness increases, but the transition from decreasing to increasing localization length at the minimum is smooth rather than abrupt. In both decreasing and increasing regions, the θ dependence of the localization length has the same asymptotic behavior ξ∝sin−2θ.

Evolution of Burgers' turbulence in the presence of external forces

1997 ◽  
Vol 331 ◽  
pp. 313-343 ◽  
Author(s):  
A. I. SAICHEV ◽  
W. A. WOYCZYNSKI
Keyword(s):  
Force Field ◽  
Random Potential ◽  
Solution Algorithm ◽  
Inviscid Limit ◽  
Necessary Condition ◽  
Interacting Particles ◽  
Least Action ◽  
Burgers Turbulence ◽  
Physical Level ◽  
External Forces

Statistical properties of multidimensional Burgers' turbulence evolving in the presence of a force field with random potential, which is delta-correlated in time and smooth in space, are studied in the inviscid limit and at the physical level of rigorousness. The solution algorithm reduces to finding multistream fields describing the motion of an auxiliary gas of interacting particles in a force field. Consequently, the statistical description of forced Burgers' turbulence is obtained by finding the largest possible value of the least action for the auxiliary gas. The exponential growth of the number of streams is found to be a necessary condition for the existence of stationary regimes.

scholarly journals Wave Propagation and Localization in a Complex Random Potential with Power-law Correlations: A Numerical Study

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Ba Phi Nguyen ◽  
Huu Dinh Dang
Keyword(s):  
Wave Propagation ◽  
Numerical Analysis ◽  
Spatial Correlation ◽  
Imaginary Part ◽  
Power Law ◽  
Random Potential ◽  
Numerical Study ◽  
Localization Length ◽  
Simultaneous Presence ◽  
Correlation Strength

In this paper, we investigate numerically wave propagation and localization in a complex random potential with power-law correlations. Using a discrete stationary Schrӧdinger equation with the simultaneous presence of the spatial correlation and the non-Hermiticity of the random potential in the diagonal on-site terms of the Hamiltonian, we calculate the disorder-averaged logarithmic transmittance and the localization length. From the numerical analysis, we find that the presence of power-law correlation in the imaginary part of the on-site disordered potential gives rise to the localization enhancement as compared with the case of absence of correlation. Depending on the disorder's strength, we show that there exist different behaviors of the dependence of the localization on the correlation strength.

scholarly journals Breit-Wigner Width for Two Interacting Particles in a One-Dimensional Random Potential

1997 ◽  
Vol 78 (5) ◽  
pp. 923-926 ◽  
Author(s):  
Ph. Jacquod ◽  
D. L. Shepelyansky ◽  
O. P. Sushkov
Keyword(s):  
Random Potential ◽  
Interacting Particles ◽  
One Dimensional
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