scholarly journals SCATTERING PHASE SHIFTS IN QUASI-ONE-DIMENSION

2002 ◽  
Vol 16 (16) ◽  
pp. 2247-2277 ◽  
Author(s):  
P. SINGHA DEO ◽  
SWARNALI BANDOPADHYAY ◽  
SOURIN DAS

Scattering of an electron in quasi-one-dimensional quantum wires have many unusual features, not found in one, two or three-dimensions. In this work we analyze the scattering phase shifts due to an impurity in a multi-channel quantum wire with special emphasis on negative slopes in the scattering phase shift versus incident energy curves and the Wigner delay time. Although at first sight, the large number of scattering matrix elements show phase shifts of different character and nature, it is possible to see some pattern and understand these features. The behavior of scattering phase shifts in one-dimension can be seen as a special case of these features observed in quasi-one-dimensions. The negative slopes can occur at any arbitrary energy and Friedel sum rule is completely violated in quasi-one-dimension at any arbitrary energy and any arbitrary regime. This is in contrast to one, two or three dimensions where such negative slopes and violation of Friedel sum rule happen only at low energy where the incident electron feels the potential very strongly (i.e. there is a very well defined regime, the WKB regime, where FSR works very well). There are some novel behavior of scattering phase shifts at the critical energies where S-matrix changes dimension.

1996 ◽  
Vol 11 (21) ◽  
pp. 1737-1744 ◽  
Author(s):  
N. GURAPPA ◽  
C. NAGARAJA KUMAR ◽  
PRASANTA K. PANIGRAHI

We study a class of Calogero-Sutherland type one-dimensional N-body quantum mechanical systems, with potentials given by [Formula: see text] where [Formula: see text] are of specific form. It is shown that, only for a few choices of U, the eigenvalue problems can be solved exactly for arbitrary g′. The eigenspectra of these Hamiltonians, when g′≠0, are nondegenerate and the scattering phase shifts are found to be energy-dependent. It is further pointed out that, the eigenvalue problems are amenable to solution for wider choices of U, if g′ is conveniently fixed. These conditionally exactly solvable problems also do not exhibit energy degeneracy and the scattering phase shifts can be computed only for a specific partial wave.


1997 ◽  
Vol 226 (6) ◽  
pp. 327-331 ◽  
Author(s):  
C.K. Au ◽  
Chi-Keung Chow ◽  
Chong-Sun Chu

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