Advanced

Coupling coefficient distribution in the doorway mechanism

Kohler, Heiner; Guhr, Thomas and Åberg, Sven LU (2010) In New Journal of Physics 12.
Abstract
In many-body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence, there is an interaction that makes the distinct states act as doorways into background states which are modeled statistically. The crucial quantities are the overlaps between the eigenstates of the full Hamiltonian and the doorway states, that is, the coupling coefficients occurring in the expansion of true eigenstates in the simple model basis. Recently, the distribution of the maximum coupling coefficients was introduced as a new, highly sensitive statistical observable. In the particularly important regime... (More)
In many-body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence, there is an interaction that makes the distinct states act as doorways into background states which are modeled statistically. The crucial quantities are the overlaps between the eigenstates of the full Hamiltonian and the doorway states, that is, the coupling coefficients occurring in the expansion of true eigenstates in the simple model basis. Recently, the distribution of the maximum coupling coefficients was introduced as a new, highly sensitive statistical observable. In the particularly important regime of weak interactions, this distribution is very well approximated by the fidelity distribution, defined as the distribution of the overlap between the doorway states with interaction and without interaction. Using a random matrix model, we calculate the latter distribution exactly for regular and chaotic background states in the cases of preserved and fully broken time-reversal invariance. We also perform numerical simulations and find excellent agreement with our analytical results. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
New Journal of Physics
volume
12
publisher
IOP Publishing Ltd.
external identifiers
  • wos:000281232700005
  • scopus:77955392810
ISSN
1367-2630
DOI
10.1088/1367-2630/12/7/073026
language
English
LU publication?
yes
id
0da9ca49-3b85-464d-bf6b-cd0687fa265b (old id 1673009)
date added to LUP
2010-09-23 12:24:05
date last changed
2018-06-17 04:07:23
@article{0da9ca49-3b85-464d-bf6b-cd0687fa265b,
  abstract     = {In many-body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence, there is an interaction that makes the distinct states act as doorways into background states which are modeled statistically. The crucial quantities are the overlaps between the eigenstates of the full Hamiltonian and the doorway states, that is, the coupling coefficients occurring in the expansion of true eigenstates in the simple model basis. Recently, the distribution of the maximum coupling coefficients was introduced as a new, highly sensitive statistical observable. In the particularly important regime of weak interactions, this distribution is very well approximated by the fidelity distribution, defined as the distribution of the overlap between the doorway states with interaction and without interaction. Using a random matrix model, we calculate the latter distribution exactly for regular and chaotic background states in the cases of preserved and fully broken time-reversal invariance. We also perform numerical simulations and find excellent agreement with our analytical results.},
  articleno    = {073026},
  author       = {Kohler, Heiner and Guhr, Thomas and Åberg, Sven},
  issn         = {1367-2630},
  language     = {eng},
  publisher    = {IOP Publishing Ltd.},
  series       = {New Journal of Physics},
  title        = {Coupling coefficient distribution in the doorway mechanism},
  url          = {http://dx.doi.org/10.1088/1367-2630/12/7/073026},
  volume       = {12},
  year         = {2010},
}