skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum chaos in one dimension?

Abstract

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N{yields}{infinity} the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.

Authors:
; ;  [1];  [2]
  1. Elmeleti Fizika Tanszek, Fizikai Intezet, Budapesti Muszaki es Gazdasagtudomanyi Egyetem, H-1521 Budapest (Hungary)
  2. (New Zealand)
Publication Date:
OSTI Identifier:
21611531
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.84.016230; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1539-3755
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; CHAOS THEORY; EIGENVALUES; MATRICES; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; QUANTUM MECHANICS; RANDOMNESS; STATISTICS; MATHEMATICAL SOLUTIONS; MATHEMATICS; MECHANICS

Citation Formats

Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016. Quantum chaos in one dimension?. United States: N. p., 2011. Web. doi:10.1103/PHYSREVE.84.016230.
Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, & Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016. Quantum chaos in one dimension?. United States. doi:10.1103/PHYSREVE.84.016230.
Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016. Fri . "Quantum chaos in one dimension?". United States. doi:10.1103/PHYSREVE.84.016230.
@article{osti_21611531,
title = {Quantum chaos in one dimension?},
author = {Ujfalusi, Laszlo and Varga, Imre and Schumayer, Daniel and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016},
abstractNote = {In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N{yields}{infinity} the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.},
doi = {10.1103/PHYSREVE.84.016230},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {1539-3755},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}