A Fredholm determinant for semiclassical quantization

Predrag Cvitanović, Per E. Rosenqvist, G. Vattay, Hans Henrik Rugh

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula, The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.

Original languageEnglish
Pages (from-to)619-636
Number of pages18
JournalChaos
Volume3
Issue number4
Publication statusPublished - 1993

Fingerprint

Fredholm Determinant
determinants
Quantization
Determinant
Axiom A
Trace Formula
Analyticity
Numerical Investigation
Riemann zeta function
Normal Form
Approximation
Model
approximation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics
  • Applied Mathematics

Cite this

Cvitanović, P., Rosenqvist, P. E., Vattay, G., & Rugh, H. H. (1993). A Fredholm determinant for semiclassical quantization. Chaos, 3(4), 619-636.

A Fredholm determinant for semiclassical quantization. / Cvitanović, Predrag; Rosenqvist, Per E.; Vattay, G.; Rugh, Hans Henrik.

In: Chaos, Vol. 3, No. 4, 1993, p. 619-636.

Research output: Contribution to journalArticle

Cvitanović, P, Rosenqvist, PE, Vattay, G & Rugh, HH 1993, 'A Fredholm determinant for semiclassical quantization', Chaos, vol. 3, no. 4, pp. 619-636.
Cvitanović P, Rosenqvist PE, Vattay G, Rugh HH. A Fredholm determinant for semiclassical quantization. Chaos. 1993;3(4):619-636.
Cvitanović, Predrag ; Rosenqvist, Per E. ; Vattay, G. ; Rugh, Hans Henrik. / A Fredholm determinant for semiclassical quantization. In: Chaos. 1993 ; Vol. 3, No. 4. pp. 619-636.
@article{528e949afc7f4d4993a82c2b113f16e1,
title = "A Fredholm determinant for semiclassical quantization",
abstract = "We investigate a new type of approximation to quantum determinants, the {"}quantum Fredholm determinant,{"} and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula, The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.",
author = "Predrag Cvitanović and Rosenqvist, {Per E.} and G. Vattay and Rugh, {Hans Henrik}",
year = "1993",
language = "English",
volume = "3",
pages = "619--636",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics Publising LLC",
number = "4",

}

TY - JOUR

T1 - A Fredholm determinant for semiclassical quantization

AU - Cvitanović, Predrag

AU - Rosenqvist, Per E.

AU - Vattay, G.

AU - Rugh, Hans Henrik

PY - 1993

Y1 - 1993

N2 - We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula, The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.

AB - We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula, The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.

UR - http://www.scopus.com/inward/record.url?scp=0001325421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001325421&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001325421

VL - 3

SP - 619

EP - 636

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 4

ER -