2000
DOI: 10.1088/0305-4470/33/50/102
|View full text |Cite
|
Sign up to set email alerts
|

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

Abstract: Abstract. We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472-1475]. For time-reversal invariant systems we obtain the leading terms of the two-point correlation function of the Gaussian symplectic ensemble. Special attention has to be paid to the rôle of Kramers' degeneracy.

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
9
0

Year Published

2001
2001
2018
2018

Publication Types

Select...
3
2

Relationship

1
4

Authors

Journals

citations
Cited by 5 publications
(9 citation statements)
references
References 14 publications
(38 reference statements)
0
9
0
Order By: Relevance
“…Here τ H stands for 1 for the orthogonal universality class and 2 for the symplectic class; such choice is equivalent to the replacement 2ε → ε in the symplectic case motivated by the Kramers degeneracy [11]. The semiclassical evaluation of the complex correlator is based on the generating function defined as the averaged ratio of four spectral determinants,…”
Section: Complex Correlator Form Factor and Generating Functionmentioning
confidence: 99%
See 1 more Smart Citation
“…Here τ H stands for 1 for the orthogonal universality class and 2 for the symplectic class; such choice is equivalent to the replacement 2ε → ε in the symplectic case motivated by the Kramers degeneracy [11]. The semiclassical evaluation of the complex correlator is based on the generating function defined as the averaged ratio of four spectral determinants,…”
Section: Complex Correlator Form Factor and Generating Functionmentioning
confidence: 99%
“…if Im ε > δ > 0. Early estimates of the oscillatory components are contained in [10,11]. Systematic approach is based on the formalism of generating functions, i.e., averaged ratios of the spectral determinants.…”
mentioning
confidence: 99%
“…. Although this assumption leads to the correct result in the case of two-point correlations [8,18], we remark that it corresponds to neglecting crosscorrelations between N fl T at different arguments, which, especially for small s, will become important. Thus, in the limit s → ∞, s/d → 0, the energy average in (6) can be performed approximately, yielding…”
mentioning
confidence: 90%
“…This last step can be done by substituting the trace formula (1) for N fl T , employing an expansion in s/d (cf. [18]) and making use of the diagonal approximation [5,4],…”
mentioning
confidence: 99%
“…It is shown that, within the same range of validity as in [21], indeed the two-point correlations agree with the GSE or GUE, respectively. Moreover, in [24] the Bogomolny-Keating method is carried over to the case of spin 1/2, with the same findings. In both studies, apart from a chaotic translational motion, ergodic properties of the combined dynamics described below (19) are needed in order to obtain an agreement with the RMT predictions.…”
Section: Applicationsmentioning
confidence: 60%