Martin Sieber 2000 J. Phys. A: Math. Gen. 33 6263 doi:10.1088/0305-4470/33/36/301
Spectral statistics in chaotic systems with a point interaction
Martin Sieber
Show affiliationsWe consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(τ) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order τ2 and τ3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.
- PACS
-
05.45.Mt Quantum chaos; semiclassical methods
03.65.Yz Decoherence; open systems; quantum statistical methods
- MSC
-
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
-
Issue 36 (15 September 2000)
Received 8 March 2000
-
Spectral statistics in chaotic systems with a point interaction
Martin Sieber 2000 J. Phys. A: Math. Gen. 33 6263
-
Electronic nanostructures templated on self-assembled DNA scaffolds
Sung Ha Park et al 2004 Nanotechnology 15 S525
-
Dynamical gauge theory for the XY gauge glass model
Yukiyasu Ozeki 2003 J. Phys. A: Math. Gen. 36 2673
-
Hierarchical reconstruction with up to second degree remainder for solving nonlinear conservation laws
Yingjie Liu et al 2009 Nonlinearity 22 2799
-
Spin-2 field theory in curved spacetime in the Fierz representation
M Novello and R P Neves 2002 Class. Quantum Grav. 19 5335
-
Application of renormalization to potential scattering
Carlos F de Araujo Jr et al 1997 J. Phys. A: Math. Gen. 30 4687
-
Bosonic quadratic actions for 11-dimensional supergravity on AdS7/4 × S4/7
Fiorenzo Bastianelli and Roberto Zucchini 1999 Class. Quantum Grav. 16 3673
-
A two-level atom coupled to a two-dimensional supersymmetric and shape-invariant system: dynamics and entanglement
A N F Aleixo and A B Balantekin 2007 J. Phys. A: Math. Theor. 40 3933
-
No sliding in time
Kirill Shtengel et al 2005 J. Phys. A: Math. Gen. 38 L589
-
Excitation and propagation of low frequency wave in a FRC plasma
S. Okada et al 2003 Nucl. Fusion 43 1140
Users also read
What's this?Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*