Semiclassical expansion of parametric correlation functions of the quantum time delay
نویسندگان
چکیده
We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factorK(τ, x, y,M), that depends on the number of open channelsM , a non-symmetry breaking parameter x, and a symmetry breaking parameter y. Several terms in the Taylor expansion about τ = 0, which depend on all parameters, are shown to be identical to those obtained from Random Matrix Theory. PACS numbers: 03.65.Sq Semiclassical theories and applications. 05.45.Mt Semiclassical chaos (“quantum chaos”). E-mail: [email protected] E-mail: [email protected] 1
منابع مشابه
Parametric Spectral Correlations
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor K(τ, x) which depends on a scaled parameter difference x. For parameter variations that do not change the symmetry of the system we show by using semiclassical per...
متن کاملSemiclassical approximations to quantum dynamical time correlation functions
Semiclassical approximations for quantum time correlation functions are presented for both electronically adiabatic and nonadiabatic dynamics along with discussions of the operator ordering and the classical limit. With the combined use of the initial-value representation of the semiclassical propagator, a discrete algorithm to evaluate the Jacobi matrices, semiclassical operator ordering rules...
متن کاملQuantum Fluctuations and Particle Production of Coherently Oscillating Inflaton
We study a massive inflaton minimally coupled to FRW Universe using the semiclassical gravity derived from canonical quantum gravity. It is found that the semiclassical quantum gravity leads to the power-law expansion t2/3 in an oscillatory phase of the inflaton. The particle production of the inflaton in the expanding Universe restricts the duration of stable coherent oscillations and parametr...
متن کاملSemiclassical relation between open trajectories and periodic orbits for the Wigner time delay.
The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive f...
متن کاملThe n-level spectral correlations for chaotic systems
We study the n-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit’s universality conjecture, it is expected that the correlation functions are in agreement with the prediction of the Circular Unitary Ensemble (CUE) of random matrices. A semiclassical resummation formalism allows us to express the ...
متن کامل