TY - JOUR

T1 - Resummation and the semiclassical theory of spectral statistics

AU - Keating, Jon P

AU - Muller, Sebastian

PY - 2007

Y1 - 2007

N2 - We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of random-matrix theory. To do so, we use a semiclassical resummation formalism that explicitly preserves the unitarity of the quantum time evolution by incorporating duality relations between short and long classical orbits. This allows us to obtain both the non-oscillatory and the oscillatory contributions to spectral correlation functions within a unified framework, thus overcoming a significant problem in previous approaches. In addition, our results extend beyond the universal regime to describe the system-specific approach to the semiclassical limit.

AB - We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of random-matrix theory. To do so, we use a semiclassical resummation formalism that explicitly preserves the unitarity of the quantum time evolution by incorporating duality relations between short and long classical orbits. This allows us to obtain both the non-oscillatory and the oscillatory contributions to spectral correlation functions within a unified framework, thus overcoming a significant problem in previous approaches. In addition, our results extend beyond the universal regime to describe the system-specific approach to the semiclassical limit.

U2 - 10.1098/rspa.2007.0178

DO - 10.1098/rspa.2007.0178

M3 - Article (Academic Journal)

VL - 463

SP - 3241

EP - 3250

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

ER -