The Bohigas-Giannoni-Schmit Conjecture

نویسنده

  • Denis Ullmo
چکیده

A The chaos hierarchy 12 A.1 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.3 K Systems (Kolmogorov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A.4 B-Systems (Bernoulli) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 A.5 A-Systems (Anosov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Periodic-orbit theory of level correlations.

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator ...

متن کامل

Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. I. Construction and numerical results.

In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star graphs in the ten symmetry classes. A generalization of the Bohigas-Giannoni-Schmit conjecture is given that covers all these symmetry classes. The conjectur...

متن کامل

Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. II. Semiclassical approach.

A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs, and on diagrammatic techniques. The appropriate spectral form factors are calculated up to one order beyond the diagonal and self-dua...

متن کامل

Quantum Cat Maps with Spin 1/2

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices...

متن کامل

Quantum chaos, irreversible classical dynamics, and random matrix theory.

The Bohigas-Giannoni-Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory (RMT) is proved. A new semiclassical field theory for individual chaotic systems is constructed in the framework of a nonlinear s model. The low lying modes are shown to be associated with the Perron-Frobenius (PF) spect...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016