Some mathematical problems in the theory of quantum chaos

DOI10.1016/0378-4371(90)90329-QzbMath0713.58057OpenAlexW2007998485MaRDI QIDQ749981

Yakov G. Sinai

Publication date: 1990

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(90)90329-q

zbMATH Keywords

Poisson distributionquantum chaos

Mathematics Subject Classification ID

Quantum chaos (81Q50) Applications of global analysis to the sciences (58Z05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (10)

Unnamed Item ⋮ Recurrence and return times of the Sierpinski carpet ⋮ Polygonal billiards: correspondence between classical trajectories and quantum eigenstates ⋮ Exact solution of a nonresonance zwanzig model and ``quantum chaos ⋮ Statistics of close visits to the indifferent fixed point of an interval map ⋮ A Poisson limit theorem for Gibbs–Markov maps ⋮ Recurrences determine the dynamics ⋮ Chaotic quantum phenomena without classical counterpart ⋮ Poisson law for Axiom A diffeomorphisms ⋮ Poisson approximation and Weibull asymptotics in the geometry of numbers

Cites Work

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• Spectral fluctuations and zeta functions
• The absence of the Poisson distribution of spacings between quasi- energies in the quantum kicked-rotator model
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• Renormalisation of curlicues
• Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
• Level clustering in the regular spectrum

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