Quantum-classical correspondence via Liouville dynamics. I. Integrable systems and the chaotic spectral decomposition

  title={Quantum-classical correspondence via Liouville dynamics. I. Integrable systems and the chaotic spectral decomposition},
  author={Joshua Wilkie and Paul Brumer},
  journal={Physical Review A},
A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these… 

Quantum-classical correspondence in the vicinity of periodic orbits.

A method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which to observe quantum-classical correspondence near periodic orbits of Floquet systems is described and used to explain the breakdown of quantum- classical correspondence in chaotic systems.

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is

Linear and nonlinear response functions of the Morse oscillator: Classical divergence and the uncertainty principle

The algebraic structure of the quantum Morse oscillator is explored to formulate the coherent state, the phase-space representations of the annihilation and creation operators, and their classical

Duality between quantum and classical dynamics for integrable billiards.

A duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards is established and these classical eigenModes can be observed in physical experiments through the autocorrelation of the transmission coefficient of waves in quantumBilliards.

Quantum Poincaré section of a two-dimensional Hamiltonian in a coherent state representation

We study the quantum behaviour of a quasi-integrable Hamiltonian. The unperturbed Hamiltonian displays degeneracies of energy levels, which become avoided crossings under a nonintegrable

Quantum-classical correspondence in entanglement production: Entropy and classical tori

We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find

Nondivergent classical response functions from uncertainty principle: quasiperiodic systems.

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) around the microcanonical energy

Hilbert space theory of classical electrodynamics

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics



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Integrable and stochastic behaviour in dynamical astronomy.- Adiabatic and stochastic motion of charged particles in the field of a single wave.- Numerical study of particle motion in two waves.-

The Principles of Quantum Mechanics

IT is now twenty years since the theory of quantum mechanics was founded, and not much less since the first edition of Dirac's book was published. Ever since, it has been a classic of scientific

Quantum mechanics

Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.

Ergodic problems of classical mechanics


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J. Chem. Phys

  • J. Chem. Phys
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Foundations of electrodynamics

Quantum Mechanics-Nonrelativistic Theory