A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide

Abstract

The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish 'intra'- from 'inter-space' entanglement.

22 pages; based on invited talk at Quantum 2010 - Advances in Foundations of Quantum mechanics and Quantum Information with Atoms and Photons (Torino, May 2010). To appear in Int. J. Qu. Info

References in corpus (11)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Dissipation and quantization
• Quantum Theory from Quantum Gravity
• Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
• Classical mechanics is not h=0 limit of quantum mechanics
• The Attractor and the Quantum States
• Pointer basis induced by collisional decoherence
• Note on the existence theorem in ``Emergent Quantum Mechanics and Emergent Symmetries''
• Quantum fields, cosmological constant and symmetry doubling

Cited by in corpus (9)

• Understanding quantum measurement from the solution of dynamical models
• Linear dynamics of quantum-classical hybrids
• Action principle for cellular automata and the linearity of quantum mechanics
• Four questions for quantum-classical hybrid theory
• General linear dynamics - quantum, classical or hybrid
• Proliferation of observables and measurement in quantum-classical hybrids
• Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• Probability representation of photon states and tomography