Non-Hermitian Hamiltonians in decoherence and equilibrium theory

Abstract

There are many formalisms to describe quantum decoherence. However, many of them give a non general and ad hoc definition of "pointer basis" or "moving preferred basis", and this fact is a problem for the decoherence program. In this paper we will consider quantum systems under a general theoretical framework for decoherence and we will present a tentative definition of the moving preferred basis. These ideas are implemented in a well-known open system model. The obtained decoherence and the relaxation times are defined and compared with those of the literature for the Lee- Friedrichs model.

23 pages. arXiv admin note: substantial text overlap with arXiv:1009.0535, arXiv:1006.2130

References in corpus (16)

• Fundamental decoherence from quantum gravity: a pedagogical review
• Decoherence without dissipation
• Relational physics with real rods and clocks and the measurement problem of quantum mechanics
• Decoherence, irreversibility and the selection by decoherence of quantum states with definite probabilities
• Decoherence time in self-induced decoherence
• Quantum chaos and the double-slit experiment
• General properties of the evolution of unstable states at long times
• Functional Approach to Quantum Decoherence and the Classical Final Limit
• The Friedrichs Model and its use in resonance phenomena
• The equilibrium limit of the Casati-Prosen model
• Predicting decoherence in discrete models
• New bases for a general definition for the moving preferred basis
• Perturbative method for generalized spectral decompositions
• Convex Quantum Logic
• Minimal irreversible quantum mechanics. The decay of unstable states
• Convex politopes and quantum separability

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• The Four Dimensional Dirac Equation in Five Dimensions
• Gamow vectors formalism applied to the Loschmidt echo
• An Approach by Representation of Algebras for Decoherence-Free Subspaces
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics