A Review of the Decoherent Histories Approach to Quantum Mechanics

Abstract

I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may predict the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is closed related to the quantum state diffusion approach of Gisin and Percival.

28 pages (plain Tex), Imperial College preprint 93-94/52

References in corpus (17)

• Classical Equations for Quantum Systems
• Quantum Mechanics as Quantum Measure Theory
• Quantum Logic and the Histories Approach to Quantum Theory
• Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory
• Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories
• Decoherent Histories and Quantum State Diffusion
• Consistent Quantum Counterfactuals
• Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime
• Quasiclassical Equations of Motion for Nonlinear Brownian Systems
• Phase-Space Decoherence: a comparison between Consistent Histories and Environment Induced Superselection
• Quantum-Mechanical Histories and the Uncertainty Principle. II. Fluctuations About Classical Predictability
• Quantum-Mechanical Histories and the Uncertainty Principle: I.Information-Theoretic Inequalities
• Decoherence Functional and Inhomogeneities in the Early Universe
• Unique Quantum Paths by Continuous Diagonalization of the Density Operator
• Decoherence Functional and Probability Interpretation
• Unique family of consistent histories in the Caldeira-Leggett model
• Inconsistency between alternative approaches to Quantum Decoherence in special systems

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• Stochastic Gravity: A Primer with Applications
• Linearly Positive Histories: Probabilities for a Robust Family of Sequences of Quantum Events
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework
• An effective stochastic semiclassical theory for the gravitational field
• Decoherent Histories Approach to the Arrival Time Problem
• A Kinetic Theory Approach to Quantum Gravity
• Probing finite coarse-grained virtual Feynman histories with sequential weak values
• On the Relationship Between Complex Potentials and Strings of Projection Operators
• First Principles Numerical Demonstration of Emergent Decoherent Histories
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states
• Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
• Realism and Time Symmetry in Quantum Mechanics
• Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure
• Probing quantum chaos with the entropy of decoherent histories
• Decoherence of Histories: Chaotic Versus Integrable Systems
• Spacetime Paths as a Whole
• Quantum Entropies and Decoherence for the Multiparticle Quantum Arnol'd Cat
• Phase Space Localization and Approach to Thermal Equilibrium for a Class of Open Systems
• Repeated measurements on non-replicable systems and their consequences for Unruh-DeWitt detectors
• Effective Theories of Coupled Classical and Quantum Variables
• Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables
• Toy Model Challenging Prevailing Definitions of Classicality