Reduction of a wave packet in quantum Brownian motion

Journal Article · Tue Aug 15 00:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.1071· OSTI ID:5537905

Unruh, W G ^[1]; Zurek, W H ^[2]

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1. Canadian Institute for Advanced Research, Cosmology Program, Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1W5 (CA)
2. Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

The effect of the environment on a quantum system is studied on an exactly solvable model: a harmonic oscillator interacting with a one-dimensional massless scalar field. We show that in an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium. In particular, we demonstrate that the density matrix decays rapidly toward a mixture of approximate eigenstates'' of the pointer observable,'' which commutes with the system-environment interaction Hamiltonian. This observable can be regarded as continuously, if inaccurately, monitored by the scalar field environment. Both because in a harmonic oscillator the state of the system rotates in the phase space and because the effective environment measurement'' is weak, the system, on the short collision'' time scale (1/{Gamma}), maintains a coherence in this pointer observable on time scales of order ({gamma}/{Omega}ln({Gamma}/{Omega})){sup 1/2} and on longer time scales settles into a mixture of coherent states with a dispersion approximately consistent with the vacuum state. The master equation satisfied by the exact solution differs from the other master equations derived both for the high-temperature limit and for {ital T}=0. We discuss these differences and study the transition region between the high- and low-temperature regimes. We also consider the behavior of the system in the short-time transient'' regime. For {ital T}=0, we find that, in the long-time limit, the system behaves as if it were subject to 1/{ital f} noise.'' The generality of our model is considered and its predictions are compared with previous treatments of related problems. Some of the possible applications of the results to experimentally realizable situations are outlined.

• OSTI ID: 5537905
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Vol. 40:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HARMONIC OSCILLATORS
EIGENSTATES
QUANTUM MECHANICS
BROWNIAN MOVEMENT
CLASSICAL MECHANICS
COSMOLOGICAL MODELS
GREEN FUNCTION
HAMILTONIANS
HEISENBERG PICTURE
PHASE SPACE
SCALAR FIELDS
THERMODYNAMIC MODEL
UNIVERSE
VACUUM STATES
WAVE PACKETS
ELECTRONIC EQUIPMENT
EQUIPMENT
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
OSCILLATORS
PARTICLE MODELS
QUANTUM OPERATORS
SPACE
STATISTICAL MODELS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics