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Physics-Uspekhi

Dissipation and decoherence in quantum systems

Михаил Борисович Менский

Published Nov 30, 2003• 50 citations
Publisher

Abstract

The theory of dissipative quantum systems and its relation to the quantum theory of continuous measurements are reviewed. Constructing a correct theory of a dissipative quantum system requires that the system's interaction with its environment (reservoir) be taken into account. Since information about the system is 'recorded' in the state of the reservoir, the quantum theory of continuous measurements can be used to account for the influence of the reservoir. If based on the use of restricted path integrals, this theory does not require an explicit reservoir model and is therefore much simpler technically.

DOI
10.1070/pu2003v046n11abeh001680

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The theory of dissipative quantum systems and its relation to the quantum theory of continuous measurements are reviewed. Constructing a correct theory of a dissipative quantum system requires that the system's interaction with its environment (reservoir) be taken into account. Since information about the system is 'recorded' in the state of the reservoir, the quantum theory of continuous measurements can be used to account for the influence of the reservoir. If based on the use of restricted path integrals, this theory does not require an explicit reservoir model and is therefore much simpler technically.
Decoherence aiid dissipation of a quantum system occurs due to its entanglement with the environment (reservoir) . In the course of interaction of the system with the reservoir information about the system is 'recorded' in the state of the reservoir. This is why influence of the reservoir on the system (i.e. the system's decoherence and dissipation) may be accounted in the framework of quantum theory of continuous measurements. Constructing such a theory with the help of restricted path integrals (RPI) gives a model-independent theory of decoherence and dissipation. The special role of information in decoherence and dissipation is explicitly revealed by this approach. This makes it possible to apply the RPI approach for the analysis of decoherence in quantum informatic devices.
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements (CQM). Reviewed are the various approaches to the CQM theory, and the approach based on the effective complex Hamiltonians is discussed in greater detail. The effective complex Hamiltonian is derived from the restricted path integral, which emphasizes the role of information in the dynamics of the system being measured. The complex Hamiltonian is used for analyzing the CQM of energy in a two-level system. Such measurement is demonstrated to be capable of monitoring the quantum transition, and the back effect of monitoring on the probability of transition is analyzed. The realization of this type of measurement by a long series of soft observations of the system is presented.
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements (CQM). Reviewed are the various approaches to the CQM theory, and the approach based on the effective complex Hamiltonians is discussed in greater detail. The effective complex Hamiltonian is derived from the restricted path integral, which emphasizes the role of information in the dynamics of the system being measured. The complex Hamiltonian is used for analyzing the CQM of energy in a two-level system. Such measurement is demonstrated to be capable of monitoring the quantum transition, and the back effect of monitoring on the probability of transition is analyzed. The realization of this type of measurement by a long series
The restricted-path-integral (RPI) theory of continuous quantum measurements including the evolution of the measured systems and phenomenon of decoherence is reviewed. The measured system is considered as an open quantum system but without usage of any model of the measurement (of the measuring medium or the system's environment). The propagator of a measured system (conditioned by the measurement readout) is presented by RPI. In the important special case of monitoring an observable the propagator and the system's wave function satisfy Schroedinger equation with a complex Hamiltonian (depending on the measurement readout). Going over to the non-selective description of the measurement leads to the Lindblad master equation. In case of non-minimally disturbing measurements this gives theory of dissipative systems avoiding difficulties of other approaches. The whole theory is deduced from first principles of quantum mechanics. This proves that quantum mechanics includes theory of measurements and is therefore conceptually closed.
Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-Ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational Approach and Effective Potential Method Unified Approach to Quantum-Statistical Metastability: From Thermal Activation to Quantum Tunneling Electron Transfer and Incoherent Tunneling Macroscopic Quantum Effects in Josephson Systems Spin-Boson Model and Qubit Dissipative Two-State System: Thermodynamics and Dynamics Single-Charge and Cooper-Pair Tunneling Magnetic and Spin Tunneling Driven Quantum Tunneling Nonequilibrium Quantum Transport Full Counting Statistics Charge Transport in Quantum Impurity Systems Duality and Self-Duality.
This chapter applies the path-integral approach to the quantum theory of continuous measurements to investigate the quantum Universe, taking into account its self-measurement. It describes the way to apply the path-integral theory of continuous measurements in quantum cosmology in a general form and develops a minisuperspace model. The path-integral approach can be applied to describe the measurement of a quantum field. The measurement of curvature in the framework of quantum gravity has been considered in such a way by Mensky using a functional integral over configurations of the gravitational field. The chapter considers the possible influence of self-measurement on the dynamics of the quantum Universe. The influence could be caused by reduction of the wavefunction of the Universe in the process of continuous measurement. Therefore the time evolution of the quantum Universe makes sense in quantum cosmology provided its self-measurement is correctly taken into account.