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Continuous Quantum Measurements and Path Integrals

By M.B Mensky

Published January 1st 1993 by Taylor & Francis – 188 pages

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Description

Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.

Contents

Preface

INTRODUCTION TO CONTINUOUS QUANTUM MEASUREMENTS

Quantum and Classical Systems

Amplitudes and Alternatives

Paths and Continuous Measurements

The Action Uncertainty Principle

INSTANTANEOUS AND SEQUENTIAL MEASUREMENTS

Measurement of a Quantum System

Quantum Zeno Paradox

Approximate and Sequential Measurements

TECHNIQUE OF PATH INTEGRALS

Propagators and Path Integrals

Definition of a Path Integral

The Path Integral for an Oscillator

Gaussian Path Integrals

CONTINUOUS MEASUREMENT AND EVOLUTION OF THE MEASURED SYSTEM

The Measurement Amplitude

Effective Lagrangian

Evolution of a Quantum System Subject to Continuous Measurement Scattering by the Measuring Medium

CONTINUOUS MEASUREMENTS OF OSCILLATORS

Position Monitoring (Path measurement)

Estimation of Force Acting on an Oscillator

Spectral Measurements of an Oscillator

Evolution of a Harmonic Oscillator Subject to Spectral Measurement

Measurement of a Path of a Nonlinear Oscillator

CONTINUOUS QUANTUM NONDEMOLITION MEASUREMENTS

Quantum Nondemolition Measurements

Monitoring of Linear Momentum

Velocity versus Momentum

QND Measurements of Oscillators

MEASUREMENT OF AN ELECTROMAGNETIC FIELD

Exposition of the Method

Measurement Amplitude

Analysis of the Results

Another Definition of the Field Strength

Explicit Model of a Meter

TIME IN QUANTUM COSMOLOGY

Statement of the Problem

Measurements in Quantum Cosmology

Minisuperspace without Measurement

Minisuperspace under Measurement

Analysis of the results

Concluding Remarks

THE ACTION UNCERTAINTY PRINCIPLE

Uncertainties in Continuous Measurements

Classical Regime of Measurements

Quantum Regime and AUP

AUP and Equations of Motion

Examples from Quantum Mechanics

Quantum Nondemolition Measurements

AUP in Quantum Gravity

Concluding Remarks

GROUP-THEORETICAL STRUCTURE OF QUANTUM CONTINUOUS MEASUREMENTS

Evolution under Measurement

Transverse Group for Alternatives

Longitudinal Semigroup for Evolution

Unification of Transverse and Longitudinal Structures

Concluding Remarks

PATHS AND MEASUREMENTS: FURTHER DEVELOPMENT

Quantum and Classical Features in Continuous Measurement

The Two-Slit Experiment

Wave-Particle Dualism

Conceptual Problems

References

Index

Related Subjects

  1. Quantum Mechanics

Name: Continuous Quantum Measurements and Path Integrals (Hardback) – Taylor & Francis 
Description: By M.B Mensky. Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown...
Categories: Quantum Mechanics