Continuous Quantum Measurements and Path Integrals [Hardcover]

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.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 ofló%