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Non-markovian quantum trajectories: an exact result.
1Dipartimento di Fisica Teorica, Università di Trieste, Strada Costiera 11, 34151 Trieste, Italy. bassi@ts.infn.it
Physical Review Letters
|October 2, 2009
Summary
We solved the non-Markovian stochastic Schrödinger equation for a free particle, offering new insights into quantum measurement and collapse models. This provides a quantitative description of quantum system dynamics under continuous position measurement.
Area of Science:
- Quantum mechanics
- Theoretical physics
Background:
- Stochastic Schrödinger equations model quantum systems under continuous observation or spontaneous state collapse.
- Understanding non-Markovian dynamics is crucial for accurately describing these processes.
Purpose of the Study:
- To provide the first explicit general solution for the non-Markovian stochastic Schrödinger equation for a free particle.
- To analyze the properties of this solution and the system's dynamics.
Main Methods:
- Solving the non-Markovian stochastic Schrödinger equation for the free particle case (H=p^2/2m).
- Analyzing the behavior of the system with an exponential correlation function for the noise.
Main Results:
- An explicit general solution for the free particle is derived.
- The study quantifies the system's dynamics and dependence on correlation time for a specific noise model.
Conclusions:
- The derived solution offers a fundamental tool for studying quantum systems under continuous position measurement or collapse.
- The analysis highlights the impact of noise correlation on quantum dynamics.
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