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Current in open quantum systems.

Ralph Gebauer1, Roberto Car

  • 1The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.

Physical Review Letters
|November 5, 2004
PubMed
Summary
This summary is machine-generated.

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A new dissipative current component arises in quantum dynamics from coarse-graining, complementing Hamiltonian evolution. This finding is crucial for maintaining current continuity in master equations.

Area of Science:

  • Quantum dynamics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Standard quantum dynamics often relies on Hamiltonian evolution.
  • Master equations are frequently used to model open quantum systems.
  • Current continuity is a fundamental principle in physical systems.

Purpose of the Study:

  • To identify and characterize a dissipative current component in Liouville-master equation dynamics.
  • To understand the origin of this dissipative current.
  • To provide a framework for incorporating this component into quantum system descriptions.

Main Methods:

  • Derivation of an explicit expression for the dissipative current.
  • Application of the Markov approximation.
  • Numerical simulation of a quantum particle coupled to a phonon bath using the Pauli master equation.

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Main Results:

  • A dissipative current component, distinct from the Hamiltonian component, is shown to exist.
  • The dissipative current arises from the coarse-graining inherent in master equations.
  • An explicit formula for this current is derived under the Markov approximation.

Conclusions:

  • The inclusion of a dissipative current is necessary for preserving current continuity in master equation dynamics.
  • The derived expression provides a quantitative tool for analyzing dissipative effects.
  • The numerical example validates the theoretical approach for quantum-phonon interactions.