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Wigner function with correlation damping.

Luigi Barletti1, Paolo Bordone2, Lucio Demeio3

  • 1Dipartimento di Matematica e Informatica "U. Dini," Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy.

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Summary
This summary is machine-generated.

Reduced correlation length due to decoherence flattens the Wigner function in 1D scattering. This leads to less reflection at low energies and less transmission at high energies.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Transport phenomena

Background:

  • Decoherence significantly impacts quantum systems by reducing correlations.
  • Understanding decoherence effects is crucial for quantum information and transport studies.
  • The Wigner function is a key tool for analyzing quantum dynamics in phase space.

Purpose of the Study:

  • To investigate how decoherence-induced reduction in correlation length affects 1D scattering.
  • To numerically solve the Wigner function evolution equation with decoherence.
  • To analyze scattering regimes (reflection-dominated, transmission-dominated, intermediate) under varying correlation lengths.

Main Methods:

  • Numerical solution of the Wigner function evolution equation using a modified splitting-scheme algorithm.
  • Incorporation of a decoherence term into the numerical method.
  • Simulation of three distinct scattering regimes and observation across different correlation lengths.

Main Results:

  • The Wigner function exhibits broadening and flattening as correlation length decreases.
  • Decoherence leads to a progressive and more pronounced distortion of the Wigner function.
  • Observed reduction in reflection probabilities at low energies.
  • Observed reduction in transmission probabilities at high energies.

Conclusions:

  • Reduced correlation length due to decoherence significantly alters quantum scattering dynamics.
  • The Wigner function's behavior provides insights into energy-dependent scattering modifications.
  • The findings have implications for quantum transport in the presence of environmental interactions.