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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.
Physical Review. E
|November 16, 2021
Summary
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.
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.
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