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Wigner Paths Method in Quantum Transportwith Dissipation
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The concept of Wigner paths in phase space both provides a pictorial representation of
the quantum evolution of the system of interest and constitutes a useful tool for
numerical solutions of the quantum equation describing the time evolution of the
system. A Wigner path is defined as the path followed by a “simulative particle”
carrying a σ‐contribution of the Wigner function through the Wigner phase‐space, and
is formed by ballistic free flights separated by scattering processes (both scattering with
phonons and with an arbitrary potential profile can be included), as for the case of
semiclassical particles. Thus, the integral transport equation can be solved by a Monte
Carlo technique by means of simulative particles following classical trajectories, in
complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation
in the integral form.
Title: Wigner Paths Method in Quantum Transportwith Dissipation
Description:
The concept of Wigner paths in phase space both provides a pictorial representation of
the quantum evolution of the system of interest and constitutes a useful tool for
numerical solutions of the quantum equation describing the time evolution of the
system.
A Wigner path is defined as the path followed by a “simulative particle”
carrying a σ‐contribution of the Wigner function through the Wigner phase‐space, and
is formed by ballistic free flights separated by scattering processes (both scattering with
phonons and with an arbitrary potential profile can be included), as for the case of
semiclassical particles.
Thus, the integral transport equation can be solved by a Monte
Carlo technique by means of simulative particles following classical trajectories, in
complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation
in the integral form.
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