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Physical scales in the Wigner-Boltzmann equation.
M Nedjalkov1, S Selberherr, D K Ferry
1Institute for Microelectronics, Vienna University of Technology, Vienna, Austria.
Annals of Physics
|March 19, 2013
Summary
The Wigner-Boltzmann equation reveals quantum evolution depends on interaction scales. Increased coupling to oscillators reduces electric potential strength and coherence length, impacting transport modes.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Statistical mechanics
Background:
- The Wigner-Boltzmann equation models quantum transport in solids, considering interactions with bosonic excitations like phonons.
- Quantum evolution involves a balance between coherent particle-potential interactions and decoherence from oscillator scattering.
Purpose of the Study:
- To investigate the influence of interaction scales on quantum evolution within the Wigner-Boltzmann framework.
- To derive a dimensionless formulation and a scaling theorem for the Wigner-Boltzmann equation.
Main Methods:
- Developed a dimensionless formulation of the Wigner-Boltzmann equation.
- Introduced dimensionless strength parameters to represent physical scales.
- Derived a scaling theorem connecting coupling strength to physical parameters.
Main Results:
- Established that increased coupling to oscillators is equivalent to reduced electric potential strength and coherence length.
- Demonstrated that the dominant quantum evolution mode (coherent vs. decoherent) is scale-dependent.
- Identified classes of physically distinct yet mathematically equivalent Wigner-Boltzmann evolution setups.
Conclusions:
- The interplay between coherent and decoherent transport modes is governed by the relative scales of physical quantities.
- The derived scaling theorem provides a unified view of how coupling strength affects quantum transport properties.
- The existence of equivalent evolution setups offers flexibility in modeling quantum systems.
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