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Related Experiment Videos

Uniform semiclassical wave function for coherent two-dimensional electron flow.

Jirí Vanícek1, Eric J Heller

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We developed a uniform semiclassical wave function to describe coherent branched flow in two-dimensional electron gases (2DEGs). This method addresses the complexities of simulating quantum coherence in electron transport phenomena.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Mesoscopic Physics

Background:

  • Coherent branched flow observed in two-dimensional electron gases (2DEGs) presents simulation challenges due to phase space catastrophes.
  • Previous explanations relied on classical arguments, lacking a quantum mechanical description of coherence.

Purpose of the Study:

  • To develop a uniform semiclassical (SC) wave function for coherent branched flow in 2DEGs.
  • To overcome difficulties in SC simulations caused by phase space catastrophes.

Main Methods:

  • Utilized expansion in terms of "replacement manifolds" to derive a uniform SC wave function for a cusp singularity.
  • Generalized the method to calculate uniform SC wave functions for a quantum-map model of 2DEG flow.
  • Extended the approach to a continuous-time model, dropping the quantum-map approximation.

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Main Results:

  • Successfully derived a uniform SC wave function describing coherent branched flow.
  • Demonstrated the method's applicability to both quantum-map and continuous-time models.
  • Provided a theoretical framework for understanding quantum coherence in electron transport.

Conclusions:

  • The developed method offers a way to find uniform SC wave functions for complex quantum phenomena.
  • This work provides a crucial theoretical tool for studying coherent electron transport in mesoscopic systems.
  • The approach is generalizable and applicable to various quantum transport models.