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Quantum stress in chaotic billiards
Karl-Fredrik Berggren1, Dmitrii N Maksimov, Almas F Sadreev
1IFM-Theory and Modeling, Linköping University, S-581 83 Linköping, Sweden.
Summary
This study investigates the Pauli quantum stress tensor in open chaotic billiards. Theoretical models and microwave experiments show good agreement for small currents, with deviations at higher flows explained by including a plane wave.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- The Pauli quantum-mechanical stress tensor describes quantum mechanical forces within a system.
- Open chaotic billiards are model systems for studying quantum transport phenomena.
- Understanding wave function statistics is crucial for characterizing quantum systems.
Purpose of the Study:
- To theoretically and experimentally investigate the Pauli quantum-mechanical stress tensor in open two-dimensional chaotic billiards.
- To derive and validate statistical distributions for quantum stress tensor components under finite current flow.
- To explore the applicability of Gaussian random field models for describing quantum phenomena in chaotic systems.
Main Methods:
- Derivation of analytic expressions for quantum stress tensor components assuming Gaussian random fields for wave functions.
- Numerical analysis of scattering wave functions from the Schrödinger equation for a Sinai billiard.
- Experimental emulation of two-dimensional quantum billiards using planar microwave analogs.
- Extraction of the quantum stress tensor analog from electric field measurements in microwave cavities.
Main Results:
- Satisfactory agreement between theoretical predictions and experimental results for quantum stress tensor distributions at small net currents.
- Observed distinct differences between theory and experiment at higher net currents.
- Successful explanation of discrepancies at higher currents by incorporating a plane wave into the Gaussian random field model to account for net current.
Conclusions:
- The Gaussian random field model provides a good description of the Pauli quantum stress tensor in open chaotic billiards, particularly for low currents.
- Deviations at higher currents highlight the need to incorporate directional plane wave components to accurately model net current effects.
- The study validates the use of microwave analogs for investigating quantum mechanical phenomena and stress tensors.
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