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Unstable Points, Ergodicity and Born's Rule in 2d Bohmian Systems
Athanasios C Tzemos1, George Contopoulos1
1Research Center for Astronomy and Applied Mathematics of the Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece.
Entropy (Basel, Switzerland)
|July 29, 2023
Summary
This study examines unstable points in Bohmian flow for two harmonic oscillators. It analyzes their impact on particle distribution, even when initial conditions deviate from Born
Area of Science:
- Quantum mechanics
- Fluid dynamics
- Classical mechanics
Background:
- Bohmian mechanics offers a deterministic interpretation of quantum mechanics.
- Harmonic oscillators are fundamental systems in physics, providing models for various phenomena.
- Unstable points in fluid flow can significantly influence system dynamics and particle trajectories.
Purpose of the Study:
- To investigate the role and behavior of unstable points in the Bohmian flow of a 2D two-non-interacting harmonic oscillator system.
- To analyze these unstable points in both inertial and moving nodal frames of reference.
- To determine the contributions of ordered and chaotic trajectories to the Born distribution.
Main Methods:
- Analysis of unstable points in different frames of reference (inertial and nodal).
- Consideration of systems with varying numbers of nodal points (1, 2, and multiple).
- Examination of trajectory contributions (ordered and chaotic) to the Born distribution.
Main Results:
- Characterization of unstable points in the Bohmian flow of the specified 2D system.
- Identification of how different frames of reference affect the analysis of unstable points.
- Quantification of trajectory contributions to the Born distribution, including non-Born-rule initial states.
Conclusions:
- Unstable points play a crucial role in shaping the Bohmian flow and particle distribution.
- The study provides insights into the accessibility of the Born distribution from non-standard initial conditions.
- Findings contribute to understanding the interplay between classical trajectories and quantum probability distributions.
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