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Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory
Yves Pomeau1, Martine Le Berre1
1Laboratoire d'Hydrodynamique, Ladhyx, CNRS UMR 7646, Ecole Polytechnique, 91128 Palaiseau, France.
Entropy (Basel, Switzerland)
|December 24, 2021
Summary
This study introduces a new method to understand quantum jumps in two-level atoms by assigning probability to the density matrix. This approach models the atom's statistical properties, offering insights into quantum randomness and information loss.
Area of Science:
- Quantum Mechanics
- Atomic Physics
- Statistical Mechanics
Background:
- Irreversible quantum phenomena present challenges in understanding randomness and information loss due to broken quantum coherence.
- The fluorescence of a single two-level atom under laser illumination exemplifies these difficulties, as deterministic equations conflict with observed random quantum jumps.
- Existing models struggle to reconcile the coherent Rabi oscillations of the atom with the instantaneous, decoherent photon emissions.
Purpose of the Study:
- To present a novel, completed approach for describing quantum jumps in a two-level atom system.
- To develop a probabilistic framework for the atom's density matrix to address quantum randomness.
- To derive a kinetic equation governing the probability distribution of the atom's state over time.
Main Methods:
- Proposed a novel approach involving assigning probability to the atom's density matrix.
- Derived a general "kinetic Kolmogorov-like" equation for the evolution of this probability.
- Analyzed the probability distribution p(θ,t) dependent on the atomic state variable θ and time t.
Main Results:
- The derived kinetic equation successfully describes the statistical properties of the two-level atom.
- The probability distribution p(θ,t) captures the system's behavior under coherent pumping and random photon emission.
- The approach allows for the description of all possible histories of the atom, akin to the many-worlds interpretation.
Conclusions:
- The novel probabilistic approach provides a solvable framework for understanding quantum jumps in two-level atoms.
- This method offers a new perspective on reconciling deterministic quantum evolution with irreversible, random phenomena.
- The framework potentially bridges statistical interpretations of quantum mechanics with concepts like Everett's many-worlds interpretation.
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