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Quantum dynamical tunneling breaks classical conserved quantities.

Lingchii Kong¹, Zongping Gong², Biao Wu^1,3

¹International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.

Physical Review. E

|June 22, 2024

Summary

This summary is machine-generated.

Quantum dynamical tunneling can break conserved quantities in pseudointegrable systems. This phenomenon, observed in quantum mechanics, leads to non-zero uncertainties in these quantities across many eigenstates.

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Area of Science:

Quantum mechanics
Chaos theory
Statistical physics

Background:

Pseudointegrable systems exhibit complex dynamics.
Conserved quantities are fundamental in classical and quantum mechanics.
Quantum dynamical tunneling allows transitions between classically forbidden regions.

Purpose of the Study:

To investigate whether quantum dynamical tunneling can break conserved quantities in pseudointegrable systems.
To rigorously prove the quantum mechanical breaking of a conserved quantity.
To analyze the statistical properties of the broken conserved quantity and its relation to quantum chaos.

Main Methods:

Rigorous mathematical proof for the breaking of conserved quantities.
Numerical computation of uncertainties for the broken conserved quantity.
Analysis of eigenstate properties and their relation to classical orbits.
Construction of a random matrix model to simulate level statistics.

Main Results:

A conserved quantity in pseudointegrable systems can be broken quantum mechanically via dynamical tunneling.
Non-zero uncertainties of the broken conserved quantity persist for a large number of eigenstates (up to 10^5).
The uncertainties exhibit universal distributions, mirroring energy level statistics.
Eigenstates with large uncertainties demonstrate superpositions of regular orbits with varying conserved quantity values, confirming dynamical tunneling.

Conclusions:

Quantum dynamical tunneling provides a mechanism for breaking conserved quantities in pseudointegrable systems.
The observed universal statistical properties link quantum tunneling to quantum chaos.
Random matrix theory effectively models the spectral properties of these systems.