Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos

Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons

We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.

Quantum Instantons and Quantum Chaos

Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.

Closed Path Integrals and Renormalisation in Quantum Mechanics

We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action is relevant for quantum chaos and quantum instantons.

Instantons and the quantum bound to chaos

We investigate why the Lyapunov exponents $λ$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $λ< 2 πk_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC satisfies the same bound as the quantum OTOC, which is caused by the stability of quantum thermal fluctuations around the instanton on the barrier. We expect that similar instantons (or other delocalised structures) will be found in many other systems with exponentially growing OTOCs.

Renormalisation group flow of the Jaynes-Cummings model

The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalisation in perturbation theory. We show, however, that exact renormalisation reveals a rich non-perturbative structure, and that the model provides a physical example of a theory with a chaotic coupling trajectory and multi-valued beta-function. We also construct an exact Wilsonian-like renormalisation group flow for the effective scattering matrix, and show how multi-valued features arise in the flow. Our results shed light on non-perturbative aspects of…

Krylov复杂度、路径积分与瞬子

Krylov complexity, path integrals, and instantons

该研究将Krylov复杂度表述为路径积分，揭示其在经典混沌系统中由量子瞬子描述，并通过玩具模型验证了这一结论。