Bootstrapping microcanonical ensemble in classical system

TL;DR

This paper shows that the quantum bootstrap method simplifies to a classical microcanonical ensemble analysis in the zero-quantum limit, revealing new classical structures for anharmonic and double-well potentials.

Contribution

It establishes a connection between quantum bootstrap and classical microcanonical ensembles, providing insights into classical structures emerging from quantum limits.

Findings

Quantum bootstrap reduces to classical microcanonical analysis as 7 o 0.

Classical structures like thin archipelagos and peninsulas are identified for specific potentials.

New classical features are revealed in the zero-7 limit for anharmonic and double-well systems.

Abstract

We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical archipelago becomes an extremely thin line for an anharmonic oscillator. For a double-well potential, a peninsula in $E\le 0$ appears.