Bootstrapping microcanonical ensemble in classical system

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 $\hslash \to 0$ 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.

5 pages; v2: some improvement in figures with new results