Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions

TL;DR

This paper investigates the formation of rainbow and cusp catastrophes in Fock space of bosonic Josephson junctions, demonstrating their regularization in second-quantized theory and establishing the ergodic nature of long-term dynamics.

Contribution

It reveals how second-quantization smooths out singularities in Fock space catastrophes and confirms the structural stability of these features through catastrophe theory.

Findings

Rainbow caustics are regularized by Airy functions in second-quantized theory

Fock space catastrophics are structurally stable against initial condition variations

Long-time dynamics exhibit ergodicity in bosonic Josephson junctions

Abstract

We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M.V. Berry, Nonlinearity 21, T19 (2008)]: are there circumstances when it is necessary to second-quantize wave theory in order to avoid singularities?