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arXiv:2610.25222

Self-Trapping and Liouvillian Spectral Transitions in a Dissipative Bose-Hubbard Dimer

Subhendu Saha, Raka Dasgupta

Published Oct 18, 2026• 0 citations

Abstract

We study the self-trapping transition in dissipative double wells using mean-field theory and exact diagonalization. We find that, similar to the conventional interaction-driven transition from oscillatory dynamics to self-trapping, dissipation alone can also induce self-trapping-like localization in one well. The resulting state, although transient and decaying, persists for a substantial time. At the mean-field level, the interaction- and dissipation-driven transitions are discontinuous and continuous, respectively. When interaction and dissipation both are present, their interplay produces three dynamical regimes: (i) at weak interaction, increasing dissipation drives a transition from oscillations to self-trapping; (ii) at moderate interaction, self-trapping at weak dissipation, oscillatory dynamics at intermediate dissipation, and re-entrant self-trapping at strong dissipation; and (iii) at strong interaction, self-trapping persists but is weakened by dissipation. We connect the transition with the Liouvillian spectrum. It is observed that purely dissipation-driven transition coincides with an exceptional point in the spectra, and a peak in the Liouvillian gap, marking the onset of the quantum-Zeno regime. In the presence of interactions, however, the onset of the Zeno regime is shifted to dissipation strengths larger than that required for the self-trapping transition.

DOI: 10.48550/arxiv.2610.25222

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Abstract We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is independent of any Hamiltonian parameter, and cannot therefore capture the competition between hopping-induced delocalization and the interaction-dominated self-trapping regime. We focus instead on the exact quantum dynamics of the particle imbalance after the system is prepared in a variety of initial states, and on the frequency-resolved spectral properties of the steady state, as encoded in the single-particle Green’s functions. We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio. We further show that a finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.

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