Emergent Dissipation from Multi-Branch Mode Coupling in Coherent Media

This work identifies a minimal, generic mechanism by which effective dissipation and viscosity emerge from fundamentally conservative dynamics in coherent systems. The analysis focuses on fields that admit an amplitude–phase decomposition and therefore support multiple excitation branches, specifically a gapped amplitude mode and gapless phase (Goldstone) modes. It is shown that mixed amplitude–phase coupling opens resonant decay channels in which energy stored in coherent amplitude excitations is transferred into pairs of phase modes. While the underlying equations of motion remain Hamiltonian and time-reversal invariant, coarse-graining over microscopic phase information converts this reversible energy exchange into effectively irreversible relaxation. The mechanism is developed analytically using a generic field-theoretic framework, supported numerically through structure-preserving simulations of a minimal two-field model, and interpreted as an emergent bulk-viscosity-like response. No explicit dissipative terms or external baths are introduced. A direct experimental realization is identified in trapped Bose–Einstein condensates, where well-established Beliaev-type mode coupling provides a laboratory analogue of the multi-branch interaction channel analyzed in this work. The results provide a unified and experimentally anchored framework for understanding how dissipation, viscosity, and relaxation can arise internally from conservative dynamics in coherent media, with relevance across condensed matter physics, field theory, and related contexts.