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Emergent Dissipation from Multi-Branch Mode Coupling in Coherent Media

Brian Doyle Lampton

Published Jan 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.18293897

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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.
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We formulate a conservative, [Formula: see text]-invariant, Hamiltonian extension of Schrödinger/Gross–Pitaevskii hydrodynamics in the rest frame of an effective coherent medium in which the complex matter field [Formula: see text] couples to a real, dimensionless phase-stiffness field [Formula: see text]. The auxiliary field dynamically modulates the Bohm quantum potential through a coupling proportional to the local Fisher-information density, while itself evolving through an inertial equation driven by amplitude gradients. The variationally consistent amplitude-gradient coefficient is [Formula: see text], so positive excursions of [Formula: see text] produce an adaptive softening of quantum pressure. From a single variational principle we obtain coupled evolution equations and a norm-conserving energy functional that is lower bounded in the positive-stiffness sector. Standard Schrödinger/Gross–Pitaevskii dynamics is recovered when [Formula: see text], whereas the classical Hamilton–Jacobi limit requires both [Formula: see text] and the disappearance of the auxiliary excitation. Linear analysis reveals an independent gapped stiffness mode in addition to the Bogoliubov branch, whose zero-momentum gap and quadratic dispersion coefficient determine the parameter ratios [Formula: see text] and [Formula: see text] governing restoration, smoothing and inertia. In the nonlinear regime the same feedback produces an oscillatory auxiliary-field response and a numerically converged, parameter-dependent reduction of wave-packet spreading. The packet remains dispersive rather than forming an interaction-free self-bound state. The framework further predicts a conditional logarithmic visibility relation under a calibrated interferometric readout and reversible finite-rate response loops under cyclic driving. These loops quantify conservative inertial lag rather than dissipated energy or intrinsic hysteretic memory. These results establish the phase-field duality as a minimal and falsifiable Hamiltonian extension in which coherence behaves as an elastic medium.
This deposit contains the paper “Emergence of a Quantum-Analogue Regime from Variational Dissipative–Conservative Dynamics” by Kevin Ellis Anderson. The paper analyses a regime of a previously introduced variational dissipative–conservative partial differential equation framework in which the conservative oscillatory sector admits an effective quantum-like description. Starting from deterministic Hamiltonian evolution coupled to auxiliary dissipative degrees of freedom, the work shows that an amplitude–phase decomposition of the oscillatory field yields a Schrödinger-type equation with an emergent effective Planck constant. The resulting dynamics are formally equivalent to quantum mechanics within a specific regime of validity, while remaining embedded in a broader variational system that also supports decoherent and classical limits. No modification of unitary evolution is introduced, and no stochastic elements, collapse postulates, or hidden variables are assumed. The paper does not propose a revision of quantum theory. Rather, it situates quantum behaviour as a regime arising from deterministic variational dynamics, with effective parameters determined by the underlying free-energy functional and coupling structure.
This preprint develops a reduced dynamical description derived from a previously introduced variational dissipative–conservative PDE framework. Starting from a coupled system consisting of a unitary oscillatory field and a dissipative auxiliary field generated by a single free-energy functional, we show how effective decoherence arises when the auxiliary degrees of freedom are coarse-grained. The full system preserves unitary Hamiltonian evolution in the oscillatory sector, while non-unitary behaviour appears only at the reduced level through irreversible coupling. No collapse postulate, stochastic terms, or modification of quantum mechanics is introduced. The work focuses exclusively on decoherence and effective localisation as emergent phenomena within the variational framework and is intended as a companion to the foundational PDE formulation.
We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and divergence-induced components yields two coupled Hamilton Jacobi equations describing a dynamically intertwined system environment pair. This motivates a Dual Sector or Dual Environmental Interpretation (DSI/DEI), in which the additional degrees of freedom behave as an image sector exchanging energy, information, and phase with the system. Applying a generalized Madelung transform produces a nonlinear dissipative wave equation whose symmetric equilibrium limit reduces to the Schroedinger equation, with the quantum potential and linearity emerging from balanced intersector coupling. In this framework, the wavefunction is not fundamental but encodes the interaction geometry between system and environment, providing a classical origin for interference, amplitude phase coupling, and probabilistic structure. Extending the imaginary structure to multiple independent directions yields a multienvironment generalization capable of representing measurement-like processes, nonMarkovian memory, and entanglement type correlations. The formulation unifies aspects of dual-system models, hydrodynamic approaches, and non-Hermitian dynamics within a single action-based framework, and suggests that quantum mechanics corresponds to a stable symmetric phase of a broader dissipative classical theory.