Selective Dissipation and Effective GKLS Generators

Roco Roco

Published Apr 1, 2026• 0 citations

Abstract

Dissipative quantum dynamics is usually described through loss, decoherence, relaxation, and the flow of information into an environment. This work proposes a conservative but conceptually important shift in emphasis: in suitably structured models, dissipation can also be read as a mechanism of selection. The paper focuses on effective generators of the form G_eff = -iD - Γ, where D = D* is the coherent self-adjoint part and Γ ≥ 0 is a dissipative term. The algebraic setting is not modified. These generators arise naturally inside the standard Gorini–Kossakowski–Lindblad–Sudarshan, or GKLS, formalism through the effective no-jump sector. The novelty is therefore not a new quantum master equation, but a different architectural reading of a familiar structure. Instead of interpreting Γ only as a loss rate, the paper treats a structured dissipator as an auditor of admissible modes. Modes that are strongly penalized decay, while compatible sectors survive the dissipative test. In finite dimensions, the work proves an exact selection mechanism under an invariant-sector hypothesis and identifies the persistent sector selected by the effective dynamics. The paper also clarifies what remains open in the infinite-dimensional setting. Extending this viewpoint to Dirac–Roco type architectures requires analytic control of domains, semigroup generation, spectral separation, and dissipative estimates. For readers in mathematical physics, open quantum systems, non-Hermitian dynamics, and operator theory, the note provides a bridge between standard GKLS dynamics and the broader idea of selective dissipation: the environment is not only a sink for lost information, but may also enforce the structural survival of particular modes.

DOI: 10.5281/zenodo.19368450

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