TL;DR
This paper introduces a novel discrete model for quantum energy relaxation involving wave function collapse, deriving power laws for dispersions, and proposing new dissipative equations to describe quantum dissipation.
Contribution
It presents a new discrete relaxation model, a dissipative Schrödinger equation, and a dissipative Liouville equation for quantum systems, advancing understanding of quantum dissipation mechanisms.
Findings
Derived power laws for coordinate and momentum dispersions.
Proposed and solved a new dissipative Schrödinger equation.
Constructed a heuristic dissipative Liouville equation.
Abstract
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new dissipative Schrodinger equation is proposed and solved for particular cases. A new dissipative Liouville equation is heuristically constructed.
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