Quantum Energy-Loop Gain: Geometric Accumulation of Energy in Closed Parameter Spaces
Abstract
The exploration of geometric phases in quantum mechanics has fundamentally transformed our understanding of cyclic adiabatic evolutions, revealing how state vectors acquire non-trivial phase factors dictated by the underlying parameter manifolds. While traditional geometric phases govern quantum state wavefunctions and superposition coefficients, the energetic consequences of cyclic parameter manipulation remain bound to instantaneous expectation values within conventional frameworks. In this paper, we introduce and formalize the concept of Quantum Energy-Loop Gain (QELG), demonstrating that quantum systems subjected to closed parameter loops can exhibit an irreducible, topologically protected net energy shift. We define this phenomenon through an energy vector potential acting directly on the parameter space, presenting its mathematical foundations, gauge transformation properties, adiabatic and non-adiabatic dynamics, and thermodynamic consistency. Furthermore, we outline potential experimental platforms capable of observing this geometric accumulation of energy, opening a novel pathway for non-dissipative energy manipulation and advanced quantum control.
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