Geometric phase and non-stationary state

Harald Grosse, W. L. Kennedy

Ross G. MacLean

This paper introduces an alternative, purely relational geometric ontology for the atom, modelling the electron as a localized, point-like entity executing a continuous, high-frequency, non-smooth trajectory across a non-commutative spherical manifold. By utilizing non-parametric intervals and a Principle of Least Algebraic Resistance, the model derives quantized atomic shells, geometric phase spins, and the Pauli Exclusion Principle purely as topological inevitabilities, bypassing wave-particle dualism and standard uncertainty paradoxes.

Boyu Wang, Milan Radonjić, Florian Otterpohl +1 more

We explore how the dissipative geometric phase evolves within the spin-boson model, focusing specifically on coupling to an Ohmic bath in the weakly coherent regime. To determine the non-unitary time evolution of the system's reduced density matrix, we employ the non-interacting blip approximation (NIBA). For the localized pure initial state used throughout, we derive a compact Bloch-sphere expression showing that the mixed-state geometric phase is a weighted azimuthal winding of the dissipative trajectory. We then map geometric-phase accumulation across various system-bath coupling strengths, temperatures, static biases, and bath cutoff frequencies. Benchmarking representative results against the numerically exact time-evolving matrix product operator (TEMPO) technique shows that NIBA reproduces the population dynamics almost indistinguishably. It also captures the geometric phase quantitatively and qualitatively, although TEMPO reveals a clearer trend in the stationary coherence. Our results show that quantum dissipation suppresses the geometric phase through two complementary mechanisms: thermal noise reduces the state's purity, while static bias localizes the dynamics and reduces the accessible geometric area.

Vivek M. Vyas

Aleksandr E. Svetogorov, Yu. Makhlin

We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of both weak short-correlated noise and slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.

Timothy R Field, Jeeva S. Anandan