Abstract
The study of non-equilibrium quantum dynamics receives attentions recently. However, the nature and effects of nonequilibirumness such as detailed-balance breaking and the relationship to the underlying intrinsic geometry is still unclear. In this study, we uncover that a gauge field will be induced by the nonequilibriumness in the coherence representation and furthermore its internal geometrical curvature is directly related to the degree of detailed balance breaking. The nonequilibriumness of the quantum system induces an intrinsic geometric curvature which can enhance the quantum coherence, leading to the possibility of the space time origin for the non-local quantum correlations or the possibility of curved space time emergence from nonequilibrium quantum dynamics. We also uncovered that the internal curvature of the gauge field provides a bridge to connect the generalized quantum fluctuation dissipation theorem to the fluctuation theorem and time irreversibility of the quantum dynamics. The quantum time irreversibility is due to the path dependent factor along any particular path in an internal curved space, which is analogous to the Wilson lines (or Wilson loops) in Abelian gauge theory. We also found that the steady state quantum coherence disappears when the non-trivial internal curvature vanishes for the quantum system coupled with environments. When the curvature is relatively small indicating weak detailed balance breaking, the coherence increases as curvature increases. The internal curvature can provide a general and direct quantitative measure of the detail-balance breaking for any quantum/classical non-equilibrium systems, even without knowing the underlying steady state distribution or the steady state flux. Using an example of two harmonic oscillators coupled to two environments with different temperatures, we explicitly show the dependence of the internal curvature and quantum coherence.
Highlights
With the recent progress made in experimental and theoretical studies on quantum synchronization, energy/charge transports in molecular junctions, and quantum information devices [1,2,3,4,5,6], non-equilibrium quantum systems characterized by detailedbalance breaking have attracted more attention
We have uncovered that non-equilibrium quantum dynamics gives rise to an intrinsic geometric curvature which can enhance quantum coherence
This may help reveal an intrinsic connection between the space time geometry/topology and the quantum nature
Summary
With the recent progress made in experimental and theoretical studies on quantum synchronization, energy/charge transports in molecular junctions, and quantum information devices [1,2,3,4,5,6], non-equilibrium quantum systems characterized by detailedbalance breaking have attracted more attention. In our recent work [14] on classical non-equilibrium systems, a connection between the curl flux or the detailedbalance breaking and an internal curvature of a gauge field [15] was uncovered. The internal curvature of the gauge field, which is derived from the fundamental dynamics without requiring numerical or analytical steady state solution, provides a direct measure of detailedbalance breaking for non-equilibrium quantum systems. It provides a new and geometric view for the general nature and behaviors of non-equilibrium quantum systems, such as the fluctuation-dissipation theorem (FDT), the fluctuation theorem, and time irreversibility. It is found that, when a quantum system is not very far away from the equilibrium, the quantum coherence increases with the internal curvature monotonically, which can be tested in future experiments
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