The power-spectrum tensor in steady-state systems and its role in quantum friction (2402.15777v1)
Abstract: For systems in equilibrium, quantum statistical physics provides a number of general theorems and relations that are not tied to specific microscopic models, one example being the fluctuation-dissipation theorem. Much less is known for nonequilibrium situations. In this work, we discuss certain properties of the power-spectrum tensor for systems in general steady-states, i.e. stationary states not necessarily corresponding to equilibrium configurations. In our analyses, we do not make any direct connection to specific models for the underlying microscopic dynamics and, therefore, our results can be applied to a large variety of systems. We also connect the power-spectrum tensor to other quantities that characterize these systems and, where appropriate, compare with the equilibrium counterparts. As an application, we consider the specific problem of quantum friction, where, at zero temperature, a contactless quantum-electrodynamic drag force acts on a particle that moves in close proximity to an arrangement of material bodies. Specifically, we show how the additional information about the system's physics facilitates the derivation of more precise constraints on the power spectrum and its functional dependencies.
- This condition can always be realized if we consider instead of d^i(t)subscript^𝑑𝑖𝑡\hat{d}_{i}(t)over^ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_t ) the operator d~^i(t)=d^i(t)−⟨d^i⟩subscript^~𝑑𝑖𝑡subscript^𝑑𝑖𝑡delimited-⟨⟩subscript^𝑑𝑖\hat{\tilde{d}}_{i}(t)=\hat{d}_{i}(t)-\langle\hat{d}_{i}\rangleover^ start_ARG over~ start_ARG italic_d end_ARG end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_t ) = over^ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_t ) - ⟨ over^ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⟩.
- In principle, we can avoid this by symmetrizing the product in the definition of Cij(τ)subscript𝐶𝑖𝑗𝜏C_{ij}(\tau)italic_C start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT ( italic_τ ).
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