Quantum Vacuum Fluctuations in Presence of Dissipative Bodies: Dynamical Approach for Non-Equilibrium and Squeezed States

Abstract

This work contributes to the study of non-equilibrium aspects of the Casimir forces with the introduction of squeezed states in the calculations. Throughout this article two main results can be found, being both strongly correlated. Primarily, the more formal result involves the development of a first-principles canonical quantization formalism to study the vacuum in presence different dissipative bodies in completely general scenarios. We considered a one-dimensional quantum scalar field interacting with the volume elements' degrees of freedom of the material bodies, which are modeled as composite systems consisting in a harmonic oscillators interacting with an environment. Solving the full dynamics of the composite system through its Heisenberg equations, we studied each contribution to the field operator by employing general properties of the Green function. We deduced the long-time limit of the field operator. In agreement with previous works, we showed that the expectation values of the components of the energy-momentum tensor present two contributions, one associated to the thermal baths and the other one associated to the field's initial conditions. This allows us to the direct study of steady situations involving different initial states for the field and arbitrary thermal states for the baths. This leads to the other main result, consisting in computing the Casimir force when the field is initially in thermal or continuum-single-mode squeezed states (characterized by a given bandwidth and frequency). Time-averaging is required for the squeezed case, showing both results in a unified way. For the thermal state, all the well-known equilibrium results can be successfully reproduced. Finally, we compared the initial conditions' contribution and the total force for each case, showing that the latter can be tuned in a wide range of values through varying the size of the bandwidth.

arXiv comment18 pages, 1 figure, 6 appendices with supplementary material

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