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The quantum Josephson Hamiltonian of two weakly linked Bose-Einstein condensates is written in an overcomplete phase representation, thus avoiding the problem of defining a Hermitian phase operator. We discuss the limit of validity of the standard, non-rigorous Mathieu equation, due to the onset of a higher order $cos 2 phi$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $phi$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models.
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems, e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suita
We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under th
In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Ca
We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown, with the pos
Colloidal heat engines are paradigmatic models to understand the conversion of heat into work in a noisy environment - a domain where biological and synthetic nano/micro machines function. While the operation of these engines across thermal baths is