Hydrodynamic Interpretation of Generic Squeezed Coherent States: A Kinetic Theory

The hydrodynamic interpretation of quantum mechanics treats a system particles in an effective manner. In this work, we investigate squeezed coherent states within the interpretation. Hamiltonian operator question is time dependent, n-dimensional and quadratic order. We start with deriving phase space Wigner probability distribution associated equilibrium entropy for states. Then, decompose joint into two portions: marginal position momentum that conditioned on post-selection positions. Our conditionally averaged momenta shown to be equal Bohm's whose connection weak measurements already known. also keep track corresponding classical evolution by identifying shear, magnification rotation components symplectic dynamics. This allows us pinpoint which portion underlying motion appears statistical concept. show our distributions satisfy Fokker-Planck equations exactly. They can used missing information positions as Sackur-Tetrode kinetic theory. Eventually, define pressure, temperature internal energy are related each other same fashion potential incorporates part fluctuations around it. suggest conditional virial relation. end, linked fractional Fourier transformer dynamics similar case where oscillator its Maslov index.