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Formulation of Liouville`s Theorem for Grand Ensemble Molecular
Formulation of Liouville`s Theorem for Grand Ensemble Molecular

... stationary solution for ρ(t), in case of a thermal bath (heat reservoir), is the density matrix of a canonical ensemble. The mathematical analysis of such concepts has been extensively done in Ref.[1] but, for our current focus, there is one important concept that we can transfer into the treatment ...
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Canonical quantization

In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the ""method of classical analogy"" for quantization, and detailed it in his classic text. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated via canonical Poisson brackets, a structure which is only partially preserved in canonical quantization.This method was further used in the context of quantum field theory by Paul Dirac, in his construction of quantum electrodynamics. In the field theory context, it is also called second quantization, in contrast to the semi-classical first quantization for single particles.
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