Formulation of statistical mechanics based on thermal pure quantum states
Abstract
Quantum statistical mechanics can be fomulated based on a single pure quantum state.In this thesis, I establish this formulation, see the properties of such a pure quantum state, and apply the formulation to a practical application.Historically, it has been found that quantum states have robust "typicality", which is the property that almost all the realizable state give equilibrium values correctly for all "mechanical variables", such as energy and a correlation function.I generally call the pure quantum states which can represent the equilibrium state "thermal pure quantum (TPQ) state".I extend the typicality so that it is applicable to "genuine thermodynamic variables", such as entropy and temperature.I introduce many kinds of the TPQ states which include a "(grand)canonical TPQ state" , which is specified by intensive variables such as temperature, and a "microcanonical TPQ state", which is easy to generate.Owing to these results, I establish the new formulation of statistical mechanics based on the TPQ states.
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