Elsevier

Nuclear Physics A

Volume 441, Issue 4, 19 August 1985, Pages 676-700
Nuclear Physics A

On the initial conditions of time-dependent mean-field equations of evolution: (I) finite temperature

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Abstract

The problem of the determination of the initial conditions in the mean-field description of time-dependent expectation values and quantum fluctuations of nuclear observables is considered within the framework of functional integration. We propose two quantization procedures by applying the saddle-point method to a temperature-dependent and time-dependent generating function. In the first method, referred to as derivation after variation, the initial condition of the TDHF equation of evolution is given by the temperature-dependent Hartree-Fock approximation of the initial many-body state of the system. In addition, the saddle-point approximation of the quadratic quantum fluctuations includes the contribution of the corresponding RPA which consists of correlated exchanges of HF-RPA phonons and TDHF-RPA phonons and improves the dispersion formula recently proposed by Balian and Veneroni. In the second method, referred to as variation after derivation, the determination of the mean-field initial condition is self-consistently coupled to the mean-field dynamics which approximates the quantum many-body propagation. In contrast to the previous method, the mean-field initial condition and the mean-field dynamics are found to be dependent upon the observable being measured.

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