Time-Dependent Variational Principle for the Expectation Value of an Observable: Mean-Field Applications

  • Marcel Vénéroni
Part of the NATO ASI Series book series (NSSB, volume 130)


In non equilibrium statistical mechanics one is often interested in making some prediction at a time t1 from the knowledge of some properties at an earlier time t0. In quantum statistical mechanics all the knowledge about the state (whether pure or not) of the system of interest is included, at a given time, in the density operator. Let us assume that this system has been prepared in such a way that the density operator D(t0), characterizing the initial state, is known. At some later time t1 one intends to perform a measurement of some observable A. The theoretical problem is the prediction of the average value of A at the time t1. In principle the calculation of this expectation value
$$A({{t}_{1}};D,{{t}_{0}})\equiv TrAD({{t}_{1}},{{t}_{0}})$$
requires only the knowledge of the Hamiltonian H of the system, since the exact evolution of the density operator D(t, t0) is given by the Liouville-von Neumann equation (2.4).


Variational Principle Density Operator Slater Determinant Heisenberg Equation Heisenberg Picture 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Marcel Vénéroni
    • 1
  1. 1.Division de Physique ThéoriqueInstitut de Physique NucléaireOrsayFrance

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