The unique quantization of classical Hamiltonians in the adiabatic time-dependent HF theory

GIOVANNI GIACHETTA, Luigi Mangiarotti, Gennadi Aleksandrovich Sardanashvily

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the adiabatic assumption. A Hamiltonian of such a system is affine in the temporal derivative of parameter functions. This leads to the geometric Berry factor phenomena.

George Rosensteel, DAVID J. ROWE

Hartree-Fock (HF) theory is generalized so as to apply to nondeterminantal densities, while retaining the fundamental HF restriction to one-body dynamics. Time development in conventional time-dependent Hartree-Fock and its extension are identical to classical Hamiltonian dynamics.

Peter C. Lichtner, James J. Griffin, Hildegard Schultheis +2 more

The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally "true" Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label "constant $〈H〉$" for this form of time-dependent Hartree-Fock theory.NUCLEAR REACTIONS Unique time-dependent Hartree-Fock Hamiltonian obtained from variational principle by norm-violating variations.

Andrei A. Kvitsinsky, Seth Putterman