Nosé–Hoover sampling of quantum entangled distribution functions

While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations (J. Phys. Chem. B 104 (2000) 159), similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic potential, it has been shown that the framework of coherent states permits to set up equations of motion for an isothermal quantum dynamics (Physica A 297 (2001) 337). In the present article, these results are generalized to indistinguishable quantum particles. We investigate the consequences of the (anti-)symmetry of the many-particle wavefunction which leads to quantum entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain new terms which cause Bose-attraction and Pauli-blocking. Questions of ergodicity are discussed for different coupling schemes.