Evolution into mixed states in quantum field theory

D. Ya. Petrina

William George Unruh, Robert M. Wald

It has been argued that any evolution law taking pure states to mixed states in quantum field theory necessarily gives rise to violations of either causality or energy-momentum conservation in such a way as to have unacceptable consequences for ordinary laboratory physics. We show here that this is not the case by giving a simple class of examples of Markovian evolution laws where rapid evolution from pure states to mixed states occurs for a wide class of states with appropriate properties at the ``Planck scale,'' suitable locality and causality properties hold for all states, and the deviations from ordinary dynamics (and, in particular, violations of energy-momentum conservation) are unobservably small for all states which one could expect to produce in a laboratory. In addition, we argue (via consideration of other, non-Markovian models) that conservation of energy and momentum for all states is not fundamentally incompatible with causality in dynamical models in which pure states evolve to mixed states.

Jayant Vishnu Narlikar, Τ. Padmanabhan

MA Mei-juan

The time evolution of atom's occupation in a double Jaynes-Cummings model,where two atoms are in mixed state,was investigated by full quantum theory and numerical method,and the influences of atomic initial state and mean photon number in cavity on atom's occupancy are discussed.The results show when the two cavities have the same photon number,evolution of atom's occupation is only related to the purity r of atomic initial state and field intensity,but not influenced by initial entanglement.If the mean photon number in cavities is not equal,the evolution of atom's occupation is not only related to the purity r and field intensity,but also strongly influenced by the initial entanglement.

R. F. Álvarez-Estrada

O. J. P. Éboli, R. Jackiw, So-Young Pi

The isoentropic, but energy-nonconserving, time evolution of mixed quantum states is studied in quantum mechanics and quantum field theory. A variational principle, which gives the Liouville--von Neumann equation, is implemented approximately by making a Gaussian Ansatz for the density matrix. The dynamical equations governing the parameters that define the Ansatz satisfy equations variously analogous to the Schr\"odinger equation and to mechanical problems. Interesting nonequilibrium evolution is found in special cases, as, for example, when the analog Schr\"odinger equation gives rise to reflectionless transmission. For field theory in an external, time-dependent metric we obtain equations that were previously derived in the many-field (spherical-model) limit.