Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics

Details Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics

2005-11-09

arxiv.org/abs/quant-ph/0511091v3

Physics

Quantum Physics

12 pages + 4 figures, revised, added more sections and numerical illustrations

Scientific paper

We derive exact relations and general inequalities that extend the usual time-energy uncertainty relations from the domain of unitary Hamiltonian dynamics to that of dissipative dynamics as described by a broad class of linear and nonlinear evolution equations for the density operator. For non-dissipative dynamics, by using the Schroedinger inequality instead of the Heisenberg-Robertson inequality, we obtain a general exact time-energy uncertainty relation which is sharper than the usual Mandelstam-Tamm-Messiah relation $\tau_F\Delta_H\ge \hbar/2$. For simultaneous unitary/dissipative dynamics, the usual time-energy uncertainty relation is replaced by a less restrictive relation that depends on the characteristic time of dissipation, $\tau$, and the uncertainty associated with the generalized nonequilibrium Massieu-function operator which defines the structure of the dissipative part of the assumed class of evolution equations. Within the steepest-entropy-ascent dissipative quantum dynamics of an isolated system introduced earlier by this author, we obtain the interesting time-energy and time-entropy uncertainty relation $(2\tau_F\Delta_H/ \hbar)^2+ (\tau_F\Delta_S/k_B\tau)^2 \ge 1$. We illustrate this result and various other inequalities by means of numerical simulations.

Affiliated with

Also associated with

No associations

Rating

Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-energy and time-entropy uncertainty relations in dissipative quantum dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104580