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

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dc.creatorBeretta, Gian Paolo
dc.date2005-11-09
dc.date2006-03-29
dc.date.accessioned2026-07-07T06:52:42Z
dc.date.available2026-07-07T06:52:42Z
dc.descriptionWe 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 $τ_FΔ_H\ge \hbar/2$. 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, $τ$, 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 $(2τ_FΔ_H/ \hbar)^2+ (τ_FΔ_S/k_Bτ)^2 \ge 1$. We illustrate this result and various other inequalities by means of numerical simulations.
dc.description12 pages + 4 figures, revised, added more sections and numerical illustrations
dc.identifierhttps://arxiv.org/abs/quant-ph/0511091
dc.identifierhttp://arxiv.org/abs/quant-ph/0511091
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105387
dc.subjectQuantum Physics
dc.titleTime-energy and time-entropy uncertainty relations in dissipative quantum dynamics
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