 07136 Y. Strauss
 Forward and backward time observables for quantum evolution and quantum stochastic processesI: The time observables
(405K, pdf)
Jun 4, 07

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. Given a Hamiltonian $\mathbf H$ on a Hilbert space $\mathcal H$ it is shown that, under the assumption that
$\sigma(\mathbf H)=\sigma_{ac}(\mathbf H)=\mathbb R^+$, there exist uniquely defined positive operators $\mathbf T_F$ and
$\mathbf T_B$ registering the Schr\"odinger time evolution generated by $\mathbf H$ in the forward (future) direction and
backward (past) direction respectively. These operators may be considered as time observables for the quantum evolution.
Moreover, it is shown that the same operators may serve as time observables in the construction of quantum stochastic
differential equations and quantum stochastic processes in the framework of the HudsonParthasarathy quantum stochastic
calculus. The basic mechanism enabling for the definition of the time observables originates from the recently developed semigroup
decomposition formalism used in the description of the time evolution of resonances in quantum mechanical scattering problems.
 Files:
07136.src(
07136.comments ,
07136.keywords ,
t_observe_paper16.pdf.mm )