Characteristic operator functions for quantum inputplantoutput models and coherent control
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear inputplantoutput systems to arbitrary quantum nonlinear Markovian inputoutput models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the inputoutput relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entries that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arisemore »
 Authors:

^{[1]}
 Department of Physics, Aberystwyth University, Aberystwyth, SY23 3BZ Wales (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22403089
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL SYSTEMS; DEGREES OF FREEDOM; EQUATIONS OF MOTION; MARKOV PROCESS; MATERIAL BALANCE; NONLINEAR PROBLEMS; TRANSFER FUNCTIONS