Synthesis of linear quantum stochastic systems via quantum feedback networks

Recent theoretical and experimental investigations of coherent feedback control, the feedback control of a quantum system with another quantum system, has raised the important problem of how to synthesize a class of quantum systems, called the class of linear quantum stochastic systems, from basic quantum optical components and devices in a systematic way. The synthesis theory sought in this case can be naturally viewed as a quantum analogue of linear electrical network synthesis theory and as such has potential for applications beyond the realization of coherent feedback controllers. In earlier work, Nurdin, James and Doherty have established that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators, together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental perspective and based on current methods and technologies, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate more tractable physical realizations of these systems, this paper develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. Explicit synthesis examples are provided to illustrate the realization of two degrees of freedom linear quantum stochastic systems using the new algorithm.Comment: 21 pages, 6 figure

Dissipative Linear Stochastic Hamiltonian Systems

This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified by a Hamiltonian, viscous damping parameters and system-environment coupling functions. We consider energy balance relations for such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems with quadratic Hamiltonians and linear coupling. For LSH systems, we also discuss stability conditions, the structure of the invariant measure and its relation with stochastic versions of the virial theorem. Using Lyapunov functions, organised as deformed Hamiltonians, dissipation relations are also considered for LSH systems driven by statistically uncertain external forces. An application of these results to feedback connections of LSH systems is outlined.Comment: 10 pages, 1 figure, submitted to ANZCC 201

Finite-time thermodynamics of port-Hamiltonian systems

In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell's demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.Comment: To appear in Physica D (accepted July 2013

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008