Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Studies on the Multifaceted Interaction of Atoms and an Electromagnetic Field

In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.Siirretty Doriast

Optimized auxiliary oscillators for the simulation of general open quantum systems

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly non-perturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present a study based on current research in the context of coherent transport in biological aggregates as a more realistic example of its use; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.Comment: 23 + 9 pages, 11 + 2 figures. No changes from previous version except publication info and updated author affiliation

Stochastic Liouville Equations for Femtosecond Stimulated Raman Spectroscopy

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period $T$, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique known as femtosecond stimulated Raman spectroscopy (FSRS) can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE) originally developed for NMR lineshapes. The SLE provides a convenient simulation protocol that can describe complex dynamics due to coupling to collective coordinates at much lower cost that a full dynamical simulation. The origin of the dispersive features which appear when there is no separation of timescales between vibrational variations and dephasing is clarified

Quantum Heat Engines, the Second Law and Maxwell's Daemon

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells.Comment: Now 18 pages, 8 figure