Author
Viacheslav P. Belavkin
Other affiliations: University of Marburg
Bio: Viacheslav P. Belavkin is an academic researcher from University of Nottingham. The author has contributed to research in topics: Quantum probability & Quantum operation. The author has an hindex of 33, co-authored 106 publications receiving 3502 citations. Previous affiliations of Viacheslav P. Belavkin include University of Marburg.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a quantum stochastic calculus of a posteriori conditional expectations in quantum observed systems is developed and a general quantum filtering equation for 2 QS process is derived, and an application to the description of spontaneous collapse of the quantum spin under continuous observation is given.
316 citations
Posted Content•
TL;DR: In this article, a *-algebraic indefinite structure of quantum stochastic calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear space.
Abstract: A *-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear space. The class of nondemolition output QS processes in quantum open systems is characterized in terms of the QS calculus, and the problem of QS nonlinear filtering with respect to nondemolition continuous measurments is investigated. The stochastic calculus of a posteriori conditional expectations in quantum observed systems is developed and a general quantum filtering stochastic equation for a QS process is derived. An application to the description of the spontaneous collapse of the quantum spin under continuous observation is given.
265 citations
TL;DR: In this paper, a quantum stochastic model for the Markovian dynamics of an open system under the nonsmoothed unsharp observation which is continuous in time is given and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described.
Abstract: A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one.
217 citations
TL;DR: In this article, a stochastic model for continuous measurement in a quantum system is given, where the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear wave equation.
161 citations
Posted Content•
TL;DR: In this paper, a stochastic model for continuous measurement in a quantum system is given, and it is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a non-linear, non-stochastic wave equation.
Abstract: A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation. For a particle in an electromagnetic field it reduces the Schroedinger equation with extra imaginary stochastic potentials.
131 citations
Cited by
More filters
01 Jan 1973
TL;DR: In this paper, the authors present a reformulation of quantum theory in a form believed suitable for application to general relativity, from which the conventional interpretation of quantum mechanics can be deduced.
Abstract: The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.
2,091 citations
TL;DR: In this paper, a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir is presented, which can be applied to a wide class of relaxation operators in the Markovian regime.
Abstract: We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.
988 citations
TL;DR: In this paper, an overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation, which requires a large separation of system and environment time scales.
Abstract: Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.
887 citations
TL;DR: The purview of cavity QED will continue to grow as researchers build on a rich infrastructure to attack some of the most pressing open questions in micro- and mesoscopic physics.
Abstract: Modern cavity quantum electrodynamics (cavity QED) illuminates the most fundamental aspects of coherence and decoherence in quantum mechanics. Experiments on atoms in cavities can be described by elementary models but reveal intriguing subtleties of the interplay of coherent dynamics with external couplings. Recent activity in this area has pioneered powerful new approaches to the study of quantum coherence and has fueled the growth of quantum information science. In years to come, the purview of cavity QED will continue to grow as researchers build on a rich infrastructure to attack some of the most pressing open questions in micro- and mesoscopic physics.
626 citations
TL;DR: In this article, a model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation, derived from a density operator equation such as the Bloch equation, and consistent with it.
Abstract: A model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation, derived from a density operator equation such as the Bloch equation, and consistent with it. The advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described. The method is applied to the nonlinear absorber, cascades of quantum transitions, second-harmonic generation and a measurement reduction process. The model provides graphic illustrations of these processes, with statistical fluctuations that mimic those of experiments. The stochastic differential equations originated from studies of the measurement problem in the foundations of quantum mechanics. The model is compared with the quantum-jump model of Dalibard (1992), Carmichael and others, which originated among experimenters looking for intuitive pictures and rules of computation.
623 citations