Rolando Rebolledo
Pontifical Catholic University of Chile
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Publication
Featured researches published by Rolando Rebolledo.
Journal of Mathematical Physics | 2002
Franco Fagnola; Rolando Rebolledo
This article introduces a concept of subharmonic projections for a quantum Markov semigroup, in view of characterizing the support projection of a stationary state in terms of the semigroup generator. These results, together with those of our previous article [J. Math. Phys. 42, 1296 (2001)], lead to a method for proving the existence of faithful stationary states. This is often crucial in the analysis of ergodic properties of quantum Markov semigroups. The method is illustrated by applications to physical models.
Journal of Mathematical Physics | 2001
Franco Fagnola; Rolando Rebolledo
We provide two criteria on the existence of stationary states for quantum dynamical semigroups. The first one is based on the semigroup itself, while the second criterion is based on the generator which is in general unbounded and interpreted as a sesquilinear form. These results are illustrated by physical examples drawn from quantum optics.
Journal of Mathematical Physics | 1994
Franco Fagnola; Rolando Rebolledo; Carlos Saavedra
A stochastic dilation of master equation for a maser is constructed using the technique of quantum stochastic differential equations with unbounded operator coefficients. The associated quantum Markov flow is characterized and turns out to extend a classical birth and death process. Furthermore, the stationary distribution of the aforementioned process, which is connected to the stationary state of the micromaser, is obtained in a closed form.
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 1998
Franco Fagnola; Rolando Rebolledo
This paper deals with the asymptotic behavior of a quantum dynamical semigroup acting on the algebra of all linear bounded operators on a given Hilbert space. In practice, all these semigroups have a generator which can be written in a well-known form named after Lindblad and Davies. If the semigroup has a faithful normal stationary state ρ, necessary and sufficient conditions are derived for the w*-convergence of to , where is the conditional expectation of an element X onto the subalgebra of fixed points. Our main results are expressed in terms of the Lindblad–Davies generator .
Annals of Applied Probability | 2008
Carlos M. Mora; Rolando Rebolledo
The paper is devoted to the study of nonlinear stochastic Schro- dinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born-Markov approximations, this class of stochastic evo- lutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.
Journal of Applied Probability | 1996
Eckhard Platen; Rolando Rebolledo
The paper introduces an approach focused towards the modelling of dynamics of financial markets. It is based on the three principles of market clearing, exclusion of instantaneous arbitrage and minimization of increase of arbitrage information. The last principle is equivalent to the minimization of the difference between the risk neutral and the real world probability measures. The application of these principles allows us to identify various market parameters, e.g. the risk-free rate of return. The approach is demonstrated on a simple financial market model, for which the dynamics of a virtual risk-free rate of return can be explicitly computed.
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2008
Franco Fagnola; Rolando Rebolledo
Let
Communications in Mathematical Physics | 2015
Franco Fagnola; Rolando Rebolledo
{\mathcal T}
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2010
Ameur Dhahri; Franco Fagnola; Rolando Rebolledo
be a uniformly continuous quantum Markov semigroup on
Infinite Dimensional Analysis, Quantum Probability and Related Topics | 2007
Carlos M. Mora; Rolando Rebolledo
{\mathcal B} ({\mathsf h})