
Rolando RebolledoUniversity of Valparaíso | CINV · Instituto de Ingeniería Matemática
Rolando Rebolledo
Docteur d'État ès-Sciences, U. Pierre et Marie Curie. Full Professor
About
158
Publications
21,702
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,684
Citations
Introduction
Research interests: Open Quantum Systems, Open System Dynamics in Ecology.
Methods: Stochastic Analysis (commutative and non commutative versions)
Additional affiliations
January 2017 - present
October 1980 - December 1981
September 1979 - September 1980
Publications
Publications (158)
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the N-replicator system and the existence of invariant distributions for a class o...
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the N-replicator system and the existence of invariant distributions for a class o...
Proceedings of the 30th conference on Quantum Probability and Related Topics.
We introduce Evolving Systems of Stochastic Differential Equations. This model generalizes the well-known stochastic differential equations with Markovian switching, enabling the countably many local systems to have solutions in regime-dependent dimension. We provide two constructions, the first one based upon general results on measure-valued proc...
We propose a stochastic model for interacting species in a metacommunity in order to study the factors affecting the intensity of the competition/colonization trade-off as a coexistence mechanism in metacommunities. We particularly focus on the role of the number of local communities and the number of refuges for the inferior competitor. The stocha...
Las líneas que siguen parten de la base de que nuestro país necesita un nuevo modelo de desarrollo, terminando con el que hoy impera, a saber, el neoliberalismo que es un sistema complejo de dominación que abarca todas las actividades humanas.
Ecosystems functioning is based on an intricate web of interactions among living entities. Most of these interactions are difficult to observe, especially when the diversity of interacting entities is large and they are of small size and abundance. To sidestep this limitation, it has become common to infer the network structure of ecosystems from t...
This paper characterises contiguity for families of states defined on a von Neumann algebra. It extends earlier research of my own published in [1], motivated by scattering theory and the celebrated work of Lucien Le Cam in classical probability. It is well-known that Le Cam did a major contribution to develop asymptotic methods in statis- tical de...
InnovatIon: economIc fetIsh or synonymous wIth creatIvIty? rolando rebolledo Berroeta* resumen el diccionario de la rae indica que "innovar'' es "mudar o alterar algo, intro-duciendo novedades''. entonces, ¿cuál es el sentido de la novedad, de la emer-gencia de un nuevo conocimiento? ¿cómo distinguir cuándo una nueva idea constituye una innovación?...
Cet article est une réflexion sur le hasard en tant qu'objet scientifique, et en partant d'un point de vue matérialiste. On considère la relation entre mouvement et complexité en introduisant la notion de système ouvert et les catégories qui en découlent : état de la Nature et observables, ce qui permet de revoir le débat sur le hasard et la certit...
Cet article est une réflexion sur le hasard en tant qu'objet scientifique, et en partant d'un point de vue matérialiste. On considère la relation entre mouvement et complexité en introduisant la notion de système ouvert et les catégories qui en découlent : ´ etat de la Nature et observables, ce qui permet de revoir le débat sur le hasard et la cert...
Simposio Poiesis y sistemas en su interpretación materialista: incidencia en las ciencias y la educación. ACHIF 2015. Presentación Este simposio es continuación del realizado en ACHIF 2013 con el título "Poiesis y sistemas: la perspectiva materialista". El término poiesis cuyo significado original es el de la creación, ha sido usado para generar co...
It is well-known that fractional Poisson processes (FPP) constitute an important example of a non-Markovian structure. That is, the FPP has no Markov semigroup associated via the customary Chapman–Kolmogorov equation. This is physically interpreted as the existence of a memory effect. Here, solving a difference-differential equation, we construct a...
The frequency of genes in interconnected populations and of species in interconnected communities are affected by similar processes, such as birth, death and immigration. The equilibrium distribution of gene frequencies in structured populations is known since the 1930s, under Wright’s metapopulation model known as the island model. The equivalent...
The frequency of genes in interconnected populations and of species in interconnected communities are affected by similar processes, such as birth, death and immigration. The equilibrium distribution of gene frequencies in structured populations is known since the 1930s, under Wright’s metapopulation model known as the island model. The equivalent...
Discusión sobre el concepto de azar y sus modelos matemáticos
La innovación se ha puesto de moda y hay quienes pretenden identificar el concepto con la creatividad. La presentación plantea interrogantes ante ciertas interpretaciones abusivas motivadas por la descarnada y reductora búsqueda de meros beneficios económicos.
Introduction to Quantum Decoherence
An introduction to the open system view on Ecological Theory Integration
Diffusion approximation of Birth-and-Death population processes
We give an explicit entropy production formula for a class of quantum Markov
semigroups, arising in the weak coupling limit of a system coupled with
reservoirs, whose generators $\mathcal{L}$ are sums of other generators
$\mathcal{L}_\omega$ associated with positive Bohr frequencies $\omega$ of the
system. As a consequence, we show that any such se...
An invariant state of a quantum Markov semigroup is an equilibrium state if it satisfies a quantum detailed balance condition. In this paper, we introduce a notion of entropy production for faithful normal invariant states of a quantum Markov semigroup on B(h) as a numerical index measuring “how far” they are from equilibrium. The entropy productio...
We give a full characterisation of decoherence free subspaces of a given quantum Markov semigroup with generator in a generalised Lindbald form which is valid also for infinite-dimensional systems. Our results, extending those available in the literature concerning finite-dimensional systems, are illustrated by some examples.
El desarrollo de nuestra investigación científica es de importancia estratégica para la nación. Así lo han entendido Brasil y otros gobiernos latinoamericanos. Una adecuada política de que pretende hacer importantes cambios estructurales en el Estado, esta comunidad está a la espera de que se promueva una amplia discusión nacional al respecto. Se h...
This paper proposes a generalized Langevin's equation for a small classical mechanical system embedded in a reservoir. The interaction of the main system with the reservoir is given by a Gaussian transform as introduced in our previous paper [8]. Thus, a first result proves the existence of a strong solution to this equation in the space where the...
The understanding of chance challenges the human intellect since the very beginning of philosophical query. Chance has been longtime a privileged terrain for non scientific speculations, hardly and late formalized through probability theories of twentieth century. To understand the nature of its laws requires a synthetic consideration of all scienc...
An invariant state of a quantum Markov semigroup is an equilibrium state if
it satisfies a quantum detailed balance condition. In this paper, we introduce
a notion of entropy production for faithful normal invariant states of a
quantum Markov semigroup on B(h) as a numerical index measuring "how much far"
they are from equilibrium. The entropy prod...
Earthquakes, as a natural phenomenon and their consequences upon structures, have been addressed from deterministic, pseudo-empirical and primary statistical-probabilistic points of view. In the latter approach, 'primary' is meant to suggest that randomness has been artificially introduced into the variables of investigation. An alternative view ha...
A model of an open system of fermion particles submitted to a constant magnetic field and immersed in a reservoir of phonons is considered within this article. The focus is set on the large time behavior of this system, the purpose being to illustrate the methods of Quantum Markov Semigroup Theory. After providing sufficient conditions to ensure th...
This article introduces the notion of consistent families (Λ (n) ) n≥1 of quantum channels. These families correspond to simultaneous observation of different copies of a given quantum system. Here, we are primarily interested in the analysis of measurements connected with them. As usual, the measurement of a quantum system requires the constructio...
Let {T} be a quantum Markov semigroup on {B}({h}) with a faithful
normal invariant state ρ whose generator is represented in a
generalised GKSL form {L}(x) = - (1)/(2) ∑ l
(Ll * Ll x - 2Ll
* xLl + xLl * ) +
i[H,x], with possibly unbounded H, Lℓ. We show that the
biggest von Neumann-subalgebra {N}( {T}) of {B}({h}) where {T} acts
as a semigroup of...
This paper introduces and investigates probabilistic properties of a class of gaussian processes connected with cosine transforms, which have been used to describe non Markovian classical open systems in Physics. Sev-eral examples of these processes are considered, namely, the Fractional Brow-nian Motion with Hurst coefficient > 1/2 and other proce...
A major problem to perform statistical inference in open quantum systems is the perturbation induced by the measurement process. However, at least theoretically, a suitable choice of the measurement process could provide a consistent approach through classical stochastic processes. This work proposes a method to perform statistical inference on ope...
Let T be a quantum Markov semigroup on B(h) with a faithful normal invariant state ρ.
The decoherence-free subalgebra N(T) of T is the biggest subalgebra of B(h) where the completely positive maps T_t act as homomorphisms. When T is the minimal semigroup whose generator is represented in a generalised GKSL form with possibly unbounded operators H,...
A number of results connecting quantum and classical Markov semigroups, as well as their dilations is reported. The method presented here is based on the analysis of the structure of the semigroup generator. In particular, measure-valued processes appear as a combination of classical reduction and classical dilation of a given quantum Markov semigr...
Complete characterization of complete positivity preserving non-Markovian master equations is presented.
Linear Stochastic Schrödinger Equations and the quantum flow of the exclusion Quantum Markov Semigroup
Let T be a uniformly continuous quantum Markov semigroup on B(h) with generator represented in a standard Gorini-Kossakowski-Sudarshan-Lindblad form by means of operators $L_\ell$ and $H$ and a faithful normal invariant state $\rho$�. In this note we give new algebraic conditions for proving that T converges towards a steady state, possibly differe...
Lectures on Complete Positivity and Quantum Markov Semigroups delivered at the VI Winter School on Stochastic Analysis and Applications, Valparaíso, Chile
The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) aris- ing from the unraveling of quantum master equations. Under the Born– Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantu...
The paper is devoted to the study of nonlinear stochastic Schr\"{o}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 evolutions equations on Hilbert spaces provides characterizations of both continuous quan...
Clase magistral sobre las energías renovables no convencionales dictada al inicio del año académico de INACAP Osorno, 2008
A sufficient condition for non-Markovian master equation which ensures the complete positivity of the resulting time evolution is presented.
Quantum Markov semigroups have been used as a predominant model of open quantum dynamics where the system interacts with the environment. Thus, the main dynamics is submitted to perturbations which change the nature of its mathematical structure. This paper explores a class of perturbations which do not change the invariant elements of the main dyn...
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely positive.
We develop linear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution X t to a LSS with regular initial condition. Moreover, we obtain...
We develop linear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution Xt to a LSS with regular initial condition. Moreover, we obtain...
Quantum Decoherence consists in the appearance of classical dynamics in the evolution of a quantum system. This paper focuses on the probabilistic interpretation of this phenomenon, connected with the analysis of classical reductions of a quantum Markov semigroup.RésuméLa décohérence quantique correspond à l'apparition d'une dynamique classique dan...
This paper addresses the discussion on probabilistic features of the concept of decoherence as it appeared in quantum physics. Given a Lindblad-type generator of an open system dynamics, we derive applicable criteria to characterize decoherent behaviour.
A Quantum Markov Semigroup consists of a family { T} = ({ T}t)_{t ∈ B R+} of normal omega*- continuous completely positive maps on a von Neumann algebra 𝔐 which preserve the unit and satisfy the semigroup property. This class of semigroups has been extensively used to represent open quantum systems. This article is aimed at studying the existence o...
There is an extensive literature on Scattering Theory, the case of the so-called “Hamiltonian dynamics” being a well known subject for anyone interested in Mathematical Physics. Thus, I want to say it loudly, these lectures do not pretend to teach that subject even though it provided an important motivation for the current research. These pages are...
The seminar on Stochastic Analysis and Mathematical Physics of the Ca tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physi...
This article introduces a concept of transience and recurrence for a Quantum Markov Semigroup and explores its main properties
via the associated potential. We show that an irreducible semigroup is either recurrent or transient and characterize transient
semigroups by means of the existence of non trivial superharmonic operators.
The notion of a Quantum Markov Semigroup (QMS) is an extension of classical Markov semigroups motivated by the study of open quantum systems. Indeed, a number of physicists interested in open quantum systems introduced the notion of Quantum Dynamical Semigroups in the Seventies. Since then the subject has been extensively discussed and improved by...
This article provides a model for the dissipative dynamics and electronic transport in Anderson insulators. This model is based upon quantum stochastic ows which satisfy a given stochastic differential equation. The Lindblad master equation follows from a projection of the quantum ow. For fixed parameters of the model, the Gibbs state is the unique...
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 sta...
A diffusion process is constructed as a model for the electromagnetic field in a laser. The process is characterized by means of a Martingale problem of Nelson’s type, under a finite entropy assumption.
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.
This article is aimed at establishing a bridge between classical Interacting Stochastic Particle systems and their quantum counterparts. More precisely, the general form of the generator of a quantum Markov semigroup which corresponds to a class of non commutative interacting particle systems is obtained. This semigroup is the natural quantization...
The interpretation provided by Schrödinger of quantum mechanics through classical stochastic processes is the root of Euclidean quantum mechanics founded on Bernstein processes. Open quantum systems have been extensively investigated during the last three decades and have motivated new probabilistic interpretations for quantum dy-namics. This artic...
The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on going research activity. Since 1995, the group has organized international workshops as a way of promoting a broader dialogue among experts in the areas of classical and quantum stochastic analysis, mathema...
The notion of wave map, inspired from Scattering Theory, was introduced in [7] within the framework of Quantum Dynamical Semigroups. The current article is addressed to classical probabilists, building up the wave map for two (classical) Feller semigroups which are recurrent in the sense of Harris and obtaining an interesting relationship with the...
This article introduces the notion of Mean Quantum Sojourn Time for a Quantum Dynamical Semigroup acting over an arbitrary von Neumann algebra. This notion is used to analyze the asymptotic behaviour of the underlying dynamics and allows one to include, as a particular case, earlier classification of states obtained in scattering theory. Furthermor...
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, necess...
The introduction of different models of phase operators in Quantum Mechanics should provide the same value, the classical phase, when evaluated in an electromagnetic field where the average number of photons is high enough. This physical principle, stated by Lerner, translates into a classical probability limit problem which is solved by the author...
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 r...
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 r...
This paper is based on the application of stochastic differential
equations in simulating the active power consumption in street lamp
operation, both in transient and steady state. The method worked as
follows. Firstly, a collection of about 400 street lamps was measured in
the laboratory. In addition, a theoretical model for the mean power
consump...