Related papers: On the structure of non-commutative white noises
Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…
We derive a uniqueness result for non-Cartesian composition of systems in a large class of process theories, with important implications for quantum theory and linguistics. Specifically, we consider theories of wavefunctions valued in…
Nonclassical phenomena of quantum mechanics such as anticorrelation and photonic de Broglie waves (PBWs) have been recently understood as a special case of coherence optics with a particular phase relation between orthogonal bases composing…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…
We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine…
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…
We consider a 2D XY model subjected to time-correlated noise, a model of direct relevance to active crystals, which were shown recently to be able to support very large deformations without melting in the presence of persistent…
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which modern technologies are founded. In general, the most prominent…
In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into…
The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works…
We generalize the concepts of Internal Time Superoperator, its associated non unitary similarity transformations and Liapounov variables, to quantum systems with diagonal singularity, and we give a constructive proof of the existence of…
We review our recent contributions to two topics that have become of interest in the field of open, dissipative quantum systems: non-Gaussian noise and decoherence in fermionic systems. Decoherence by non-Gaussian noise, i.e. by an…
We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…
We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…
We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian…