Related papers: On The Generators Of Quantum Stochastic Operator C…
We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…
In this article, we study the cohomology ring of real moment-angle complexes over a simplicial complex $K$. Combinatorial generators for the cohomology can be given in terms of $K$. For $K$ the boundary of an $n$-gon, we give a full…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
In this paper we give a definition of cyclic orthonormal generators (cogs) in R^N. We give a general canonical form for their expression. Further, we give an explicit formula for computing the canonical form of any given cog.
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics are shown to be fully reducible when they are realized in terms of the generators of a generalized deformed oscillator algebra and a ${\rm Z}_{p+1}$-grading structure is…
We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the…
Some classical polar spaces admit polar spaces of the same rank as embedded polar spaces (often arisen as the intersection of the polar space with a non-tangent hyperplane). In this article we look at sets of generators that behave…
In this work, we study regularity problems of certain Markov generators, which naturally appear in the context of analysis in functional spaces associated to probability measures on nilpotent Lie groups.
Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a one-dimensional attractor, which must be a limit cycle in the absence of…
Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.
We show that the notion of $3$-hyperconvexity on oriented flag manifolds defines a partial cyclic order. Using the notion of interval given by this partial cyclic order, we construct Schottky groups and show that they correspond to images…
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings.…
A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the…
Let $\mathfrak{g}'\subset \mathfrak{g}$ be the pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces $\mathbb{C}^{N-2}\subset \mathbb{C}^N$ and $U_q(\mathfrak{g}')\subset…
In this article, we study the multi-parameter quantum groups defined by generators and relations associated with symmetrizable generalized Cartan matrices, together with their representations in the category $\mathcal O$. This presentation…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
The exponential rate of convergence for some Markov operators is established. The operators correspond to continuous iterated function systems which are a very useful tool in some cell cycle models.
Quantum dynamical semigroups play an important role in the description of physical processes such as diffusion, radiative decay or other non-equilibrium events. Taking strongly continuous and trace preserving semigroups into consideration,…
A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.