相关论文: Generators of Dynamical Systems on Hilbert Modules
In this paper, we study Markov dynamics on unitary duals of compact quantum groups. We construct such dynamics from characters of quantum groups. Then we show that the dynamics have generators, and we give an explicit formula of the…
Let $A$ be an algebra over a field $K$ of characteristic zero, let $\d_1, >..., \d_s\in \Der_K(A)$ be {\em commuting locally nilpotent} $K$-derivations such that $\d_i(x_j)=\d_{ij}$, the Kronecker delta, for some elements $x_1,..., x_s\in…
We give a detailed account of a combinatorial construction, due to Cherednik, of cyclic generators for irreducible modules of the affine Hecke algebra of the general linear group with generic parameter q.
High harmonic generation (HHG) is a highly nonlinear emission process in which systems driven by intense laser pulses emit integer multiples (harmonics) of the driving field. This feature is considered universal to all occurrences of HHG.…
A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the…
Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
Let $p$ be a prime number, $F$ a field of characteristic $p$, and $G$ a cyclic group of order $q =p^a$ for some positive integer $a$. Under these circumstances every indecomposable $F G$-module is cyclic. For indecomposable $F G$-modules…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and…
We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional sheaves on $\mathbb{P}^2$ of any degree. We obtain a minimal set of tautological generators, which implies an optimal generation result for both the…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
We introduce a class of Markovian quantum master equations, able to describe the dissipative dynamics of a quantum system weakly coupled to one or several heat baths. The dissipative structure is driven by an entropic operator, the so…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
Power system dynamics are naturally nonlinear. The nonlinearity stems from power flows, generator dynamics, and electromagnetic transients. Characterizing the nonlinearity of the dynamical power system model is useful for designing superior…
We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…
Heisenberg modules over noncommutative tori may also be viewed as Gabor frames. Building on this fact, we relate to deformations of noncommutative tori a bundle of Banach spaces induced by Heisenberg modules. The construction of this bundle…