Related papers: On the Hilbert space dimension of systems with sec…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous…
In an infinite dimensional separable Hilbert space $X$, we study compactness properties and the hypercontractivity of the Ornstein-Uhlenbeck evolution operators $P_{s,t}$ in the spaces $L^p(X,\gamma_t)$, $\{\gamma_t\}_{t\in\R}$ being a…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…
Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…
Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We prove that $H^2(SL_3(\mathbb{Z}[t]); \mathbb{Q})$ is infinite dimensional. The proof follows an outline similar to recent results by Cobb, Kelly, and Wortman, using the Euclidean building for $SL_3(\mathbb{Q}((t^{-1})))$ and a Morse…
This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…
Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator…
In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is,…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems…
We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system with a constraint algebra generating the non-compact $SL(2,\mathbb{R})$ group. In particular, we consider three…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…