Related papers: On the Hilbert space dimension of systems with sec…
We give some account of investigations for the role of infinite dimensional algebras in time dependent systems.
We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
In this paper we discuss constraints on two-dimensional quantum-mechanical systems living in domains with boundaries. The constrains result from the requirement of hermicity of corresponding Hamiltonians. We construct new two-dimensional…
Recently, several hybrid approaches to quantum information emerged which utilize both continuous- and discrete-variable methods and resources at the same time. In this work, we investigate the bipartite hybrid entanglement between a…
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are closely…
We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a…
The relative position of one subfactor of a factor has been proved quite rich since the work of Jones. We shall show that the theory of relative position of several subspaces of a separable infinite-dimensional Hilbert space is also rich.…
In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treatment.
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
We discuss and extend some aspects pertaining to the canonical quantisation of JT gravity in de Sitter space, including the problem of time and the construction of a Hilbert space. We then extend this discussion to other two dimensional…
We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…
A pedagogical introduction to solving classical and quantum many-body models in infinite spatial dimensions is given. The solution of the Hubbard model obtained in this limit is discussed in detail. It corresponds to a dynamical mean-field…