相关论文: Reachable states and holomorphic function spaces f…

We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure $\mu$ on…

We show that an analogue of the (four dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model of a real massless scalar field on the initial globally hyperbolic region IGH of two-dimensional…

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations…

Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $L^p$. Derivation…

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the…

Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…

We address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem applied to mixed states, and investigate the difference between pure and…

Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…

In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…

The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…

In this note we study the control problem for the heat equation on $\mathbb{R}^d$, $d\geq 1$, with control set $\omega\subset\mathbb{R}^d$. We provide a necessary and sufficient condition (called $(\gamma, a)$-\emph{thickness}) on $\omega$…

Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples…

Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…

In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE)…

In this paper we explore the correlations in the geometric states. Here the geometric state means the state in CFTs that can be effectively described by classical geometry in the bulk in the semi-classical limit $G\to 0$. By using the upper…

We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\mathcal{D}'_{E'_{\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent…

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and…

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…