We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in an extra dimension. This amounts to the equivalence of the quantum measurement boundary-value problem in infinite number particles space to the stochastic calculus in Fock space. It is shown that this exactly solvable model can be obtained from a Schrödinger bound...

Multipoint boundary value problems BVPs for second-order differential equations in a finite interval have been studied extensively and many results for the existence of solutions, positive solutions, multiple solutions are obtained by use of the Leray-Schauder continuation theorem, Guo-Krasnosel’skii fixed point theorem, and so on; for details see 1–4 and the references therein. In the last sev...

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor prog...

Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The an...

We construct integrals of motion (IM) for the sine-Gordon model with boundary at the free Fermion point (β2 = 4π) which correctly determine the boundary S matrix. The algebra of these IM (“boundary quantum group” at q = 1) is a one-parameter family of infinite-dimensional subalgebras of twisted ŝl(2). We also propose the structure of the fractional-spin IM away from the free Fermion point (β2 6...

On any given compact manifold M with boundary ∂M , it is proved that the moduli space E of Einstein metrics on M is a smooth, infinite dimensional Banach manifold. The Dirichlet and Neumann boundary maps to data on ∂M are smooth Fredholm maps of index 0. These results also hold for manifolds with compact boundary which have a finite number of locally asymtotically flat ends, as well as for the ...

Sufficient conditions are given for the solvability of boundary value problems on an infinite interval for nonlinear two dimensional generalized and impulsive differential systems.

The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as t → ∞ to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.

In this paper, the optimal boundary control problem for distributed parabolic systems, involving second order operator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. Some specific properties of the optimal control are discussed.

The paper is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c, 0) of the Euler system there is a control which is supported in a given bounded part of the boundary of the strip and stabilizes the system to (c, 0).