相关论文: Infinite plane wave evolution in a 1-D square quan…

Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…

This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value…

This work is directed towards investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial…

The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…

The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…

We show how to solve time-harmonic wave scattering problems on unbounded domains without truncation. The technique, first developed in numerical relativity for time-domain wave equations, maps the unbounded domain to a bounded domain and…

The existence of co-rotational finite time blow up solutions to the wave map problem from R^{2+1} into N, where N is a surface of revolution with metric d\rho^2+g(\rho)^2 d\theta^2, g an entire function, is proven. These are of the form…

We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time…

We study propagation of high-frequency wave packets along a large-scale background wave which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on…

We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding…

Gravitational waves (GWs) generated by a first-order phase transition at the electroweak scale are detectable by future space-based detectors like LISA. The lifetime of the resulting shock waves plays an important role in determining the…

The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time…

There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The…

We show that by adding a quadratic phase to an initial arbitrary wavefunction, its free evolution maintains an invariant structure while it spreads by the action of an squeeze operator. Although such invariance is an approximation, we show…

We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…

We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially…

Kucha{\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially-symmetric scalar field along arbitrary axially-symmetric foliations of a fixed…

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…

In this work, a scattering process of quantum particles through a potential barrier is considered. The statistical complexity and the Fisher-Shannon information are calculated for this problem. The behaviour of these entropy-information…