Related papers: Piecewise constant potentials and discrete ambigui…
Many studies in uncertainty quantification have been carried out under the assumption of an input random field in which a countable number of independent random variables are each uniformly distributed on an interval, with these random…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
In the theory of neutral differential equations with pulse influence (neutral impulsive differential equations), there are many unsolved problems related to certain results in the theory of integral and integro-differential equations. In…
We study spiky configurations of membranes in the SO(d)xSU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schroedinger equation for an arbitrary N is discussed. If the large N limit is…
An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities. The existence of phase probability density…
We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…
We discuss a method based on a segmentary approximation of solutions of the Schr\"odinger by quadratic splines, for which the coefficients are determined by a variational method that does not require the resolution of complicated algebraic…
We compare the bottom of the spectrum of discrete and continuous Schr\"odinger operators with periodic potentials with barriers at the boundaries of their fundamental domains. Our results show that these energy levels coincide in the…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet…
We demonstrate a quantitative version of the usual properties related to unique continuation from an interior datum for the Schr\"odinger equation with bounded or unbounded potential. The inequalities we establish have constants that…
A typical classical interference pattern of two waves with intensities I_1, I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3 observables p = sqrt{I_1 I_2}, p cos\phi and -p sin\phi. They are, e.g. the starting point…
The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
Nontrivial twisted boundary conditions associated with extra compact dimensions produce an ambiguity in the value of the four dimensional coupling constants of the renormalizable interactions of the twisted fields' zero modes. Resolving…