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Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a…
Quantum dynamics of the electron wave function on one-dimensional lattice is considered. The lattice consists of $N$ equal sites and one impurity site. The impurity site differs from other sites by the on-site electron energy $E$ and the…
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the…
Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…
In this work the role of magnetic Landau quantization in the dynamics and spectrum of Diced Lattice charge carriers is studied in terms of the associated pseudospin 1 Green's function. The equations of motion for the 9 matrix elements of…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
A new scheme has been proposed to solve the B.E. condenstates in terms of Green's function approach. It has been shown that the radial wave function of two interacting atoms, moving in a common harmonic oscillator potential modified by an…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between…
The time delay between gravitational wave signals arriving at widely separated detectors can be used to place upper and lower bounds on the speed of gravitational wave propagation. Using a Bayesian approach that combines the first three…
In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established $GW$ approximation provides accurate ionization potentials…
The basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene, and carbon nanotubes. The CE is equal to twice the surface energy and is closely related to…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
We prove that 3-dimensional Schrodinger operator with slowly decaying sparse potential has an a.c. spectrum that fills positive half-line. A new kind of WKB asymptotics for Green's function is found. The absense of positive eigenvalues is…
In J. Stat. Phys. 115, 415-449 (2004) Brydges, Guadagni and Mitter proved the existence of multiscale expansions of a class of lattice Green's functions as sums of positive definite finite range functions (called fluctuation covariances).…
Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular,…
We study the effective conductivity $\sigma_e$ for a random wire problem on the $d$-dimensional cubic lattice ${\mathbb Z}^d, d \geq 2$ in the case when random conductivities on bonds are independent identically distributed random…
We study the long-time behavior of \textit{several} point particles in a 1D viscous compressible fluid. It is shown that the velocities of the point particles all obey the power law $t^{-3/2}$. This result extends author's previous works on…
Primordial Gravitational Waves, i.e. a background of metric perturbations sourced by the quantum inflationary fluctuations, if measured, could both provide a substantial evidence for primordial inflation and shed light on physics at…