Related papers: The infinite potential well with moving walls
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…
We construct infinite time bubble tower solutions to the critical wave maps equation taking values in the two-sphere. More precisely, for any integers $k\geq3$ and $J\geq1$, we construct a solution that is global in one time direction, has…
To study the onset of a stationary dynamo in the presence of inner or outer walls of various electromagnetic properties, we propose a simple 1D-model in which the flow is replaced by an alpha effect. The equation of dispersion of the…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
Evidence for dynamical tunneling is observed in studies of the transmission, and wave functions, of a soft-walled microwave cavity resonator. In contrast to previous work, we identify the conditions for dynamical tunneling by monitoring the…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
In this paper we consider the local energy decay result for wave equations with a short-range potential. It is important to note that one never uses a finite speed of propagation property unlike the historical previous papers. The essential…
The Bohm interpretation of quantum mechanics is applied to a transmission and reflection process in a double potential well. We consider a time dependent periodic wave function and study the particle trajectories. The average time,…
This paper is concerned with the long-time dynamics of semilinear wave equation subject to dissipative boundary condition. To do so, we first analyze the set of equilibria, and show it could contain infinitely many elements. Second, we show…
Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an…
We show in spatially one dimensional Madelung fluid that a simple requirement on local stability of the maximum of quantum probability density will, if combined with the global scale invariance of quantum potential, lead to a class of…
An analytical solution to the nonlinear differential equation describing the equation of motion of a particle moving in an unforced physical system with linear damping, governed by a cubic potential well, is presented in terms of the Jacobi…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)^{-b} with exponent depending on the…
In this article we give evaluations of certain series of hyperbolic functions using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space}…
We study the quantum mechanical motion of massive particles in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock and allows particle velocities to be determined.…
We analytically analyse the motion of a nonrelativistic charged particle in a cylindrical single capillary. The effective potential for interaction of a charged particle with the inner surface of a capillary is derived as a sum of the…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of…