Related papers: The infinite potential well with moving walls
Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle in such a potential can be approximately…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal,…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
Generalizations of the Jacobi and Weyl theorems on finite-dimensional linear flows to the case of linear flows on infinite-dimensional tori are presented. Conditions for periodicity, non-wandering, ergodicity and transitivity of…
We analyze possible motion control of microparticles by means of external electromagnetic fields which induce potential wells having fixed spatial distribution but deepening over time up to some limit. It is assumed that given particles are…
The effect of an externally applied force upon dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a linear potential term. The potential…
The possibility of controlling the tunneling time between quantum wells by relocation of the subband wave function within the quantum well by varying the configuration of thin tunnel-transparent barriers embedded into the well is…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
In this papwe we consider an effective role of the potential of the wave equations with/without damping on the L^{2}-estimate of the solution itself. In the free wave equation case it is known that the L^{2}-norm of the solution itself…
The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic…
We study the streamlines of $\infty$-harmonic functions in planar convex rings. We include convex polygons. The points where streamlines can meet are characterized: they lie on certain curves. The gradient has constant norm along…
We study a class of quadratic, infinite-dimensional dynamical systems, inspired by models for viscoelastic fluids. We prove that these equations define a semi-flow on the cone of positive, essentially bounded functions. As time tends to…
Long, flexible fibers transported by a turbulent channel flow sample non-linear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them…
Time-dependent domain wall solutions with infinitesimal thickness are obtained in the theory of a scalar field coupled to gravity with the dilaton, i.e. the Jordan-Brans-Dicke gravity. The value of the dilaton is determined in terms of the…
We investigate (theoretically and numerically) the dynamics of a soliton moving in an asymmetrical potential well with a finite barrier. For large values of the width of the well, the width of the barrier and/or the height of the barrier,…
The time evolution of a particle, caught in an infinitely deep square well, displays unexpected features, when one includes tiny relativistic effects. Indeed, even the smallest corrections to the non-relativistic quadratic spectrum manifest…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
The fields in rectangular and circular waveguides are derived from Maxwell's equations by superposition of plane waves. Subsequently the results are applied to explain cavity modes. Interaction of the cavity modes with a charged particle…
Motivated by mixing processes in analytical laboratories, this work investigates enhanced dissipation in non-autonomous flows. We study the evolution of concentrations governed by the advection-diffusion equation, where the velocity field…