Related papers: Real Tunneling Solutions and the Hartle-Hawking Wa…
It is shown that the Hartman-Fletcher effect is valid for all the known expressions of the mean tunnelling time, in various nonrelativistic approaches, for the case of finite width barriers without absorption. Then, we show that the same…
We develop a new method for estimating the decay probability of the false vacuum via regularized instantons. Namely, we consider the case where the potential is either unbounded from below or the second minimum corresponding to the true…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…
Quantum cosmology uses a wave function to model the universe, but finding solutions for this poses a problem as it is difficult to define the boundary conditions or identify the correct path for a path integral. We begin the discussion by…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…
We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the…
Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave…
Within the framework of the instanton approach we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact…
We investigate in detail the properties of oscillating instanton solutions discussed recently in the literature. We find that the solutions with N nodes contain exactly N homogeneous negative modes in their spectrum of linear perturbations.…
We investigate the cosmological signatures of instantons mediating tunneling between de Sitter minima. For generic potentials the Coleman-de Luccia instanton does not necessarily exist; when it does not, the instanton which contributes to…
We analyze the tunneling time problem via the presence time formalism. With this method we reproduce previous results for very long wavepackets and we are able to calculate the tunneling time for general wavepackets of arbitrary shape and…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
The problem of finding the convex hull of an IFS fractal is relevant in both theoretical and computational settings. Various methods exist that approximate it, but our aim is its exact determination. The finiteness of extremal points is…
We consider tunneling processes in QFT induced by collisions of elementary particles. We propose a semiclassical method for estimating the probability of these processes in the limit of very high collision energy. As an illustration, we…
We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian…
For the Allen-Cahn equation, it is well known that there is a monotone standing wave joining with the balanced wells of the potential. In this paper we study the existence of traveling wave solutions for the Allen-Cahn equation on an…
Hall-MHD is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other…
Tunneling from a two-dimensional contact into quantum-Hall edges is considered theoretically for a case where the barrier is extended, uniform, and parallel to the edge. In contrast to previously realized tunneling geometries, details of…