Related papers: Total Absorption in Finite Time in an $i\delta$ Po…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schr\"odinger equation with strong infrared fields. This is demonstrated by computing high harmonic…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
In this paper we study the time dependent Schr\"odinger equation with all possible self-adjoint singular interactions located at the origin, which include the $\delta$ and $\delta'$-potentials as well as boundary conditions of Dirichlet,…
The one-dimensional time-independent Green's function $G_0$ of a quantum simple harmonic oscillator system ($V_0(x)=m \omega^2 x^2/2$) can be obtained by solving the equation directly. It has a compact expression, which gives correct…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
We general-quantize the dynamics of the quantum harmonic oscillator to obtain a covariant finite quantum dynamics in a finite quantum time. The usual central (``superselected'') time results from a self-organization. Unitarity necessarily…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential…
The change in entropy, /DeltaS, associated with the quasi-static absorption of a particle of energy u by a Schwarzschild black hole (ScBH) is approximately (u/T)-s, where T is the Hawking temperature of the black hole and s is the entropy…
In this paper, we investigate the initial value problem for a Caputo space-time fractional Schrodinger equation for the delta potential. To solve this equation, we use the joint Laplace transform on the spatial coordinate and the Fourier…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
New corrections to the equation of motion and total collapsing time of an empty spherical cavity immersed in an infinite incompressible medium are proposed on the assumption of a non-uniform density. The dimensionless number quantifying the…
We identify the characteristic times of the evolution of a quantum wave generated by a point source with a sharp onset in an absorbing medium. The "traversal'' or "B\"uttiker-Landauer'' time (which grows linearly with the distance to the…
The complex-time formalism is developed in the framework of the path-integral formalism, to be used for analysis of the quantum tunneling phenomena. We show that subleading complex-time saddle-points do not account for the right WKB result.…
The Keller-Segel equation, a classical chemotaxis model, and many of its variants have been extensively studied for decades. In this work, we focus on 3D Keller-Segel equation with a quadratic logistic damping term $-\mu \rho^2$ (modeling…
For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…