Related papers: Tunnelling of plane waves through a square barrier
We provide a full account of our recent report (EPL, 141 (2023) 10001}) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a…
Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each…
A non-stationary method for tunneling description of non-relativistic particles and photons through a barrier on the basis of consideration of the multiple internal reflections of vawe packets in relation of barrier boundaries is presented.…
We report on a multi-year, multi-institution study to investigate student reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews, and…
The recent theoretical discovery of families of travelling wave solutions in pipe flow at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series…
Diffraction in time of matter waves incident on a shutter which is removed at time $t=0$ is studied in the presence of a linear potential. The solution is also discussed in phase space in terms of the Wigner function. An alternative…
A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed.…
Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a…
The collision of a quantum Gaussian wave packet with a square barrier is solved explicitly in terms of known functions. The obtained formula is suitable for performing fast calculations or asymptotic analysis. It also provides physical…
The transmission of wave packets through tunneling barriers is studied in detail by the method of quantum molecular dynamics. The distribution function of the times describing the arrival of a tunneling packet in front of and behind a…
A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes…
We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula…
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared…
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…
In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths $\ell_\pm$ separated by a window of length 2a. It is known that if the barriers are semiinfinite,…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer…