Related papers: Quantum reflection and Liouville transformations f…
Liouville transformations of Schr\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows…
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…
We describe an experimentally realistic situation of the quantum reflection of helium atoms from an oscillating surface. The temporal modulation of the potential induces clear sidebands in the reflection probability as a function of…
A theory of light transmission through a quantum well (QW) in a magnetic field perpendicular to the QW plane is developed. The light wave length is supposed comparable with the QW width. The formulas for reflection, absorption and…
Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed…
We use time-independent canonical transformation methods to discuss the energy eigenfunctions for the simple linear potential, pedagogically setting the stage for some field theory calculations to follow. We then discuss the Schr\"odinger…
In low energy atom-surface scattering, it is possible for the atom to be reflected in a region of attractive potential with no classical turning point. This phenomenon has come to be known as quantum reflection and it can reduce the…
We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection…
A propagation method for the scattering of a quantum wave packet from a potential surface is presented. It is used to model the quantum reflection of single atoms from a corrugated (metallic) surface. Our numerical procedure works well in…
We explore the analogy between following the motion of a reflected wave packet, and a quantum measurement of the spatial delay imposed on the particle by the scattering potential. It is shown that converting such delays into temporal…
We show that the quantum reflection coefficient of ultracold heavy atoms scattering off a dielectric surface can be tuned in a wide range by suitable choice of surface and environment temperatures. This effect results from a temperature…
We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is…
Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schr\"odinger equation as multistep potentials allows us to determine the reflection coefficient…
Quantum reflection is a universal property of atoms and molecules when scattered from surfaces in ultracold collisions. Recent experimental work has documented the quantum reflection and diffraction of He atoms, dimers, trimers and Neon…
A general approach to the analysis of optical properties of photonic crystals based on multiple-quantum-well structures is developed. The effect of the polarization state and a non-perpendicular incidence of the electromagnetic wave is…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the B\"acklund transformations. Several new examples of such transformations are found. In particular we obtained the B\"acklund…
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…
Black holes are presumed to have an ideal ability to absorb and keep matter. Whatever comes close to the event horizon, a boundary separating the inside region of a black hole from the outside world, inevitably goes in and remains inside…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…