Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the two-dimensional quantum confined Stark effect in strong electric fields
174
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
rate research
Read More
In cite{Cipriani2016}, the authors proved that, with the appropriate rescaling, the odometer of the (nearest neighbours) divisible sandpile on the unit torus converges to a bi-Laplacian field. Here, we study $alpha$-long-range divisible sandpiles, similar to those introduced in cite{Frometa2018}. We show that, for $alpha in (0,2)$, the limiting field is a fractional Gaussian field on the torus with parameter $alpha/2$. However, for $alpha in [2,infty)$, we recover the bi-Laplacian field. This provides an alternative construction of fractional Gaussian fields such as the Gaussian Free Field or membrane model using a diffusion based on the generator of Levy walks. The central tool for obtaining our results is a careful study of the spectrum of the fractional Laplacian on the discrete torus. More specifically, we need the rate of divergence of the eigenvalues as we let the side length of the discrete torus go to infinity. As a side result, we obtain precise asymptotics for the eigenvalues of discrete fractional Laplacians. Furthermore, we determine the order of the expected maximum of the discrete fractional Gaussian field with parameter $gamma=min {alpha,2}$ and $alpha in mathbb{R}_+backslash{2}$ on a finite grid.
Electric field-controlled, two-dimensional (2D) exciton dynamics in transition metal dichalcogenide monolayers is a current research focus in condensed matter physics. We have experimentally investigated the spectral and temporal properties of the A-exciton in a molybdenum diselenide (MoSe2) monolayer under controlled variation of a vertical, electric dc field at room temperature. By using steady-state and time-resolved photoluminescence spectroscopies, we have observed dc field-induced spectral shifts and linewidth broadenings that are consistent with the shortening of the excitons non-radiative lifetime due to field-induced dissociation. We discuss the implications of the results for future developments in nanoscale metrology and exploratory, optoelectronics technologies based on layered, 2D semiconductors.
We investigate the effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic $^{87}$Rb$^{133}$Cs molecules, for light of wavelength $lambda = 1064~mathrm{nm}$. Near this wavelength we observe unexpected two-photon transitions that may cause trap loss. We measure the ac Stark effect in external magnetic and electric fields, using microwave spectroscopy of the first rotational transition. We quantify the isotropic and anisotropic parts of the molecular polarizability at this wavelength. We demonstrate that a modest electric field can decouple the nuclear spins from the rotational angular momentum, greatly simplifying the ac Stark effect. We use this simplification to control the ac Stark shift using the polarization angle of the trapping laser.
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or gener
We classify zeroth-order conservation laws of systems from the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The classification is carried out up to equivalence generated by the equivalence group of this class. We find additional point equivalences between some of the listed cases of extensions of the space of zeroth-order conservation laws, which are inequivalent up to transformations from the equivalence group. Hamiltonian structures of systems of shallow water equations are used for relating the classification of zeroth-order conservation laws of these systems to the classification of their Lie symmetries. We also construct generating sets of such conservation laws under action of Lie symmetries.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
