Search results for "Formula"
showing 10 items of 755 documents
Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons
2018
We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to non-integrability of the system and hints on the possibility of quantum chaos emerging. Such a behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization…
Gradual freezing of orientational degrees of freedom in cubicAr1−x(N2)xmixtures
1995
The mixed crystal ${\mathrm{Ar}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ is studied by Monte Carlo (MC) methods for x=0.33, 0.67, and 1.0 over a wide range of temperatures. For x=1 we find first-order transition from ordered cubic to disordered cubic, while for x=0.33 and x=0.67 we find broad nonuniform distribution functions of the local quadrupole Edwards-Anderson order parameter at low temperature. The short-range order of the quadrupolar mass distribution of the ${\mathrm{N}}_{2}$ molecules in the mixed systems is different from that observed in the pure ${\mathrm{N}}_{2}$ crystal, although the fcc symmetry has been chosen for the translational degrees…
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Debye representation of dispersive focused waves
2006
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matri…
Solvation of triplet Rydberg states of molecular hydrogen in superfluid helium
2004
We report ab initio interaction potentials, transition dipole moments, and radiative lifetimes for the four lowest triplet states of ${\mathrm{H}}_{2}:$ $b$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ $c$ ${}^{3}{\ensuremath{\Pi}}_{u},$ $a$ ${}^{3}{\ensuremath{\Sigma}}_{g}^{+},$ and $e$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and their response to the perturbation due to approaching ground state He atom. Hybrid density functional\char21{}quantum Monte Carlo calculations employing the ab initio interaction potentials are then used for calculating the liquid structure around the molecular excimers in bulk superfluid ${}^{4}\mathrm{He}.$ Calculations demonstrate a wide variety of possible solvation …
Phototransition of Na(3p3/2) into high Rydberg states and the ionization continuum
2005
A model potential method is used to investigate photoabsorption from the Na(3p3/2) state. Absorption cross sections into higher Rydberg states and photoionization cross sections are presented as an analytical function of photo electron energy. Einstein coefficients for spontaneous emissions 3p3/2 ← ns1/2, nd5/2, nd3/2 are tabulated for n up to 50. The Einstein coefficients and low-energy ionization cross sections are believed to be accurate to better than 2–3%, above 1 eV the error may increase to 4–6%.
Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions
2006
We study the questions of existence and uniqueness of weak and entropy solutions for equations of type -div a(x, Du)+γ(u) ∋ φ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x, Du)·η+β(u) ∋ ψ. The nonlinear elliptic operator div a(x, Du) is modeled on the p-Laplacian operator Δp(u) = div (|Du|p−2Du), with p > 1, γ and β are maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) and 0 ∈ β(0), and the data φ ∈ L1 (Ω) and ψ ∈ L1 (∂Ω). We also study existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with c…
Probing Rydberg atoms through collisions with helium in the presence of static electric and magnetic fields
2005
We report on field induced inelasticity effects in state-to-state transitions caused by collisions of helium with Rydberg atoms in the presence of parallel static electric and magnetic fields. Due to the phases accumulated by the wavefunctions of the states involved into the collision events, the transition cross sections plotted as a function of the external fields exhibit modulations. When the relative velocity of the colliding atoms is high enough, these modulations are wiped out, while sizable modifications of the cross sections may take place due to the alteration of the wavefunctions' spatial localization. The possibility of using the field-assisted collisions as a probe giving inform…
Controlling the interactions of a few cold Rb Rydberg atoms by radiofrequency-assisted F\"orster resonances
2014
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using F\"orster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly-resolved radio-frequency-assisted F\"orster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced F\"orster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf-field. This method can be applied to enhance the interactions of a…