Review of Classical Analytical Results for the Motion of a Rydberg Electron around a Polar Molecule under Magnetic or Electric Fields of Arbitrary Strengths in Axially Symmetric Configurations

We review classical studies of the oscillatory-precessional motion of an electron in the field of an electric dipole (the latter representing the polar molecule) with or without external magnetic or electric fields. The focus is on the most recent studies. In one study (at zero external field), it was shown that, generally, the oscillations being in the meridional direction and the precession being along parallels of latitude can take place on the same time scale—contrary to the statement from the previous literature. In another study, it was shown that a magnetic field enables new ranges of the bound oscillatory-precessional motion of the Rydberg electron and that in one of the new ranges, the period of the θ-oscillations has the non-monotonic dependence on primary parameter of the system. This is a counterintuitive result. In yet another study, it was shown that under the electric field there are two equilibrium circular states of a positive energy and one equilibrium state of a negative energy. The existence of the equilibrium state of the negative energy is a counterintuitive result since at the absence of the field, the bound state was possible only for the zero energy. Thus, it is a counterintuitive result that in this case the electric field can play the role of a stabilizing factor.

Thermoelectric precession in turbulent magnetoconvection

We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large-scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics.

Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau--Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann--Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.

Effect of charge-transfer enhancement on the efficiency and rotary mechanism of an oxindole-based molecular motor

A novel oxindole-based light-driven molecular motor with pronounced push–pull character was investigated. The rotary mechanism stands in between the precessional motion of fluorene-based motors and the axial motion of biomimetic photoswitches.

Nutation of the non-rigid Earth: Effect of the mass redistribution

In this research, we computed the nutation of the figure axis for a non-rigid Earth model due to the mass redistribution resulting from the lunisolar attraction on the deformable Earth, thus extending our previous work on the precessional motion. The basic Earth model is a two-layer structure composed of a fluid core and an anelastic mantle. We used the Hamiltonian approach, leading to closed-form analytical formulae that describe the nutations in longitude and obliquity of the figure axis as a sum of Poisson and Oppolzer terms. Those formulae were evaluated assuming different Earth rheologies by means of the Love number formalism. In particular, we first computed the effect using the standard model of the International Earth Rotation and Reference Systems Service Conventions (2010) solid tides, and then the Love numbers computed by Williams and Boggs, accounting for the complete oceanic tide contribution, which should provide more consistent and updated values for the nutations. The main amplitudes correspond to the 18.6 yr nutation component and reach 201 μas and −96 μas in the in-phase components in longitude and obliquity, respectively. The obtained values differ greatly from those considered in the current nutation model, IAU2000, of the International Astronomical Union (IAU) – and later similar studies – which includes this effect under the denomination of non-linear terms and derives its numerical contribution on the basis of the Sasao, Okubo, and Saito framework. The differences are significant and reach more than 30 μas for some nutation amplitudes. They can be likely attributed to several factors: an incomplete modelling of the redistribution potential; a different treatment of the permanent tide; and the use of different oceanic tide models.

Oscillatory-Precessional Motion of a Rydberg Electron Around a Polar Molecule

We provide a detailed classical description of the oscillatory-precessional motion of an electron in the field of an electric dipole. Specifically, we demonstrate that in the general case of the oscillatory-precessional motion of the electron (the oscillations being in the meridional direction (θ-direction) and the precession being along parallels of latitude (φ-direction)), both the θ-oscillations and the φ-precessions can actually occur on the same time scale—contrary to the statement from the work by another author. We obtain the dependence of φ on θ, the time evolution of the dynamical variable θ, the period Tθ of the θ-oscillations, and the change of the angular variable φ during one half-period of the θ-motion—all in the forms of one-fold integrals in the general case and illustrated it pictorially. We also produce the corresponding explicit analytical expressions for relatively small values of the projection pφ of the angular momentum on the axis of the electric dipole. We also derive a general condition for this conditionally-periodic motion to become periodic (the trajectory of the electron would become a closed curve) and then provide examples of the values of pφ for this to happen. Besides, for the particular case of pφ = 0 we produce an explicit analytical result for the dependence of the time t on θ. For the opposite particular case, where pφ is equal to its maximum possible value (consistent with the bound motion), we derive an explicit analytical result for the period of the revolution of the electron along the parallel of latitude.