On the preservation of coherence in the electronic wavepacket of a neutral and rigid polyatomic molecule

We present various types of reduced models including five vibrational modes and three electronic states for the pyrazine molecule in order to investigate the lifetime of electronic coherence in a rigid and neutral system. Using an ultrafast optical pumping in the ground state (1 1 A g ), we prepare a coherent superposition of two bright excited states, 1 1 B 2u and 1 1 B 1u , and reveal the effect of the nuclear motion on the preservation of the electronic coherence induced by the laser pulse. More specifically, two aspects are considered: the anharmonicity of the potential energy surfaces and the dependence of the transition dipole moments (TDMs) with respect to the nuclear coordinates. To this end, we define an ideal model by making three approximations: (i) only the five totally symmetric modes move, (ii) which correspond to uncoupled harmonic oscillators, and (iii) the TDMs from the ground electronic state to the two bright states are constant (Franck-Condon approximation). We then lift the second and third approximations by considering, first, the effect of anharmonicity, second, the effect of coordinate-dependence of the TDMs (first-order Herzberg- Teller contribution), third, both. Our detailed numerical study with quantum dynamics confirms long-term revivals of the electronic coherence even for the most realistic model

Critical current of a Josephson junction containing a conical magnet

We calculate the critical current of a superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in which the FM layer has a conical magnetic structure composed of an in-plane rotating antiferromagnetic phase and an out-of-plane ferromagnetic component. In view of the realistic electronic properties and magnetic structures that can be formed when conical magnets such as Ho are grown with a polycrystalline structure in thin-film form by methods such as direct current sputtering and evaporation, we have modeled this situation in the dirty limit with a large magnetic coherence length ($\xi_f$). This means that the electron mean free path is much smaller than the normalized spiral length $\lambda/2\pi$ which in turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete spiral makes along the growth direction of the FM). In this physically reasonable limit we have employed the linearized Usadel equations: we find that the triplet correlations are short ranged and manifested in the critical current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid oscillations in the critical current are superimposed on a slower oscillation which is related to the singlet correlations. Both oscillations decay on the scale of $\xi_f$. We derive an analytical solution and also describe a computational method for obtaining the critical current as a function of the conical magnetic layer thickness.Comment: Extended version of the published paper. Additional information about the computational method is included in the appendi

Attosecond electronic and nuclear quantum photodynamics of ozone: time-dependent Dyson orbitals and dipole

A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently. An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited Hartley band. In this situation neither the electrons nor the nuclei are in a stationary state. The multiconfiguration time dependent Hartree method was used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schr\"odinger equation. The resulting wave packet shows an oscillation of the electron density between the two chemical bonds. As a first step for probing the electronic motion we computed the time-dependent molecular dipole and the Dyson orbitals. The latter play an important role in the explanation of the photoelectron angular distribution. Calculations of the Dyson orbitals are presented both for the time-independent as well as the time-dependent situations. We limited our description of the electronic motion to the Franck-Condon region only due to the localization of the nuclear wave packets around this point during the first 5-6 fs

Probing topological order with R\'enyi entropy

We present an analytical study of the quantum phase transition between the topologically ordered toric-code-model ground state and the disordered spin-polarized state. The phase transition is induced by applying an external magnetic field, and the variation in topological order is detected via two non-local quantities: the Wilson loop and the topological Renyi entropy of order 2. By exploiting an equivalence with the transverse-field Ising model and considering two different variants of the problem, we investigate the field dependence of these quantities by means of an exact treatment in the exactly solvable variant and complementary perturbation theories around the limits of zero and infinite fields in both variants. We find strong evidence that the phase transition point between topological order and disorder is marked by a discontinuity in the topological Renyi entropy and that the two phases around the phase transition point are characterized by its different constant values. Our results therefore indicate that the topological Renyi entropy is a proper topological invariant: its allowed values are discrete and can be used to distinguish between different phases of matter.Comment: 13 pages, 8 figures, published version with structural changes onl

Supra-oscillatory critical temperature dependence of Nb-Ho bilayers

We investigate the critical temperature Tc of a thin s-wave superconductor (Nb) proximity coupled to a helical rare earth ferromagnet (Ho). As a function of the Ho layer thickness, we observe multiple oscillations of Tc superimposed on a slow decay, that we attribute to the influence of the Ho on the Nb proximity effect. Because of Ho inhomogeneous magnetization, singlet and triplet pair correlations are present in the bilayers. We take both into consideration when solving the self consistent Bogoliubov-de Gennes equations, and we observe a reasonable agreement. We also observe non-trivial transitions into the superconducting state, the zero resistance state being attained after two successive transitions which appear to be associated with the magnetic structure of Ho.Comment: Main article: 5 pages, 4 figures; Supplementary materials: 4 pages, 5 figure

The Littlewood-Gowers problem

We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 - \epsilon} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.Comment: 31 pp. Corrected typos. Updated references

Higher order corrections for shallow-water solitary waves: elementary derivation and experiments

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation, while the second-order equation is solved numerically. The propagation velocity found for the solitary waves of the second-order equation coincides with a known expression, but it is obtained in a simpler way. By measuring the propagation velocity of solitary waves in the laboratory, we demonstrate that the second-order theory gives a considerably improved fit to experimental results.Comment: 15 pages, 8 EPS figures, uses IOP class file for LaTeX2e, slightly revised versio

Two Skyrmion Dynamics with Omega Mesons

We present our first results of numerical simulations of two skyrmion dynamics using an $\omega$-meson stabilized effective Lagrangian. We consider skyrmion-skyrmion scattering with a fixed initial velocity of $\beta=0.5$, for various impact parameters and groomings. The physical picture that emerges is surprisingly rich, while consistent with previous results and general conservation laws. We find meson radiation, skyrmion scattering out of the scattering plane, orbiting and capture to bound states.Comment: 19 pages, 22 figure