Engineering adiabaticity at an avoided crossing with optimal control

We investigate ways to optimize adiabaticity and diabaticity in the Landau-Zener model with non-uniform sweeps. We show how diabaticity can be engineered with a pulse consisting of a linear sweep augmented by an oscillating term. We show that the oscillation leads to jumps in populations whose value can be accurately modeled using a model of multiple, photon-assisted Landau-Zener transitions, which generalizes work by Wubs et al. [New J. Phys. 7, 218 (2005)]. We extend the study on diabaticity using methods derived from optimal control. We also show how to preserve adiabaticity with optimal pulses at limited time, finding a non-uniform quantum speed limit

Molecular mode-coupling theory for supercooled liquids: Application to water

We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with ``exact'' results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones.Comment: 22 pages 4 figures Late

Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems

A general electrodynamic theory of a grating coupled two dimensional electron system (2DES) is developed. The 2DES is treated quantum mechanically, the grating is considered as a periodic system of thin metal strips or as an array of quantum wires, and the interaction of collective (plasma) excitations in the system with electromagnetic field is treated within the classical electrodynamics. It is assumed that a dc current flows in the 2DES. We consider a propagation of an electromagnetic wave through the structure, and obtain analytic dependencies of the transmission, reflection, absorption and emission coefficients on the frequency of light, drift velocity of 2D electrons, and other physical and geometrical parameters of the system. If the drift velocity of 2D electrons exceeds a threshold value, a current-driven plasma instability is developed in the system, and an incident far infrared radiation is amplified. We show that in the structure with a quantum wire grating the threshold velocity of the amplification can be essentially reduced, as compared to the commonly employed metal grating, down to experimentally achievable values. Physically this is due to a considerable enhancement of the grating coupler efficiency because of the resonant interaction of plasma modes in the 2DES and in the grating. We show that tunable far infrared emitters, amplifiers and generators can thus be created at realistic parameters of modern semiconductor heterostructures.Comment: 28 pages, 15 figures, submitted to Phys. Rev.

A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index $\ell = 1$ and $\ell = 2$ near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the $\alpha$-process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin

The Debye-Waller factor of liquid silica: Theory and simulation

We show that the prediction of mode-coupling theory for a model of a network-forming strong glass-former correctly describes the wave-vector dependence of the Debye-Waller factor. To obtain a good description it is important to take into account the triplet correlation function c_3, which we evaluate from a computer simulation. Our results support the possibility that this theory is able to accurately describe the non-ergodicity parameters of simple as well as of network-forming liquids.Comment: 5 pages of Latex, 3 figure

Magnetohydrodynamics of Cloud Collisions in a Multi-phase Interstellar Medium

We extend previous studies of the physics of interstellar cloud collisions by beginning investigation of the role of magnetic fields through 2D magnetohydrodynamic (MHD) numerical simulations. We study head-on collisions between equal mass, mildly supersonic diffuse clouds. We include a moderate magnetic field and two limiting field geometries, with the field lines parallel (aligned) and perpendicular (transverse) to the colliding cloud motion. We explore both adiabatic and radiative cases, as well as symmetric and asymmetric ones. We also compute collisions between clouds evolved through prior motion in the intercloud medium and compare with unevolved cases. We find that: In the (i) aligned case, adiabatic collisions, like their HD counterparts, are very disruptive, independent of the cloud symmetry. However, when radiative processes are taken into account, partial coalescence takes place even in the asymmetric case, unlike the HD calculations. In the (ii) transverse case, collisions between initially adjacent unevolved clouds are almost unaffected by magnetic fields. However, the interaction with the magnetized intercloud gas during the pre-collision evolution produces a region of very high magnetic energy in front of the cloud. In collisions between evolved clouds with transverse field geometry, this region acts like a ``bumper'', preventing direct contact between the clouds, and eventually reverses their motion. The ``elasticity'', defined as the ratio of the final to the initial kinetic energy of each cloud, is about 0.5-0.6 in the cases we considered. This behavior is found both in adiabatic and radiative cases.Comment: 40 pages in AAS LaTeX v4.0, 13 figures (in degraded jpeg format). Full resolution images as well as mpeg animations are available at http://www.msi.umn.edu:80/Projects/twj/mhd-cc/ . Accepted for publication in The Astrophysical Journa

Test of the semischematic model for a liquid of linear molecules

We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].Comment: Revtex, 10 pages, 4 figure

Influence of retardation effects on 2D magnetoplasmon spectrum

Within dissipationless limit the magnetic field dependence of magnetoplasmon spectrum for unbounded 2DEG system found to intersect the cyclotron resonance line, and, then approaches the frequency given by light dispersion relation. Recent experiments done for macroscopic disc-shape 2DEG systems confirm theory expectations.Comment: 2 pages,2 figure

Radial orbit instability: review and perspectives

This paper presents elements about the radial orbit instability, which occurs in spherical self-gravitating systems with a strong anisotropy in the radial velocity direction. It contains an overview on the history of radial orbit instability. We also present the symplectic method we use to explore stability of equilibrium states, directly related to the dissipation induced instability mechanism well known in theoretical mechanics and plasma physics.Comment: 10 pages, submitted to Transport Theory and Statistical Physics, proceedings of Vlasovia 2009 International Conference. Corrected for typos, redaction, and references adde