Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flowComment: 13 pages, 3 figure

Coulombic effects on magnetoconductivity oscillations induced by microwave excitation in multisubband two-dimensional electron systems

We develop a theory of magneto-oscillations in photoconductivity of multisubband two-dimensional electron systems which takes into account strong Coulomb interaction between electrons. In the presence of a magnetic field oriented perpendicular, internal electric fields of fluctuational origin cause fast drift velocities of electron orbit centers which affect probabilities of inter-subband scattering and the photoconductivity. For the electron system formed on the liquid helium surface, internal forces are shown to suppress the amplitude of magneto-oscillations, and change positions of magnetoconductivity minima which evolve in zero-resistance states for high radiation power.Comment: 9 pages, 6 figure

Impurity in the Tomonaga-Luttinger model: a Functional Integral Approach

In this tutorial notes we review a functional bosonization approach in the Keldysh technique to one-dimensional Luttinger liquid in the presence of an impurity.Comment: 15 pages, 1 figure, Proceedings of LXXXI Les Houches School on "Nanoscopic quantum transport", Les Houches, France, June 28-July 30, 200

Probability Distributions and Hilbert Spaces: Quantum and Classical Systems

We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular class of linear Hamiltonian systems.Comment: LATEX,13pages,accepted by Physica Scripta (1999

Light absorption coefficient of an ordered array of spherical quantum dot chains

We considered intersubband electron transitions in an array of one-dimensional chains of spherical quantum dots in the GaAs/Al$_{x}$Ga$_{1-x}$As semiconductor system. The absorption coefficient caused by these transitions was calculated depending on frequency and polarization of incident light and on Fermi level position, and temperature. We established the existence of two maxima of the absorption coefficient at the edges of the absorption band. It is shown that the absorption coefficient reaches its maximal value at the center of the region between the $s$-, $p$-like subbands and slightly varies with temperature. The change of the direction of the linearly polarized light wave incident on the chains from perpendicular to parallel leads to a sharp narrowing of the absorption band. It is obtained that the absorption bandwidth increases with the reduction of the quantum dot radius. We also analyzed the dependence of the absorption coefficient of GaAs/Al$_{x}$Ga$_{1-x}$As superlattice on concentration of aluminium in the matrix.Comment: 9 pages, 7 figure

Fast magnetization reversal of nanoclusters in resonator

An effective method for ultrafast magnetization reversal of nanoclusters is suggested. The method is based on coupling a nanocluster to a resonant electric circuit. This coupling causes the appearance of a magnetic feedback field acting on the cluster, which drastically shortens the magnetization reversal time. The influence of the resonator properties, nanocluster parameters, and external fields on the magnetization dynamics and reversal time is analyzed. The magnetization reversal time can be made many orders shorter than the natural relaxation time. The reversal is studied for both the cases of a single nanocluster as well as for the system of many nanoclusters interacting through dipole forces.Comment: latex file, 21 pages, 7 figure