1,095 research outputs found
Yang-Mills, Complex Structures and Chern's Last Theorem
Recently Shiing-Shen Chern suggested that the six dimensional sphere
has no complex structure. Here we explore the relations between
his arguments and Yang-Mills theories. In particular, we propose that Chern's
approach is widely applicable to investigate connections between the geometry
of manifolds and the structure of gauge theories. We also discuss several
examples of manifolds, both with and without a complex structure.Comment: Chern's proof remains incomplete, and we have edited some statements
in our article accordingl
The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins
We develop a transfer matrix formalism to visualize the framing of discrete
piecewise linear curves in three dimensional space. Our approach is based on
the concept of an intrinsically discrete curve, which enables us to more
effectively describe curves that in the limit where the length of line segments
vanishes approach fractal structures in lieu of continuous curves. We verify
that in the case of differentiable curves the continuum limit of our discrete
equation does reproduce the generalized Frenet equation. As an application we
consider folded proteins, their Hausdorff dimension is known to be fractal. We
explain how to employ the orientation of carbons of amino acids along
a protein backbone to introduce a preferred framing along the backbone. By
analyzing the experimentally resolved fold geometries in the Protein Data Bank
we observe that this framing relates intimately to the discrete
Frenet framing. We also explain how inflection points can be located in the
loops, and clarify their distinctive r\^ole in determining the loop structure
of foldel proteins.Comment: 14 pages 12 figure
Intershell resistance in multiwall carbon nanotubes: A Coulomb drag study
We calculate the intershell resistance R_{21} in a multiwall carbon nanotube
as a function of temperature T and Fermi level (e.g. a gate voltage), varying
the chirality of the inner and outer tubes. This is done in a so-called Coulomb
drag setup, where a current I_1 in one shell induces a voltage drop V_2 in
another shell by the screened Coulomb interaction between the shells neglecting
the intershell tunnelling. We provide benchmark results for R_{21}=V_2/I_1
within the Fermi liquid theory using Boltzmann equations. The band structure
gives rise to strongly chirality dependent suppression effects for the Coulomb
drag between different tubes due to selection rules combined with mismatching
of wave vector and crystal angular momentum conservation near the Fermi level.
This gives rise to orders of magnitude changes in R_{21} and even the sign of
R_{21} can change depending on the chirality of the inner and outer tube and
misalignment of inner and outer tube Fermi levels. However for any tube
combination, we predict a dip (or peak) in R_{21} as a function of gate
voltage, since R_{21} vanishes at the electron-hole symmetry point. As a
byproduct, we classified all metallic tubes into either zigzag-like or
armchair-like, which have two different non-zero crystal angular momenta m_a,
m_b and only zero angular momentum, respectively.Comment: 17 pages, 10 figure
Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships
Network structure strongly constrains the range of dynamic behaviors
available to a complex system. These system dynamics can be classified based on
their response to perturbations over time into two distinct regimes, ordered or
chaotic, separated by a critical phase transition. Numerous studies have shown
that the most complex dynamics arise near the critical regime. Here we use an
information theoretic approach to study structure-dynamics relationships within
a unified framework and how that these relationships are most diverse in the
critical regime
Weisskopf-Wigner model for wave packet excitation
We consider a laser induced molecular excitation process as a decay of a
single energy state into a continuum. The analytic results based on
Weisskopf-Wigner approach and perturbation calculations are compared with
numerical wave packet results. We find that the decay model describes the
excitation process well within the expected parameter region.Comment: 14 pages, Latex2.09, 9 Postscript figures embedded using psfig, see
also http://www.physics.helsinki.fi/~kasuomin
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
In the mean-field limit the dynamics of a quantum Bose gas is described by a
Hartree equation. We present a simple method for proving the convergence of the
microscopic quantum dynamics to the Hartree dynamics when the number of
particles becomes large and the strength of the two-body potential tends to 0
like the inverse of the particle number. Our method is applicable for a class
of singular interaction potentials including the Coulomb potential. We prove
and state our main result for the Heisenberg-picture dynamics of "observables",
thus avoiding the use of coherent states. Our formulation shows that the
mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato
smoothing estimate (Lemma 6.1
Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices
We present an analytical study of one-dimensional semiconductor superlattices
in external electric fields, which may be time-dependent. A number of general
results for the (quasi)energies and eigenstates are derived. An equation of
motion for the density matrix is obtained for a two-band model, and the
properties of the solutions are analyzed. An expression for the current is
obtained. Finally, Zener-tunneling in a two-band tight-binding model is
considered. The present work gives the background and an extension of the
theoretical framework underlying our recent Letter [J. Rotvig {\it et al.},
Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations
were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache
Vortex nucleation in Bose-Einstein condensates in time-dependent traps
Vortex nucleation in a Bose-Einstein condensate subject to a stirring
potential is studied numerically using the zero-temperature, two-dimensional
Gross-Pitaevskii equation. It is found that this theory is able to describe the
creation of vortices, but not the crystallization of a vortex lattice. In the
case of a rotating, slightly anisotropic harmonic potential, the numerical
results reproduce experimental findings, thereby showing that finite
temperatures are not necessary for vortex excitation below the quadrupole
frequency. In the case of a condensate subject to stirring by a narrow rotating
potential, the process of vortex excitation is described by a classical model
that treats the multitude of vortices created by the stirrer as a continuously
distributed vorticity at the center of the cloud, but retains a potential flow
pattern at large distances from the center.Comment: 22 pages, 7 figures. Changes after referee report: one new figure,
new refs. No conclusions altere
Bloch oscillations, Zener tunneling and Wannier-Stark ladders in the time-domain
We present a time-domain analysis of carrier dynamics in a semiconductor
superlattice with two minibands. Integration of the density-matrix equations of
motion reveals a number of new features: (i) for certain values of the applied
static electric field strong interband transitions occur; (ii) in static fields
the complex time-dependence of the density-matrix displays a sequence of stable
plateaus in the low field regime, and (iii) for applied fields with a periodic
time-dependence the dynamic response can be understood in terms of the
quasienergy spectra.Comment: 4 pages, 6 PostScript figures available from [email protected], REVTEX
3.
Atom optical elements for Bose condensates
A simple model for atom optical elements for Bose condensate of trapped,
dilute alkali atomns is proposed and numerical simulations are presented to
illustrate its characteristics. We demonstrate ways of focusing and splitting
the condensate by modifying experimentally adjustable parameters. We show that
there are at least two ways of implementing atom optical elements: one may
modulate the interatomic scattering length in space, or alternatively, use a
sinusoidal, externally applied potential.Comment: 7 pages, 10 figure
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