8,878 research outputs found
Integrable Systems and Factorization Problems
The present lectures were prepared for the Faro International Summer School
on Factorization and Integrable Systems in September 2000. They were intended
for participants with the background in Analysis and Operator Theory but
without special knowledge of Geometry and Lie Groups. In order to make the main
ideas reasonably clear, I tried to use only matrix algebras such as
and its natural subalgebras; Lie groups used are either GL(n)
and its subgroups, or loop groups consisting of matrix-valued functions on the
circle (possibly admitting an extension to parts of the Riemann sphere). I hope
this makes the environment sufficiently easy to live in for an analyst. The
main goal is to explain how the factorization problems (typically, the matrix
Riemann problem) generate the entire small world of Integrable Systems along
with the geometry of the phase space, Hamiltonian structure, Lax
representations, integrals of motion and explicit solutions. The key tool will
be the \emph{% classical r-matrix} (an object whose other guise is the
well-known Hilbert transform). I do not give technical details, unless they may
be exposed in a few lines; on the other hand, all motivations are given in full
scale whenever possible.Comment: LaTeX 2.09, 69 pages. Introductory lectures on Integrable systems,
Classical r-matrices and Factorization problem
Triple and quartic interactions of Higgs bosons in the two-Higgs-doublet model with CP violation
We consider the two-Higgs-doublet model with explicit CP-violation, where the
effective Higgs potential is not CP-invariant at the tree-level. Three neutral
Higgs bosons of the model are the mixtures of CP-even and CP-odd bosons which
exist in the CP-conserving limit of the theory. The mass spectrum and
tree-level couplings of the neutral Higgs bosons to gauge bosons and fermions
are significantly dependent on the parameters of the Higgs boson mixing matrix.
We calculate the Higgs-gauge boson, Higgs-fermion, triple and quartic Higgs
self-interactions in the MSSM with explicit CP-violation in the Higgs sector
and CP-violating Yukawa interactions of the third generation scalar quarks. In
some regions of the MSSM parameter space substantial changes of the
self-interaction vertices take place, leading to significant suppression or
enhancement of the multiple Higgs boson production cross sections.Comment: 29 pages, 4 figures. Minor changes in section 3, misprints in (47)
corrected. Version accepted by EPJ
Engineering physics of superconducting hot-electron bolometer mixers
Superconducting hot-electron bolometers are presently the best performing
mixing devices for the frequency range beyond 1.2 THz, where good quality
superconductor-insulator-superconductor (SIS) devices do not exist. Their
physical appearance is very simple: an antenna consisting of a normal metal,
sometimes a normal metal-superconductor bilayer, connected to a thin film of a
narrow, short superconductor with a high resistivity in the normal state. The
device is brought into an optimal operating regime by applying a dc current and
a certain amount of local- oscillator power. Despite this technological
simplicity its operation has been found to be controlled by many different
aspects of superconductivity, all occurring simultaneously. A core ingredient
is the understanding that there are two sources of resistance in a
superconductor: a charge conversion resistance occurring at an
normal-metal-superconductor interface and a resistance due to time- dependent
changes of the superconducting phase. The latter is responsible for the actual
mixing process in a non-uniform superconducting environment set up by the
bias-conditions and the geometry. The present understanding indicates that
further improvement needs to be found in the use of other materials with a
faster energy-relaxation rate. Meanwhile several empirical parameters have
become physically meaningful indicators of the devices, which will facilitate
the technological developments.Comment: This is an author-processed copy of an Invited contribution to the
Special Issue of the IEEE Transactions on Terahertz Science and Technology
dedicated to the 28th IEEE International Symposium on Space Terahertz
Technology (ISSTT2017
Mixed Quantum/Classical Approach for Description of Molecular Collisions in Astrophysical Environments
An efficient and accurate mixed quantum/classical theory approach for computational treatment of inelastic scattering is extended to describe collision of an atom with a general asymmetric-top rotor polyatomic molecule. Quantum mechanics, employed to describe transitions between the internal states of the molecule, and classical mechanics, employed for description of scattering of the atom, are used in a self-consistent manner. Such calculations for rotational excitation of HCOOCH3 in collisions with He produce accurate results at scattering energies above 15 cm–1, although resonances near threshold, below 5 cm–1, cannot be reproduced. Importantly, the method remains computationally affordable at high scattering energies (here up to 1000 cm–1), which enables calculations for larger molecules and at higher collision energies than was possible previously with the standard full-quantum approach. Theoretical prediction of inelastic cross sections for a number of complex organic molecules observed in space becomes feasible using this new computational tool
Conductivity and permittivity of dispersed systems with penetrable particle-host interphase
A model for the study of the effective quasistatic conductivity and
permittivity of dispersed systems with particle-host interphase, within which
many-particle polarization and correlation contributions are effectively
incorporated, is presented. The structure of the system's components, including
the interphase, is taken into account through modelling their low-frequency
complex permittivity profiles. The model describes, among other things, a
percolation-type behavior of the effective conductivity, accompanied by a
considerable increase in the real part of the effective complex permittivity.
The percolation threshold location is determined mainly by the thickness of the
interphase. The "double" percolation effect is predicted. The results are
contrasted with experiment.Comment: 10 pages, 10 figure
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