4,479 research outputs found
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
SDiff(2) and uniqueness of the Pleba\'{n}ski equation
The group of area preserving diffeomorphisms showed importance in the
problems of self-dual gravity and integrability theory. We discuss how
representations of this infinite-dimensional Lie group can arise in
mathematical physics from pure local considerations. Then using Lie algebra
extensions and cohomology we derive the second Pleba\'{n}ski equation and its
geometry. We do not use K\"ahler or other additional structures but obtain the
equation solely from the geometry of area preserving transformations group. We
conclude that the Pleba\'{n}ski equation is Lie remarkable
Anomalous Diffusion at Edge and Core of a Magnetized Cold Plasma
Progress in the theory of anomalous diffusion in weakly turbulent cold
magnetized plasmas is explained. Several proposed models advanced in the
literature are discussed. Emphasis is put on a new proposed mechanism for
anomalous diffusion transport mechanism based on the coupled action of
conductive walls (excluding electrodes) bounding the plasma drain current (edge
diffusion) together with the magnetic field flux "cutting" the area traced by
the charged particles in their orbital motion. The same reasoning is shown to
apply to the plasma core anomalous diffusion. The proposed mechanism is
expected to be valid in regimes when plasma diffusion scales as Bohm diffusion
and at high , when collisions are of secondary importance.Comment: 9 pages, 4 figure
Exact results for scattering on ultrashort plane wave backgrounds
We give exact results for the emission spectra of both nonlinear
Breit-Wheeler pair production and nonlinear Compton scattering in
ultra-intense, ultra-short duration plane wave backgrounds, modelled as
delta-function pulses. This includes closed form expressions for total
scattering probabilities. We show explicitly that these probabilities do not
exhibit the power-law scaling with intensity associated with the conjectured
breakdown of (Furry picture) perturbation theory, instead scaling
logarithmically in the high-intensity limit.Comment: 9 pages, 4 pdf figure
Dynamical lattice instability versus spin liquid state in a frustrated spin chain system
The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested
to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system
shows unbound spinon excitations and a resonating valence bond ground state due
spin frustration. Our Raman scattering study demonstrates phonon anomalies as
well as the suppression of a broad magnetic scattering continuum for
temperatures below a characteristic temperature, T<T*=100K. We interpret these
effects as evidence for a dynamical interplay of spin and lattice degrees of
freedom that might lead to a further transition into a dimerized or
structurally distorted phase at lower temperatures.Comment: 5 pages, 6 figure
Phase Diagram of Multilayer Magnetic Structures
Multilayer "ferromagnet-layered antiferromagnet" (Fe/Cr) structures
frustrated due to the roughness of layer interfaces are studied by numerical
modeling methods. The "thickness-roughness" phase diagrams for the case of thin
ferromagnetic film on the surface of bulk antiferromagnet and for two
ferromagnetic layers separated by an antiferromagnetic interlayer are obtained
and the order parameter distributions for all phases are found. The phase
transitions nature in such systems is considered. The range of applicability
for the "magnetic proximity model" proposed by Slonczewski is evaluated.Comment: 8 pages, 8 figure
Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer
We have studied temperature dependences of electron transport in graphene and
its bilayer and found extremely low electron-phonon scattering rates that set
the fundamental limit on possible charge carrier mobilities at room
temperature. Our measurements have shown that mobilities significantly higher
than 200,000 cm2/Vs are achievable, if extrinsic disorder is eliminated. A
sharp (threshold-like) increase in resistivity observed above approximately
200K is unexpected but can qualitatively be understood within a model of a
rippled graphene sheet in which scattering occurs on intra-ripple flexural
phonons
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