378 research outputs found
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Effect of a Magnetic Field on the Dipole Echo in Glasses with Nuclear Quadrupole Moments
The effect of a magnetic field on the dipole echo amplitude in glasses at
temperatures of about 10 mK caused by nonspherical nuclei with electric
quadrupole moments has been studied theoretically. It has been shown that in
this case, the two-level systems (TLS's) that determine the glass properties at
low temperatures are transformed into more complicated multilevel systems.
These systems have new properties as compared to usual TLS's and, in
particular, exhibit oscillations of electric dipole echo amplitude in magnetic
field. A general formula that describes the echo amplitude in an arbitrary
split TLS has been derived with perturbation theory. Detailed analytic and
numerical analysis of the formula has been performed. The theory agrees
qualitatively and quantitatively well with experimental data.Comment: 5 pages, 3 figure
The Boson Peak and its Relation with Acoustic Attenuation in Glasses
Experimental results on the density of states and on the acoustic modes of
glasses in the THz region are compared to the predictions of two categories of
models. A recent one, solely based on an elastic instability, does not account
for most observations. Good agreement without adjustable parameters is obtained
with models including the existence of non-acoustic vibrational modes at THz
frequency, providing in many cases a comprehensive picture for a range of glass
anomalies.Comment: 4 pages, 3 figures, Physical Review Letters in pres
Maximum propagation speed and Cherenkov effect in optical phonon transport through periodic molecular chains
Optical phonons serve as the fast and efficient carriers of energy across
periodic polymers due to their delocalization, large group velocity because of
covalent bonding and large energy quantum compared to that for acoustic
phonons, as it was observed in a number of recent measurements in different
oligomers. However, this transport is dramatically sensitive to anharmonic
interactions, including the unavoidable interaction with acoustic phonons
responsible for the transport decoherence, suppressing ballistic transport at
long distances. Here we show that this decoherence is substantially suppressed
if the group velocity of optical phonons is less than the sound velocity of
acoustic phonons; otherwise ballistic transport is substantially suppressed by
a Cherenkov's like emission of acoustic phonons. This conclusion is justified
considering energy and momentum conservation during phonon absorption or
emission and supported by the numerical evaluation of lifetimes of the optical
phonons. It is also consistent with the recent experimental investigations of
ballistic optical phonon transport in oligomers with minor exception of
relatively short oligophenylenes.Comment: 35 pages, 16 figures, to appear in Journal of Chemical Physic
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