462 research outputs found
On a Ring of Formal Pseudo-differential Operators
We study the notion of non-commumative higher dimensional local fields. A
simplest example is the ring P of formal pseudo- differential operators. As an
application we extend the KP hierarchy to the space .Comment: LaTe
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
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
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