1,707 research outputs found
Spectral properties of fractional differentiation operators
We consider fractional differentiation operators in various senses and show
that the strictly accretive property is the common property of fractional
differentiation operators. Also we prove that the sectorial property holds for
differential operators second order with a fractional derivative in the final
term, we explore a location of the spectrum and resolvent sets and show that
the spectrum is discrete. We prove that there exists a two-sided estimate for
eigenvalues of the real component of operators second order with the fractional
derivative in the final term.Comment: The research results were discussed and presented at the 8th
International Conference on Differential and Functional Differential
Equations. Moscow, Russia, August 13-20, 201
Magneto-optical evidence of the percolation nature of the metal-insulator transition in the 2D electron system
We compare the results of the transport and time-resolved
magneto-luminescence measurements in disordered 2D electron systems in
GaAs-AlGaAs heterostructures in the extreme quantum limit, in particular, in
the vicinity of the metal-insulator transition (MIT). At filling factors , the optical signal has two components: the single-rate exponentially
decaying part attributed to a uniform liquid and a power-law long-living tail
specific to a microscopically inhomogeneous state of electrons. We interprete
this result as a separation of the 2D electron system into a liquid and
localized phases, especially because the MIT occurs strikingly close to those
filling factors where the liquid occupies of the sample area (the
percollation threshold condition in two-component media).Comment: 5 pages RevTex + 4 fig., to appear in PRB, Rapid Com
- …