Electron mobility on a surface of dielectric media: influence of surface level atoms

We calculate the contribution to the electron scattering rate from the surface level atoms (SLA), proposed in [A.M. Dyugaev, P.D. Grigoriev, JETP Lett. 78, 466 (2003)]. The inclusion of these states into account was sufficient to explain the long-standing puzzles in the temperature dependence of the surface tension of both He isotopes and to reach a very good agreement between theory and experiment. We calculate the contribution from these SLA to the surface electron scattering rate and explain some features in the temperature dependence of the surface electron mobility. This contribution is essential at low temperature $T<0.5$ when the He vapor concentration is exponentially small. For an accurate calculation of the electron mobility one also needs to consider the influence of the clamping electric field on the surface electron wave function and the temperature dependence of the He3 chemical potential.Comment: 6 pages, 1 figur

Hierarchy of general invariants for bivariate LPDOs

We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of general invariants are studied and some examples are presented. We also show that classical Laplace invariants correspond to some particular cases of general invariants.Comment: to appear in J. "Theor.Math.Phys." in May 200

Hidden quantum phase transition in Mn1−x_{1-x}Fex_{x}Ge: evidence brought by small-angle neutron scattering

The magnetic system of the Mn$_{1-x}$Fe$_{x}$Ge solid solution is ordered in a spiral spin structure in the whole concentration range of $x \in [0 \div 1]$. The close inspection of the small-angle neutron scattering data reveals the quantum phase transition from the long-range ordered (LRO) to short range ordered (SRO) helical structure upon increase of Fe-concentration at $x \in [0.25 \div 0.4]$. The SRO of the helical structure is identified as a Lorentzian contribution, while LRO is associated with the Gaussian contribution into the scattering profile function. The scenario of the quantum phase transition with $x$ as a driving parameter is similar to the thermal phase transition in pure MnGe. The quantum nature of the SRO is proved by the temperature independent correlation length of the helical structure at low and intermediate temperature ranges with remarkable decrease above certain temperature $T_Q$. We suggest the $x$-dependent modification of the effective Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism to explain the quantum critical regime in Mn$_{1-x}$Fe$_{x}$Ge.Comment: 6 pages, 4 figure

Constructive factorization of LPDO in two variables

We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process consists of solving, recursively, systems of linear equations, subject to certain differential compatibility conditions. In the generic case of partial differential operators one does not have to solve a differential equation. In special degenerate cases, such as ordinary differential, the problem is finally reduced to the solution of some Riccati equation(s). The conditions of factorization are given explicitly for second- and, and an outline is given for the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005

Dirac and Majorana neutrinos in matter

We consider the matter effects on neutrinos moving in background on the basis of the corresponding quantum wave equations. Both Dirac and Majorana neutrino cases are discussed. The effects for Dirac neutrino reflection and trapping as well as neutrino-antineutrino annihilation and $\nu\overline{\nu}$ pair creation in matter at the interface between two media with different densities are considered. The spin light of neutrino in matter is also discussed.Comment: 11 pages, 2 figures, in: Proceedings of the 5th International Conference on Non-Accelerator New Physics (Dubna, Russia, June 20-25, 2005). V2: typos correcte