Noncommutative Novikov algebras

The class of Novikov algebras is a popular object of study among classical nonassociative algebras. The generic example of a Novikov algebra may be obtained from a differential associative and commutative algebra. We consider a more general class of linear algebras which may be obtained in the same way from not necessarily commutative associative algebras with a derivation.Comment: 18 page

Short-time critical dynamics of the three-dimensional systems with long-range correlated disorder

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Comment: 24 RevTeX pages, 12 figure

Interface states in junctions of two semiconductors with intersecting dispersion curves

A novel type of shallow interface state in junctions of two semiconductors without band inversion is identified within the envelope function approximation, using the two-band model. It occurs in abrupt junctions when the interband velocity matrix elements of the two semiconductors differ and the bulk dispersion curves intersect. The in-plane dispersion of the interface state is found to be confined to a finite range of momenta centered around the point of intersection. These states turn out to exist also in graded junctions, with essentially the same properties as in the abrupt case.Comment: 1 figur

Planar Heterostructure Graphene -- Narrow-Gap Semiconductor -- Graphene

We investigate a planar heterostructure composed of two graphene films separated by a narrow-gap semiconductor ribbon. We show that there is no the Klein paradox when the Dirac points of the Brillouin zone of graphene are in a band gap of a narrow-gap semiconductor. There is the energy range depending on an angle of incidence, in which the above-barrier damped solution exists. Therefore, this heterostructure is a "filter" transmitting particles in a certain range of angles of incidence upon a potential barrier. We discuss the possibility of an application of this heterostructure as a "switch".Comment: 9 pages, 2 figure

Graded associative conformal algebras of finite type

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\Gamma$ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\simeq \Gamma$. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained

On pre-Novikov algebras and derived Zinbiel variety

For a non-associative algebra $A$ with a derivation $d$, its derived algebra $A^{(d)}$ is the same space equipped with new operations $a\succ b = d(a)b$, $a\prec b = ad(b)$, $a,b\in A$. Given a variety Var of algebras, its derived variety is generated by all derived algebras $A^{(d)}$ for all $A$ in Var and for all derivations $d$ of $A$. The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for the variety Zinb of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation.Comment: 14 pages, minor revisio

Singlet-Triplet Excitations in the Unconventional Spin-Peierls System TiOBr

We have performed time-of-flight neutron scattering measurements on powder samples of the unconventional spin-Peierls compound TiOBr using the fine-resolution Fermi chopper spectrometer (SEQUOIA) at the SNS. These measurements reveal two branches of magnetic excitations within the commensurate and incommensurate spin-Peierls phases, which we associate with n = 1 and n = 2 triplet excitations out of the singlet ground state. These measurements represent the first direct measure of the singlet-triplet energy gap in TiOBr, which is determined to be Eg = 21.2 +/- 1.0 meV.Comment: 5 pages, 4 figures, submitted for publicatio