Spaces of quasi-exponentials and representations of gl_N

We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights \lambda^{(1)},...,\lambda^{(k)}, respectively. The Bethe algebra depends on N complex numbers K=(K_1,...,K_N). Under the assumption that K_1,...,K_N are distinct, we prove that the image of B_K in the endomorphisms of (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the algebra of functions on the intersection of k suitable Schubert cycles in the Grassmannian of N-dimensional spaces of quasi-exponentials with exponents K. We also prove that the B_K-module (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the coregular representation of that algebra of functions. We present a Bethe ansatz construction identifying the eigenvectors of the Bethe algebra with points of that intersection of Schubert cycles.Comment: Latex, 29 page

Bethe eigenvectors of higher transfer matrices

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting operators on the tensor product, called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.Comment: 48 pages, amstex.tex (ver 2.2), misprints correcte

Evidence of electro-active excitation of the spin cycloid in TbMnO3

Terahertz electromagnetic excitations in the multiferroic TbMnO3 at the field-induced magnetic transition are investigated for different orientations of the magnetic cycloid. In addition to the electromagnon along the a-axis, the detailed polarization analysis of the experimental spectra suggests the existence of an electro-active excitation for ac electric fields along the crystallographic c-axis. This excitation is possibly the electro-active eigenmode of the spin cycloid in TbMnO3, which has been predicted within the inverse Dzyaloshinskii-Moriya mechanism of magnetoelectric coupling.Comment: 5 page

Asymmetric Lineshape due to Inhomogeneous Broadening of the Crystal-Field Transitions in Mn12ac Single Crystals

The lineshape of crystal-field transitions in single crystals of Mn12ac molecular magnets is determined by the magnetic history. The absorption lines are symmetric and Gaussian for the non-magnetized state obtained by zero-field cooling (zfc). In the magnetized state which is reached when the sample is cooled in a magnetic field (fc), however, they are asymmetric even in the absence of an external magnetic field. These observations are quantitatively explained by inhomogeneous symmetrical (Gaussian) broadening of the crystal-field transitions combined with a contribution of off-diagonal components of the magnetic susceptibility to the effective magnetic permeability.Comment: 4 pages, 3 figure

Quantum spin chains and integrable many-body systems of classical mechanics

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem for quantum Hamiltonians of the former models is closely related to a sort of inverse spectral problem for Lax matrices of the latter ones. For simplicity, we focus on the most transparent and familiar case of spin chains on N sites constructed by means of the GL(2)-invariant R-matrix. They are related to the classical Ruijsenaars-Schneider system of N particles, which is known to be an integrable deformation of the Calogero-Moser system. As an explicit example the case N=2 is considered in detail.Comment: 17 pages, misprints corrected, written for Proceedings of the International School and Workshop "Nonlinear Mathematical Physics and Natural Hazards", Sofia, Bulgaria, November 28 - December 2, 2013, to be published in Lecture Notes in Physic

Terahertz spectroscopy of electromagnons in Eu_{1-x}Y_xMnO_3

Dielectric permittivity spectra of yttrium-doped EuMnO$_3$ in the composition range 0 =< x =< 0.5 have been investigated in the terahertz frequency range. Magnetoelectric contributions to the permittivity were observed in all compositions for ac electric fields parallel to the crystallographic a-axis. Well defined electromagnons exist for x >= 0.2 close to \nu ~ 20 cm^{-1} and with dielectric strength strongly increasing on doping. In addition to electromagnons, a broad contribution of magnetoelectric origin is observed for all compositions. For Eu_{0.8}Y_{0.2}MnO_3 the electromagnons can be suppressed by external magnetic fields which induce a canted antiferromagnetic phase. Magnetoelectric effects in the different doping regimes are discussed in detail.Comment: 7 pages, 9 figures include