Local Asymmetry and the Inner Radius of Nodal Domains

Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue \lambda. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/\lambda^n. We apply this result to prove that each nodal domain contains a ball of radius > C/\lambda^n.Comment: 12 pages, 1 figure; minor corrections; to appear in Comm. PDE

Equivalences between GIT quotients of Landau-Ginzburg B-models

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.Comment: v3: Added two references. Final version, to appear in Comm. Math. Phy

Frustration induced Raman scattering in CuGeO_3

We present experimental data for the Raman intensity in the spin-Peierls compound CuGeO_3 and theoretical calculations from a one-dimensional frustrated spin model. The theory is based on (a) exact diagonalization and (b) a recently developed solitonic mean field theory. We find good agreement between the 1D-theory in the homogeneous phase and evidence for a novel dimerization of the Raman operator in the spin-Peierls state. Finally we present evidence for a coupling between the interchain exchange, the spin-Peierls order parameter and the magnetic excitations along the chains.Comment: Phys. Rev. B, Rapid Comm, in Pres

Field-induced first-order magnetic phase transition in an intermetallic compound, Nd7Rh3: Evidence for kinetic-hindrance, phase co-existence and percolative conduction

The compound, Nd7Rh3, crystallizing in Th7Fe3-type hexagonal structure, was previously known to exhibit two magnetic transitions, one at 32 K and the other at 10 K (in zero magnetic field). Here, we report the existence of a field-induced first-order antiferromagnetic to ferromagnetic transition at 1.8 K in this compound. On the basis of the measurements of isothermal magnetization and magnetoresistance, we provide evidence for the occurence of kinetic-hindrance, proposed in the literature, resulting in phase co-existence (super-cooled ferromagnetic + antifferomagnetic) and percolative electrical conduction in this stoichiometric intermetallic compound. A point of emphasis, as inferred from ac susceptibility data, is that such a co-existing phase is different from spin-glasses, thereby clarifying a question raised in the field of phase-separation.Comment: A Shortened version will appear in print in PRB (Rapid Comm). Phys. Rev. B (Rapid Comm), in pres

Comments on "Plasma current drive by injection of photons with helicity" [Comm. Plasma Phys. Controlled Fusion 12, 165 (1989)]

Ohkawa has proposed a tokamak current-drive scheme [Comm. Plasma Phys. Controlled Fusion 12, 165 (1989)], which relies on the injection of circularly polarized magnetohydrodynamic waves. It is shown here that the favorable current-drive efficiency predicted by Ohkawa is not attained because excessive power is dissipated by the fluctuating fields. The ratio of power absorbed by the plasma to the dc Ohmic power required to drive the same current is Pabsorbed/POhmic[approximately-equal-to]4(Ba/b)^2, where Ba is the static toroidal field strength and b is the strength of the fluctuating field