Lower bounds for the first eigenvalue of the magnetic Laplacian

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate.Comment: Replaces in part arXiv:1611.0193

Fourier transform spectroscopy and coupled-channel deperturbation treatment of the A1Sigma+ ~ b3Pi complex of KCs molecule

The laser induced fluorescence (LIF) spectra A1Sigma ~ b3Pi --> X1Sigma+ of KCs dimer were recorded in near infrared region by Fourier Transform Spectrometer with a resolution of 0.03 cm-1. Overall more than 200 LIF spectra were rotationally assigned to 39K133Cs and 41K133Cs isotopomers yielding with the uncertainty of 0.003-0.01 cm-1 more than 3400 rovibronic term values of the strongly mixed singlet A1Sigma+ and triplet b3Pi states. Experimental data massive starts from the lowest vibrational level v_A=0 of the singlet and nonuniformly cover the energy range from 10040 to 13250 cm-1 with rotational quantum numbers J from 7 to 225. Besides of the dominating regular A1Sigma+ ~ b3P Omega=0 interactions the weak and local heterogenous A1S+ ~ b3P Omega=1 perturbations have been discovered and analyzed. Coupled-channel deperturbation analysis of the experimental 39K133Cs e-parity termvalues of the A1S+ ~ b3P complex was accomplished in the framework of the phenomenological 4 x 4 Hamiltonian accounting implicitly for regular interactions with the remote states manifold. The resulting diabatic potential energy curves of the interacting states and relevant spin-orbit coupling matrix elements defined analytically by Expanded Morse Oscillators model reproduce 95% of experimental data field of the 39K133Cs isotopomer with a standard deviation of 0.004 cm-1 which is consistent with the uncertainty of the experiment. Reliability of the derived parameters was additionally confirmed by a good agreement between the predicted and experimental termvalues of 41K133Cs isotopomer. Calculated intensity distributions in the A ~ b --> X LIF progressions are also consistent with their experimental counterparts.Comment: 17 pages, 14 figure

Level-crossing spectroscopy of the 7, 9, and 10D_5/2 states of 133Cs and validation of relativistic many-body calculations of the polarizabilities and hyperfine constants

We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for these states are also presented and checked for consistency with experimental values.Comment: 12 pages, revtex4, 11 figure file

Two-Dimensional Copolymers and Exact Conformal Multifractality

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 199

BPS states in M-theory and twistorial constituents

We provide a complete algebraic description of BPS states in M-theory in terms of primary constituents that we call BPS preons. We argue that any BPS state preserving $k$ of the 32 supersymmetries is a composite of (32-k) BPS preons. In particular, the BPS states corresponding to the basic M2 and M5 branes are composed of 16 BPS preons. By extending the M-algebra to a generalized D=11 conformal superalgebra $osp(1|64)$ we relate the BPS preons with its fundamental representation, the D=11 supertwistors.Comment: 4 pages. Refs. updated, two cosmetic changes, to appear in PR

Covariant Quantization of d=4 Brink-Schwarz Superparticle with Lorentz Harmonics

Covariant first and second quantization of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of maslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized.Comment: V2: 1 + 26 pages, published versio