1,721 research outputs found
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 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 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
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