Can a polynomial interpolation improve on the Kaplan-Yorke dimension?

The Kaplan-Yorke dimension can be derived using a linear interpolation between an h-dimensional Lyapunov exponent λ(h)>0 and an h+1-dimensional Lyapunov exponent λ(h+1)<0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems.     

Can VMD improve the estimate of the muon g－2?

We show that a VMD based theoretical input allows for a significantly improved accuracy for the hadronic vacuum polarization of the photon which contributes to the theoretical estimate of the muon g-2. We also show that the only experimental piece of information in the τ decay which cannot be accounted for within this VMD framework is the accepted value for Br（τ→ππvτ）, while the T spectum lineshape is in agreement with expectations from e^＋e^- annihilations.     

Can VMD improve the estimate of the muon g－2?

We show that a VMD based theoretical input allows for a significantly improved accuracy for the hadronic vacuum polarization of the photon which contributes to the theoretical estimate of the muon g-2.We also show that the only experimental piece of information in the τ decay which cannot be accounted for within this VMD framework is the accepted value for Br(τ→ππντ),while the τ spectum lineshape is in agreement with expectations from e+e-annihilations.     

Can the breaking of time-reversal symmetry remove degeneracies in quantum mechanics?

Reduction of spatial symmetry can remove the degeneracy of energy levels in quantum mechanics. The break of time-reversal symmetry by inclusion of a dissipative environment can have a similar effect. The corresponding time-evolution of position and momentum fluctuations can be described by a nonlinear differential equation that can lead to bifurcations and, thus, splitting of energy levels.     

Can a linearly polarized light beam polarize atomic spin?

Lax et al. [Phys. Rev. 11 (1975) 1365] discovered that a light beam in vacuum is not a transverse wave but does have a longitudinal field component. We investigate atomic and molecular electric dipole transitions induced by such a light beam, in particular, linearly polarized in a transverse plane. We derive the selection rules and the transition rates for various quantization axes using the paraxial approximation up to the first order of 1/kw, where k is the wave number and w is the transverse size of the light beam. The light beam is able to yield atomic spin polarization in the direction perpendicular to both the optical axis and the transverse electric field, and its magnitude is approximately 1/kw times that generated by a circularly polarized light wave with the similar intensity.     

Quantum nondemolition measurement of photon—number distribution for a weak cavity field with resonant atoms

We propose a quantum nondemolition measurement of the photon-number distribution for a weak cavity field with no more than two photons. The scheme is based on the resonant interaction of atoms with the cavity field, and thus the required interaction time is much shorter than that using dispersive interaction. This is important in view of decoherence. Our scheme can also be used to generate even and odd coherent states for a weak cavity field with resonant atoms.     

Can one hear the dimension of a fractal?

We consider the spectrum of the Laplacian in a bounded open domain of ⁿ with a rough boundary (i.e. with possibly non-integer dimension) and we discuss a conjecture by M. V. Berry generalizing Weyl's conjecture. Then using ideas Mark Kac developed in his famous study of the drum, we give upper and lower bounds for the second term of the expansion of the partition function. The main thesis of the paper is to show that the relevant measure of the roughness of the boundary should be based on Minkowski dimensions and on Minkowski measures rather than on Haussdorff ones.Dedicated to the memory of Mark Kac     

Can one count the shape of a drum?

Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of revolution. Arranging the wave functions by increasing values of the eigenvalues, and counting the number of their nodal domains, we obtain the nodal sequence whose properties we study. This sequence is expressed as a trace formula, which consists of a smooth (Weyl-like) part which depends on global geometrical parameters, and a fluctuating part, which involves the classical periodic orbits on the torus and their actions (lengths). The geometrical content of the nodal sequence is thus explicitly revealed.     

Where is the shot noise of a quantum point contact?

Reznikov et al. [Phys. Rev. Lett. 75, 3340 (1995)]] have presented definitive observations of nonequilibrium noise in a quantum point contact. Especially puzzling is the "anomalous" peak structure of the excess noise measured at constant current; to date it remains unexplained. We show that their experiment directly reveals the deep link between conservation principles in the electron gas and its low-dimensional, mesoscopic behavior. The keys to that connection are gauge invariance and the compressibility sum rule. These are central not only to the experiment of Reznikov et al., but to the very nature of all mesoscopic transport.     

Can an electric field induce an antiferroelectric phase out of a ferroelectric phase?

It has been widely accepted that electric fields favor the ferroelectric phase with parallel electric dipoles over the antiferroelectric phase. With detailed measurements in polycrystalline ceramics of Pb(0.99)Nb(0.02[(Zr(0.57)Sn(0.43)(1-y)Ti(y)](0.98)O(3), we demonstrate in this Letter that electric fields can induce an antiferroelectric phase out of a ferroelectric phase, i.e., trigger an apparently unlikely ferroelectric-to-antiferroelectric phase transition. We suggest that it is caused by the volume contraction from the converse piezoelectric effect at the coercive field with a reversed polarity.     

Can extra dimensions accessible to the SM explain the recent measurement of anomalous magnetic moment of the muon?

We investigate whether models with flat extra dimensions in which SM fields propagate can give a significant contribution to the anomalous magnetic moment of the muon (MMM). In models with only SM gauge and Higgs fields in the bulk, the contribution to the MMM from Kaluza–Klein (KK) excitations of gauge bosons is very small. This is due to the constraint on the size of the extra dimensions from tree-level effects of KK excitations of gauge bosons on precision electroweak observables such as Fermi constant. If the quarks and leptons are also allowed to propagate in the (same) bulk (“universal” extra dimensions), then there are no contributions to precision electroweak observables at tree-level. However, in this case, the constraint from one-loop contribution of KK excitations of (mainly) the top quark to T parameter again implies that the contribution to the MMM is small. We show that in models with leptons, electroweak gauge and Higgs fields propagating in the (same) bulk, but with quarks and gluon propagating in a sub-space of this bulk, both the above constraints can be relaxed. However, with only one Higgs doublet, the constraint from the process b→sγ requires the contribution to the MMM to be smaller than the SM electroweak correction. This constraint can be relaxed in models with more than one Higgs doublet.     

Does the integrability of a classical hamiltonian imply its quantum integrability?

By considering a simple example of a nonlinear integrable classical system and then quantizing it, we show that completely integrable hamiltonians in classical dynamics are not necessarily integrible in quantum mechanics.     

Can One See the Fundamental Frequency of a Drum?

We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of Ω which is defined as the maximal possible radius of a ball B with a negligible intersection with the complement of Ω. Here negligibility of means that cap(F)≤ γ cap (B), where cap a means the Wiener (harmonic) capacity and is arbitrarily fixed with the sole restriction . We provide explicit values of constants in the two-sided estimates.     

Can atomic force microscopy achieve atomic resolution in contact mode?

Atomic force microscopy operating in the contact mode is studied using total-energy pseudopotential calculations. It is shown that, in the case of a diamond tip and a diamond surface, it is possible for a tip terminated by a single atom to sustain forces in excess of 30 nN. It is also shown that imaging at atomic resolution may be limited by blunting of the tip during lateral scanning.