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.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique in the case of different quark masses

The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as \(q\bar s(with q = u,d),q\bar Q\), and \(s\bar Q\) (with Q = c, b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M²) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.     

Investigation of hybrid states in the VES experiment at the Institute for High Energy Physics (Protvino)

Experimental investigations of candidates for hybrid mesons in the VES experiment at the Institute for High Energy Physics (Protvino) are surveyed. The data in question concern π ₁ (1400) characterized by the exotic quantum numbers of J ^PC = 1^?+ and observed in the ηπ ^? final state; JPC = 1^?+ π ₁ (1600) in the ηπ ^?, b ₁ (1235)π, and f ₁(1285)π ^? final states; and J _PC = 0^?+ π(1800) in the f ₀(980)π ^?, f ₀(1300)π ^?, f ₀(1500)π ^?, and a ₀ ^? (980)η final states. New results are given along with data published previously.     

Stable diode lasers for hydrogen precision spectroscopy

We report on an external cavity diode laser at 972 nmstabilized to a mid-plane mounted Fabry-Perot (FP) resonator with afinesse of 400000. The 0.5 Hz optical beat note line width betweentwo similar lasers (Allan deviation 2 × 10^-15) is limitedby thermal noise properties of two independent FP resonators. Thelong term drift of the FP resonator and mirror substrates made fromUltra-Low-Expansion glass (ULE) is small and can be well predictedon time intervals up to many hours if the resonator is stabilized atthe zero thermal expansion temperature T_c. Using a Peltierelement in a vacuum chamber for temperature stabilization allowsstabilization of the FP cavity to T_c which is usually below theroom temperature. Beat note measurements with a femtosecond opticalfrequency comb referenced to a H-maser during 15 hours have shown awell defined linear drift of the FP resonance frequency of about 60 mHz/s with residual frequency excursions of less than ±20 Hz.     

Hole mobility and trapping in PVK films doped with CdSe/CdS and CdSe quantum dots

Experimental study of the hole mobility in polyvinylcarbazole (PVK) films doped with two kinds of nanocrystals, on bare core CdSe and core-shell CdSe/CdS quantum dots, with concentrations ranging from 3 · 10¹⁰ to 3 · 10¹⁵ cm⁻³, is presented. The quantum dots investigated were made using colloidal chemistry. The hole mobility was measured using the time-of-flight technique as a function of the applied electrical field in the range 10⁵–10⁶ V/cm and for temperatures from 20°C to 50°C. The transient curves, being featureless on a linear plot, show on a double logarithmic scale a sharp inflection point indicating a dispersive carrier drift process. The recovered values of the mobility are in the range 3 · 10⁻⁸–10⁻⁶ cm²·V⁻¹·s⁻¹ and their field and temperature dependences can be analyzed formally within the framework of the Gaussian disorder model proposed by B?ssler. The energetic disorder is, within the experimental accuracy, independent of the concentration and type of quantum dots for the CdSe quantum dots at all concentrations and for the CdS/CdSe quantum dots up to 10¹⁴ cm⁻³. The spatial disorder factors are very large (from 5.3 to 8.7) and do not depend in a systematic way upon the type and concentration of quantum dots (QDs). The experiments show that the apparent mobility does not change considerably with concentration, but it was found that the samples with CdSe/CdS quantum dots at concentrations from 10¹⁵ to 3 · 10¹⁵ cm⁻³ show a decreased photocurrent response. The dependence of the time-integrated transients (corresponding to the full charge value) upon the quantum-dot concentration has been determined. Differences in total photogenerated charge for pure and doped polymer films imply that the quantum dots of that type are the hole traps with capture times much more smaller than the transit time and with emission times a few orders longer than the transit time. CdSe quantum dots without a shell do not seem to exhibit the same properties as core shells and do not produce considerable changes in the charge transfer, even at a density of 10¹⁵ cm⁻³.