Hyperelliptic Szpiro inequality

We generalize the classical Szpiro inequality to the case of a semistable family of hyperelliptic curves. We show that for a semistable symplectic Lefschetz fibration of hyperelliptic curves of genus $g$, the number $N$ of non-separating vanishing cycles and the number $D$ of singular fibers satisfy the inequality $N \leq (4g+2)D$.Comment: LaTeX2e, 27 page

Rationality of quotients by linear actions of affine groups

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show that the answer to this question is positive if the dimension of V is sufficiently large and V is indecomposable. We have a more precise theorem if V is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.Comment: 18 pages; dedicated to Fabrizio Catanese on the occasion of his 60th birthda

Symplectic Lefschetz fibrations with arbitrary fundamental groups

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections in symplectic Lefschetz fibrations and their relation to the structure of the monodromy group.Comment: 45 pages, LaTeX2e. Minor mistakes corrected. New appendix by Ivan Smith added, proving the non-existence of SLF with monodromy contained in the Torelli grou

Luttinger-liquid-like transport in long InSb nanowires

Long nanowires of degenerate semiconductor InSb in asbestos matrix (wire diameter is around 50 \AA, length 0.1 - 1 mm) were prepared. Electrical conduction of these nanowires is studied over a temperature range 1.5 - 350 K. It is found that a zero-field electrical conduction is a power function of the temperature $G\propto T^\alpha$ with the typical exponent $\alpha \approx 4$. Current-voltage characteristics of such nanowires are found to be nonlinear and at sufficiently low temperatures follows the power law $I\propto V^\beta$. It is shown that the electrical conduction of these nanowires cannot be accounted for in terms of ordinary single-electron theories and exhibits features expected for impure Luttinger liquid. For a simple approximation of impure LL as a pure one broken into drops by weak links, the estimated weak-link density is around $10^3-10^4$ per cm.Comment: 5 pages, 2 figure

Diffusion and Transport Coefficients in Synthetic Opals

Opals are structures composed of the closed packing of spheres in the size range of nano-to-micro meter. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation between the diffusion coefficient and the termal and electrical conductivity makes possible to estimate the transport coefficients of opal structures. We estimate this changes as function of the neck size and the mean-free path of the carriers. The theory presented is also applicable to the diffusion problem in other periodic structures.Comment: Submitted to PR

A New Limit on the Antiproton Lifetime

Measurements of the cosmic ray pbar/p ratio are compared to predictions from an inhomogeneous disk-diffusion model of pbar production and propagation within the Galaxy, combined with a calculation of the modulation of the interstellar cosmic ray spectra as the particles propagate through the heliosphere to the Earth. The predictions agree with the observed pbar/p spectrum. Adding a finite pbar lifetime to the model, we obtain the limit tau_pbar > 0.8 Myr (90 % C.L.).Comment: 13 pages, 3 encapsulated Postscript figures, uses AASTeX; accepted by Astrophysical Journal; minor change

Variations in geoacoustic emissions in a deep borehole and its correlation with seismicity

Continuous geoacoustic emission (GAE) measurements were acquired using a three-component geophone placed in a borehole at a depth of near 1000 m at Petropavlovsk-Kamchatsky starting in August 2000. Using geophones consisting of magneto-elastic crystal ferromagnetic sensors, and installed at such a depth allows measurement of natural geoacoustic background with signal amplitude less than 1×10-4 m/s3 in frequency band from 3 to 1500 Hz. According to the data from a 4-year survey period the characteristics of diurnal geoacoustic variations change before every earthquake with MLH≥ 5.0 that occurs at a distance of less than 300 km from the observation point or before each earthquake with MLH≥5.5 occurring at distance R≤550 km from the observation point. The changes in GAE regime correlate with the strongest earthquakes that occurred during survey period. Measurements of the natural electromagnetic field of the Earth were carried out simultaneously with the help of an underground electric antenna. The behavior of GAE in aseismic periods appears to be related to the effect of diurnal variations of the natural electromagnetic field

Polaron Transport in the Paramagnetic Phase of Electron-Doped Manganites

The electrical resistivity, Hall coefficient, and thermopower as functions of temperature are reported for lightly electron-doped Ca(1-x)La(x)MnO(3)(0 <= x <= 0.10). Unlike the case of hole-doped ferromagnetic manganites, the magnitude and temperature dependence of the Hall mobility for these compounds is found to be inconsistent with small-polaron theory. The transport data are better described by the Feynman polaron theory and imply intermediate coupling (alpha \~ 5.4) with a band effective mass, m*~4.3 m_0, and a polaron mass, m_p ~ 10 m_0.Comment: 7 pp., 7 Fig.s, to be published, PR

Effect of pressure on the polarized infrared optical response of quasi-one-dimensional LaTiO3.41_{3.41}

The pressure-induced changes in the optical properties of the quasi-one-dimensional conductor LaTiO$_{3.41}$ were studied by polarization-dependent mid-infrared micro-spectroscopy at room temperature. For the polarization of the incident radiation parallel to the conducting direction, the optical conductivity spectrum shows a pronounced mid-infrared absorption band, exhibiting a shift to lower frequencies and an increase in oscillator strength with increasing pressure. On the basis of its pressure dependence, interpretations of the band in terms of electronic transitions and polaronic excitations are discussed. Discontinuous changes in the optical response near 15 GPa are in agreement with a recently reported pressure-induced structural phase transition and indicate the onset of a dimensional crossover in this highly anisotropic system.Comment: 7 pages, 7 figure

On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi