On a heuristic point of view concerning the motion of matter. From random metric to Schroedinger equation

The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it is shown that the evolution of the probability density is given by Schroedinger equation.Comment: 13 pages, minor changes, publication reference give

World-Sheet Supersymmetry Without Contact Terms

Green and Seiberg showed that, in simple treatments of fermionic string theory, it is necessary to introduce contact interactions when vertex operators collide. Otherwise, certain superconformal Ward identities would be violated. In this note, we show how these contact terms arise naturally when proper account is taken of the superconformal geometry involved when punctures collide. More precisely, we show that there is no contact term at all! Rather, corrections arise to the ``na\"\i ve" formula when the boundary of moduli space is described correctly.Comment: 14pp., 2 figures (included

Dilaton Contact Terms in the Bosonic and Heterotic Strings

Dilaton contact terms in the bosonic and heterotic strings are examined following the recent work of Distler and Nelson on the bosonic and semirigid strings. In the bosonic case dilaton two-point functions on the sphere are calculated as a stepping stone to constructing a `good' coordinate family for dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton contact terms are improperly normalized, suggesting that the interpretation of the dilaton as the first variation of string coupling breaks down when other dilatons are present. It seems likely that this can be attributed to the tachyon divergence found in \TCCT. For the heterotic case, it is found that there is no tachyon divergence and that the dilaton contact terms are properly normalized. Thus, a dilaton equation analogous to the one in topological gravity is derived and the interpretation of the dilaton as the string coupling constant goes through.Comment: 44 pages, Figures now included. This replacement version includes the 7 figures as PostScript files appended to the end and the macros to insert them into the text. Also some typos in intermediate formulae were correcte

Pattern formation on the surface of cationic-anionic cylindrical aggregates

Charged pattern formation on the surfaces of self--assembled cylindrical micelles formed from oppositely charged heterogeneous molecules such as cationic and anionic peptide amphiphiles is investigated. The net incompatibility $\chi$ among different components results in the formation of segregated domains, whose growth is inhibited by electrostatics. The transition to striped phases proceeds through an intermediate structure governed by fluctuations, followed by states with various lamellar orientations, which depend on cylinder radius $R_c$ and $\chi$. We analyze the specific heat, susceptibility $S(q^*)$, domain size $\Lambda=2\pi/q^*$ and morphology as a function of $R_c$ and $\chi$.Comment: Sent to PRL 11Jan05 Transferred from PRL to PRE 10Jun0

The Dilaton Theorem and Closed String Backgrounds

The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. It is given by the action of the BRST operator on another state \x, but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and \x insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of \x. Surprisingly, the ghost number anomaly makes this a trivial deformation. While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. Thus the ``dilaton theorem'', familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.Comment: 51 pages, plain tex with phyzzx, two uuencoded figure

B-Function Expression in the Flower Center Underlies the Homeotic Phenotype of Lacandonia schismatica (Triuridaceae)

Spontaneous homeotic transformations have been described in natural populations of both plants and animals, but little is known about the molecular-genetic mechanisms underlying these processes in plants. In the ABC model of floral organ identity in Arabidopsis thaliana, the B- and C-functions are necessary for stamen morphogenesis, and C alone is required for carpel identity. We provide ABC model-based molecular-genetic evidence that explains the unique inside-out homeotic floral organ arrangement of the monocotyledonous mycoheterotroph species Lacandonia schismatica (Triuridaceae) from Mexico. Whereas a quarter million flowering plant species bear central carpels surrounded by stamens, L. schismatica stamens occur in the center of the flower and are surrounded by carpels. The simplest explanation for this is that the B-function is displaced toward the flower center. Our analyses of the spatio-temporal pattern of B- and C-function gene expression are consistent with this hypothesis. The hypothesis is further supported by conservation between the B-function genes of L. schismatica and Arabidopsis, as the former are able to rescue stamens in Arabidopsis transgenic complementation lines, and Ls-AP3 and Ls-PI are able to interact with each other and with the corresponding Arabidopsis B-function proteins in yeast. Thus, relatively simple molecular modifications may underlie important morphological shifts in natural populations of extant plant taxa

Extra States and Symmetries in D<2 Closed String Theory

We show that there is (p-1)(p'-1) dimensional semi-relative BRST cohomology at each non-positive ghost number in the (p,p') minimal conformal field theory coupled to two dimensional quantum gravity. These closed string states are related to currents and symmetry charges of `exotic' ghost number. We investigate the symmetry structure generated by the most conventional currents (those of vanishing total ghost number), and make a conjecture about the extended algebra which results from incorporating the currents at negative ghost number.Comment: 15 page

Evidence for vortex staircases in the whole angular range due to competing correlated pinning mechanisms

We analyze the angular dependence of the irreversible magnetization of YBa$_2$Cu$_3$O$_7$ crystals with columnar defects inclined from the c-axis. At high fields a sharp maximum centered at the tracks' direction is observed. At low fields we identify a lock-in phase characterized by an angle-independent pinning strength and observe an angular shift of the peak towards the c-axis that originates in the material anisotropy. The interplay among columnar defects, twins and ab-planes generates a variety of staircase structures. We show that correlated pinning dominates for all field orientations.Comment: 9 figures, 4 figure

Probing galaxy evolution through the internal colour gradients, the Kormendy relations and the Photometric Plane of cluster galaxies at z~0.2

We present a detailed analysis of the photometric properties of galaxies in the cluster \A2163B at redshift z~0.2. R-, I- and K-band structural parameters, (half light radius r_e, mean surface brightness _e within r_e and Sersic index n) are derived for N~60 galaxies, and are used to study their internal colour gradients. For the first time, we use the slopes of optical-NIR Kormendy relations to study colour gradients as a function of galaxy size, and we derive the Photometric Plane at z~0.2 in the K band. Colour gradients are negligible at optical wavelengths, and are negative in the optical-NIR, implying a metallicity gradient in galaxies of ~0.2 dex per radial decade. The analysis of the Kormendy relation suggests that its slope increases from the optical to the NIR, implying that colour gradients do not vary or even do become less steep in more massive galaxies. Such a result is not simply accomodated within a monolithic collapse scenario, while it can be well understood within a hierarchical merging framework. Finally, we derive the first NIR Photometric Plane at z~0.2, accounting for both the correlations on the measurement uncertainties and the selection effects. The Photometric Plane at z~0.2 is consistent with that at z~0, with an intrinsic scatter significantly smaller than the Kormendy relation but larger than the Fundamental Plane.Comment: 18 pages, 12 figures, A&A in pres