SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern-Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.Comment: 15 pages, 7 figure

Strongly Enhanced Low Energy Alpha-Particle Decay in Heavy Actinide Nuclei and Long-Lived Superdeformed and Hyperdeformed Isomeric States

Relatively low energy and very enhanced alpha-particle groups have been observed in various actinide fractions produced via secondary reactions in a CERN W target which had been irradiated with 24-GeV protons. In particular, 5.14, 5.27 and 5.53 MeV alpha-particle groups with corresponding half-lives of 3.8(+ -)1.0 y, 625(+ -)84 d and 26(+ -)7 d, have been seen in Bk, Es and Lr-No sources, respectively. The measured energies are a few MeV lower than the known g.s. to g.s. alpha-decays in the corresponding neutron-deficient actinide nuclei. The half-lives are 4 to 7 orders of magnitude shorter than expected from the systematics of alpha-particle decay in this region of nuclei. The deduced evaporation residue cross sections are in the mb region, about 4 orders of magnitude higher than expected. A consistent interpretation of the data is given in terms of production of long-lived isomeric states in the second and third wells of the potential-energy surfaces of the parent nuclei, which decay to the corresponding wells in the daughters. The possibility that the isomeric states in the third minimum are actually the true or very near the true ground states of the nuclei, and consequences regarding the production of the long-lived superheavy elements, are discussed.Comment: 27 pages including 8 figures and 4 table

Patchy Amphiphilic Dendrimers Bind Adenovirus and Control Its Host Interactions and in Vivo Distribution

The surface of proteins is heterogeneous with sophisticated but precise hydrophobic and hydrophilic patches, which is essential for their diverse biological functions. To emulate such distinct surface patterns on macromolecules, we used rigid spherical synthetic dendrimers (polyphenylene dendrimers) to provide controlled amphiphilic surface patches with molecular precision. We identified an,. I optimal spatial arrangement of these patches on certain dendrimers that enabled their interaction with human adenovirus 5 (Ads). Patchy dendrimers bound to the surface of Ads formed a synthetic polymer corona that greatly altered various host interactions of Ads as well as in vivo distribution. The dendrimer corona (1) improved the ability of Ad5-derived gene transfer vectors to transduce cells deficient for the primary Ad5 cell membrane receptor and (2) modulated the binding of Ads to blood coagulation factor X, one of the most critical virus host interactions in the bloodstream. It significantly enhanced the transduction efficiency of Ad5 while also protecting it from neutralization by natural antibodies and the complement system in human whole blood. Ads with a synthetic dendrimer corona revealed profoundly altered in vivo distribution, improved transduction of heart, and dampened vector sequestration by liver and spleen. We propose the design of bioactive polymers that bind protein surfaces solely based on their amphiphilic surface patches and protect against a naturally occurring protein corona, which is highly attractive to improve Ad5-based in vivo gene therapy applications

The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations

The Berry-Keating operator H_{\mathrm{BK}}:= -\ui\hbar(x\frac{ \phantom{x}}{ x}+{1/2}) [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in the Hilbert space L^2(\rz_>, x) and on compact quantum graphs. It is proved that the spectrum of $H_{\mathrm{BK}}$ defined on L^2(\rz_>, x) is purely continuous and thus this quantization of $H_{\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the "squared" Berry-Keating operator $H_{\mathrm{BK}}^2:= -x^2\frac{ ^2\phantom{x}}{ x^2}-2x\frac{ \phantom{x}}{ x}-{1/4}$ which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for $H_{\mathrm{BK}}^2$ on compact quantum graphs. While the spectra of both $H_{\mathrm{BK}}$ and $H_{\mathrm{BK}}^2$ on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither $H_{\mathrm{BK}}$ nor $H_{\mathrm{BK}}^2$ can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p

The cosmological origin of the Tully-Fisher relation

We use high-resolution cosmological simulations that include the effects of gasdynamics and star formation to investigate the origin of the Tully-Fisher relation in the standard Cold Dark Matter cosmogony. Luminosities are computed for each model galaxy using their full star formation histories and the latest spectrophotometric models. We find that at z=0 the stellar mass of model galaxies is proportional to the total baryonic mass within the virial radius of their surrounding halos. Circular velocity then correlates tightly with the total luminosity of the galaxy, reflecting the equivalence between mass and circular velocity of systems identified in a cosmological context. The slope of the relation steepens slightly from the red to the blue bandpasses, and is in fairly good agreement with observations. Its scatter is small, decreasing from \~0.45 mag in the U-band to ~0.34 mag in the K-band. The particular cosmological model we explore here seems unable to account for the zero-point of the correlation. Model galaxies are too faint at z=0 (by about two magnitudes) if the circular velocity at the edge of the luminous galaxy is used as an estimator of the rotation speed. The Tully-Fisher relation is brighter in the past, by about ~0.7 magnitudes in the B-band at z=1, at odds with recent observations of z~1 galaxies. We conclude that the slope and tightness of the Tully-Fisher relation can be naturally explained in hierarchical models but that its normalization and evolution depend strongly on the star formation algorithm chosen and on the cosmological parameters that determine the universal baryon fraction and the time of assembly of galaxies of different mass.Comment: 5 pages, 4 figures included, submitted to ApJ (Letters

Interplay between Coulomb Blockade and Resonant Tunneling studied by the Keldysh Green's Function Method

A theory of tunneling through a quantum dot is presented which enables us to study combined effects of Coulomb blockade and discrete energy spectrum of the dot. The expression of tunneling current is derived from the Keldysh Green's function method, and is shown to automatically satisfy the conservation at DC current of both junctions.Comment: 4 pages, 3 figures(mail if you need), use revtex.sty, error corrected, changed titl