Classification of irreducible quasifinite modules over map Virasoro algebras

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian commutative associative unital algebra over the complex numbers. It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir \otimes A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.Comment: 25 pages. v2: Minor changes, published versio

Analyticity and the NcN_c counting rule of SS matrix poles

By studying $\pi\pi$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, \Gamma\sim O(1)$. Especially the properties of $\sigma$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.Comment: This paper replaces hep-ph/0412175. The latter is withdraw

Dynamic polarizabilities and related properties of clock states of ytterbium atom

We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s^2 ^1S_0 and the first excited $6s6p ^3P^o_0$ states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s^2 ^1S_0 - 6s6p ^3P^o_0 transition. We determine (i) the first four {\em magic} wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the forth magic wavelengths to be 551 nm, 465 nm, and 413 nm. (ii) We reevaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at $T=300 \mathrm{K}$ being $-1.41(17)$ Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C_6(6s^2 ^1S_0 +6s^2 ^1S_0) = 1909(160), C_6(6s^2 ^1S_0 + 6s6p ^3P_0) =2709(338) , and $C_6(6s6p ^3P_0 + 6s6p ^3P_0) =3886(360)$. Finally, we determine the atom-wall interaction coefficients (in a.u.), C_3 (6s^2 ^1S_0) =3.34 and $C_3 (6s6p ^3P_0) =3.68$. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.Comment: 11 pages, 1 figur

Quantum theory of electric polarization nonlinearity in metal nanofilms

We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used.Comment: Accepted to PRB in this for

Learning Temporal Transformations From Time-Lapse Videos

Based on life-long observations of physical, chemical, and biologic phenomena in the natural world, humans can often easily picture in their minds what an object will look like in the future. But, what about computers? In this paper, we learn computational models of object transformations from time-lapse videos. In particular, we explore the use of generative models to create depictions of objects at future times. These models explore several different prediction tasks: generating a future state given a single depiction of an object, generating a future state given two depictions of an object at different times, and generating future states recursively in a recurrent framework. We provide both qualitative and quantitative evaluations of the generated results, and also conduct a human evaluation to compare variations of our models.Comment: ECCV201

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 μm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at ∼560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow (≤2 μm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 μm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2–16 μm range. For the smallest pillar (d = 2 μm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm “global” blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs

A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics

It is shown that a one-channel mesoscopic conductor in an ohmic environment can be mapped to the problem of a backscattering impurity in a Tomonaga-Luttinger liquid (TLL). This allows to determine non perturbatively the effect of the environment on $I-V$ curves, and to find an exact relationship between dynamic Coulomb blockade and shot noise. We investigate critically how this relationship compares to recent proposals in the literature. The full counting statistics is determined at zero temperature.Comment: 5 pages, 2 figures, shortened version for publication in Phys. Rev. Let

Cross-link governed dynamics of biopolymer networks

Cytoskeletal networks of biopolymers are cross-linked by a variety of proteins. Experiments have shown that dynamic cross-linking with physiological linker proteins leads to complex stress relaxation and enables network flow at long times. We present a model for the mechanical properties of transient networks. By a combination of simulations and analytical techniques we show that a single microscopic timescale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times, resulting in a weak power-law dependence of the shear modulus on frequency. By performing rheological experiments, we demonstrate that our model quantitatively describes the frequency behavior of actin network cross-linked with $\alpha$-Actinin-$4$ over four decades in frequency.Comment: 4 page