Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Heavy-to-light transition form factors and their relations in light-cone QCD sum rules

The improved light-cone QCD sum rules by using chiral current correlator is systematically reviewed and applied to the calculation of all the heavy-to-light form factors, including all the semileptonic and penguin ones. By choosing suitable chiral currents, the light-cone sum rules for all the form factors are greatly simplified and depend mainly on one leading twist distribution amplitude of the light meson. As a result, relations between these form factors arise naturally. At the considered accuracy these relations reproduce the results obtained in the literature. Moreover, since the explicit dependence on the leading twist distribution amplitudes is preserved, these relations may be more useful to simulate the experimental data and extract the information on the distribution amplitude.Comment: 1+16 pages, no figure

Structure of the axial-vector meson Ds1(2460)D_{s1}(2460) and the strong coupling constant gDs1D∗Kg_{D_{s1} D^* K} with the light-cone QCD sum rules

In this article, we take the point of view that the charmed axial-vector meson $D_{s1}(2460)$ is the conventional $c\bar{s}$ meson and calculate the strong coupling constant $g_{D_{s1} D^* K}$ in the framework of the light-cone QCD sum rules approach. The numerical values of strong coupling constants $g_{D_{s1} D^* K}$ and $g_{D_{s0} D K}$ are very large, and support the hadronic dressing mechanism. Just like the scalar mesons $f_0(980)$ and $a_0(980)$, the scalar meson $D_{s0}(2317)$ and axial-vector meson $D_{s1}(2460)$ may have small $c\bar{s}$ kernels of the typical $c\bar{s}$ meson size, the strong couplings to the hadronic channels (or the virtual mesons loops) may result in smaller masses than the conventional $c\bar{s}$ mesons in the constituent quark models, and enrich the pure $c\bar{s}$ states with other components.Comment: 17 pages, 7 figures, revised version. In the first version, I take the value $f_{D_{s1}}= (0.25\pm0.02)GeV$ in numerical calculation, in the revised version, I take a small value $f_{D_{s1}}=(0.225 \pm0.020)GeV$, the value of the strong coupling constant is also change

The Semileptonic Decays D→π(ρ)eνD\to \pi(\rho) e \nu and B→π(ρ)eνB\to \pi (\rho) e \nu from QCD Sum Rules

We investigate the semileptonic decays of B and D mesons into $\pi$ and $\rho$ mesons, respectively, by means of QCD sum rules. We find that for the vector formfactors involved the pole dominance hypothesis is valid to good accuracy with pole masses in the expected range. Pole dominance, however, does not apply to the axial formfactors which results in specific predictions for the predominant polarization of the $\rho$ meson and the shape of the lepton spectrum. For the total decay rates we find $\Gamma (\bar B^0 \to \pi^+ e^- \bar\nu) = (5.1\pm 1.1)\,|V_{ub}|^2\, 10^{12}\,{\rm s^{-1}}$, $\Gamma ( D^0 \to \pi^- e^+ \nu) = (8.0\pm 1.7)\,|V_{cd}|^2\, 10^{10}\,{\rm s^{-1}}$, $\Gamma (\bar B^0 \to \rho^+ e^- \bar\nu) = (1.2\pm 0.4\,)\,|V_{ub}|^2\, 10^{13}\,{\rm s^{-1}}$ and $\Gamma (D^0 \to \rho^- e^+\nu) = (2.4\pm 0.7)\,|V_{cd}|^2\, 10^{9}\,{\rm s^{-1}}$.Comment: 23 pages, 12 figures included as uu-encoded file, needs REVTEX, TUM--T31--39/9

On almost randomizing channels with a short Kraus decomposition

For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a channel is epsilon-randomizing with high probability, which means that it maps every state within distance epsilon/d (in operator norm) of the maximally mixed state. This slightly improves on a result by Hayden, Leung, Shor and Winter by optimizing their discretization argument. Moreover, for general mu, we obtain a epsilon-randomizing channel provided N > d (\log d)^6/epsilon^2$. For d=2^k (k qubits), this includes Kraus operators obtained by tensoring k random Pauli matrices. The proof uses recent results on empirical processes in Banach spaces.Comment: We added some background on geometry of Banach space

The predictability of wind and virtual temperature profiles for flight and static test operations Final report, Jul. 1, 1965 - Mar. 31, 1966

Predictability of wind and virtual temperature profiles for flight and static test operation

All work and no pay: consequences of unpaid work experience in the creative industries

This research note evaluates the benefits and pitfalls of unpaid work as an entry route into employment in the creative industries and investigates the consequences of this practice for those who already work in the sector. Based on a qualitative study of perspectives of stakeholders in unpaid work, this article argues that the social capital thesis, often used as a rationale for unpaid work, inadequately explains the practice of unpaid work experience, primarily because it does not take cognisance of the consequences of this practice for other people working in the sector. The study also highlights methodological issues that need to be considered in the future. As well as the importance of a plurality of stakeholder perspectives, the study emphasizes the need to consider the perspectives of those who are excluded from unpaid work and those who are potentially displaced by it