Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot

Tunneling spectroscopy of a Nb coupled carbon nanotube quantum dot reveals the formation of pairs of Andreev bound states (ABS) within the superconducting gap. A weak replica of the lower ABS is found, which is generated by quasi-particle tunnelling from the ABS to the Al tunnel probe. An inversion of the ABS-dispersion is observed at elevated temperatures, which signals the thermal occupation of the upper ABS. Our experimental findings are well supported by model calculations based on the superconducting Anderson model.Comment: 6 pages, 7 figure

Nonlocal Hardy type inequalities with optimal constants and remainder terms

Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha}{2}}\dif x \dif y \le \mathcal{C}_{N,\alpha, 0}\int_{\R^N} \abs{\varphi}^2,] and of its combinations with the Hardy inequality by Beckner [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, 1} \int_{\R^N} \abs{\nabla \varphi}^2,] and with the fractional Hardy inequality [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, s} \mathcal{D}_{N, s} \int_{\R^N} \int_{\R^N} \frac{\bigabs{\varphi (x) - \varphi (y)}^2}{\abs{x-y}^{N+s}}\dif x \dif y] where (I_\alpha) is the Riesz potential, (0 < \alpha < N) and (0 < s < \min(N, 2)). We also prove the optimality of the constants. The method is flexible and yields a sharp expression for the remainder terms in these inequalities.Comment: 9 page

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization

We study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topological phase (NTP). These complex properties can be detected by tunneling conductance between normal metal / RSC junctions.Comment: 5 pages, 6 figure

Correlation, price discovery and co-movement of ABS and equity

Asset-backed securitization (ABS) has become a viable and increasingly attractive risk management and refinancing method either as a standalone form of structured finance or as securitized debt in Collateralized Debt Obligations (CDO). However, the absence of industry standardization has prevented rising investment demand from translating into market liquidity comparable to traditional fixed income instruments, in all but a few selected market segments. Particularly low financial transparency and complex security designs inhibits profound analysis of secondary market pricing and how it relates to established forms of external finance. This paper represents the first attempt to measure the intertemporal, bivariate causal relationship between matched price series of equity and ABS issued by the same entity. In a two-dimensional linear system of simultaneous equations we investigate the short-term dynamics and long-term consistency of daily secondary market data from the U.K. Sterling ABS/MBS market and exchange traded shares between 1998 and 2004 with and without the presence of cointegration. Our causality framework delivers compelling empirical support for a strong co-movement between matched price series of ABS-equity pairs, where ABS markets seem to contribute more to price discovery over the long run. Controlling for cointegration, risk-free interest and average market risk of corporate debt hardly alters our results. However, once we qualify the magnitude and direction of price discovery on various security characteristics, such as the ABS asset class, we find that ABS-equity pairs with large-scale CMBS/RMBS and credit card/student loan ABS reveal stronger lead-lag relationships and joint price dynamics than whole business ABS. JEL Classifications: G10, G12, G2

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely B\"acklund transformations and initial conservation laws, follow from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for generation of symmetries is developed and applied to discrete KdV. It can also be applied to all the other ABS equations