Generalized Ricci solitons and Einstein metrics on weak KK-contact manifolds

We study metric structures on a smooth manifold (introduced in our recent works and called a weak contact metric structure and a weak K-structure) which generalize the metric contact and K-contact structures, and allow a new look at the classical theory. First, we characterize weak K-contact manifolds among all weak contact metric manifolds by the property well known for K-contact manifolds, and find when a Riemannian manifold endowed with a unit Killing vector field forms a weak K-contact structure. Second, we find sufficient conditions for a weak K-contact manifold with parallel Ricci tensor or with a generalized Ricci soliton structure to be an Einstein manifold.Comment: 10 page

Contact structures on principal circle bundles

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an invariant contact structure, only provided the trivial bundle does. In particular, all circle bundles over 4-manifolds admit invariant contact structures. We also discuss the Bourgeois construction of contact structures on odd-dimensional tori in this context, and we relate our results to recent work of Massot, Niederkrueger and Wendl on weak symplectic fillings in higher dimensions.Comment: 14 pages, 1 figure; v2: changes to exposition, Sections 5.2, 5.3 and 6 are ne

Electrostatic tailoring of magnetic interference in quantum point contact ballistic Josephson junctions

The magneto-electrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, to modify continuously the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity h/2e whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent novel tunable structures that might lead to the study of the elusive Majorana fermions.Comment: 4.5 pages, 4 color figure

Mechanical Stretching of Proteins: Calmodulin and Titin

Mechanical unfolding of several domains of calmodulin and titin is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. It is shown that this simple model captures the experimentally observed difference between the two proteins: titin is a spring that is tough and strong whereas calmodulin acts like a weak spring with featureless force-displacement curves. The difference is related to the dominance of the alpha secondary structures in the native structure of calmodulin. The tandem arrangements of calmodulin unwind simultaneously in each domain whereas the domains in titin unravel in a serial fashion. The sequences of contact events during unraveling are correlated with the contact order, i.e. with the separation between contact making amino acids along the backbone in the native state. Temperature is found to affect stretching in a profound way.Comment: To be published in a special bio-issue of Physica A; 14 figure

The topology of Stein fillable manifolds in high dimensions II

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 admits a weakly fillable contact structure provided M admits a weak symplectic filling. We also study the connection between Stein fillability and connected sums: we give examples of almost contact manifolds for which the connected sum is Stein fillable, while the components are not. Concerning obstructions to Stein fillings, we show that the (8k-1)-dimensional sphere has an almost contact structure which is not Stein fillable once k > 1. As a consequence we deduce that any highly connected almost contact (8k-1)-manifold (with k > 1) admits an almost contact structure which is not Stein fillable. The proofs rely on a new number-theoretic result about Bernoulli numbers.Comment: We corrected mistakes in the proofs of Lemma 2.9 and Corollary 2.10. This lead to an assumption being removed from the statement of Theorem 1.3. The paper is now published in Geometry and Topology. The appendix was written by Bernd C. Kellne

Patterned Irradiation of YBa_2Cu_3O_(7-x) Thin Films

We present a new experiment on YBa_2Cu_3O_{7-x} (YBCO) thin films using spatially resolved heavy ion irradiation. Structures consisting of a periodic array of strong and weak pinning channels were created with the help of metal masks. The channels formed an angle of +/-45 Deg with respect to the symmetry axis of the photolithographically patterned structures. Investigations of the anisotropic transport properties of these structures were performed. We found striking resemblance to guided vortex motion as it was observed in YBCO single crystals containing an array of unidirected twin boundaries. The use of two additional test bridges allowed to determine in parallel the resistivities of the irradiated and unirradiated parts as well as the respective current-voltage characteristics. These measurements provided the input parameters for a numerical simulation of the potential distribution of the Hall patterning. In contrast to the unidirected twin boundaries in our experiment both strong and weak pinning regions are spatially extended. The interfaces between unirradiated and irradiated regions therefore form a Bose-glass contact. The experimentally observed magnetic field dependence of the transverse voltage vanishes faster than expected from the numerical simulation and we interpret this as a hydrodynamical interaction between a Bose-glass phase and a vortex liquid.Comment: 7 pages, 8 Eps figures included. Submitted to PR

Patterned Irradiation of YBa_2Cu_3O_(7-x) Thin Films

We present a new experiment on YBa_2Cu_3O_{7-x} (YBCO) thin films using spatially resolved heavy ion irradiation. Structures consisting of a periodic array of strong and weak pinning channels were created with the help of metal masks. The channels formed an angle of +/-45 Deg with respect to the symmetry axis of the photolithographically patterned structures. Investigations of the anisotropic transport properties of these structures were performed. We found striking resemblance to guided vortex motion as it was observed in YBCO single crystals containing an array of unidirected twin boundaries. The use of two additional test bridges allowed to determine in parallel the resistivities of the irradiated and unirradiated parts as well as the respective current-voltage characteristics. These measurements provided the input parameters for a numerical simulation of the potential distribution of the Hall patterning. In contrast to the unidirected twin boundaries in our experiment both strong and weak pinning regions are spatially extended. The interfaces between unirradiated and irradiated regions therefore form a Bose-glass contact. The experimentally observed magnetic field dependence of the transverse voltage vanishes faster than expected from the numerical simulation and we interpret this as a hydrodynamical interaction between a Bose-glass phase and a vortex liquid.Comment: 7 pages, 8 Eps figures included. Submitted to PR