The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Age and structure of the Shyok Suture in the Ladakh region of Northwestern India: Implications for slip on the Karakoram Fault System

A precise age for the collision of the Kohistan-Ladakh block with Eurasia along the Shyok suture zone (SSZ) is one key to understanding the accretionary history of Tibet and the tectonics of Eurasia during the India-Eurasia collision. Knowing the age of the SSZ also allows the suture to be used as a piercing line for calculating total offset along the Karakoram Fault, which effectively represents the SE border of the Tibetan Plateau and has played a major role in plateau evolution. We present a combined structural, geochemical, and geochronologic study of the SSZ as it is exposed in the Nubra region of India to test two competing hypotheses: that the SSZ is of Late Cretaceous or, alternatively, of Eocene age. Coarse-continental strata of the Saltoro Molasse, mapped in this area, contain detrital zircon populations suggestive of derivation from Eurasia despite the fact that the molasse itself is deposited unconformably onto Kohistan-Ladakh rocks, indicating that the molasse is postcollisional. The youngest population of detrital zircons in these rocks (approximately 92 Ma) and a U/Pb zircon date for a dike that cuts basal molasse outcrops (approximately 85 Ma) imply that deposition of the succession began in the Late Cretaceous. This establishes a minimum age for the SSZ and rules out the possibility of an Eocene collision between Kohistan-Ladakh and Eurasia. Our results support correlation of the SSZ with the Bangong suture zone in Tibet, which implies a total offset across the Karakoram Fault of approximately 130–190 km

Smooth adiabatic evolutions with leaky power tails

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure

The influence of a seed crystal on the texture of a bulk YBaCuO specimen

Die ordnende Wirkung eines Saat-Kristalles auf die Textur einer massiven YBaCuO-Probe Um die Abhängigkeit der lokalen Textur von Teilen einer zylindrischen YBaCuO-Probe vom Abstand zum Saatkristall zu untersuchen, wurde eine sehr gut texturierte YBaCuO-Probe in 9 rechteckige und in 12 Randstücke zerschnitten. Von den einzelnen Teilen der YBaCuO-Probe wurden die Texturen mit Hilfe der Neutronen-Beugung am Reaktor in Geesthacht gemessen und zwar mit einem "equal-area"-Raster. Die Maschenweite betrug 1° bis zu einer Achsabweichung der Zylinderachse der originären YBaCuO-Probe von 10° und von 10° Achsabweichung bis zu 20° Achsabweichung betrug die Maschenweite 2°. Aus der Summe der gezählten Neutronen auf Kleinkreisen der Polkugel wurden die einzelnen Werte der Verteilung der Achsabweichungen der c-Achsen der kristallinen Domänen von der Zylinderachse berechnet. Die mittlere Achsabweichung der c-Achsen der kristallinen Domänen von der Zylinderachse der unzerschnittenen YBaCuO-Probe wächst vom inneren Stück mit dem Saatkristall zu den Randstücken der zylindrischen Probe hin an

Large oxygen-isotope effect in Sr_{0.4}K_{0.6}BiO_{3}: Evidence for phonon-mediated superconductivity

Oxygen-isotope effect has been investigated in a recently discovered superconductor Sr_{0.4}K_{0.6}BiO_{3}. This compound has a distorted perovskite structure and becomes superconducting at about 12 K. Upon replacing ^{16}O with ^{18}O by 60-80%, the T_c of the sample is shifted down by 0.32-0.50 K, corresponding to an isotope exponent of alpha_{O} = 0.40(5). This isotope exponent is very close to that for a similar bismuthate superconductor Ba_{1-x}K_{x}BiO_{3} with T_c = 30 K. The very distinctive doping and T_c dependencies of alpha_{O} observed in bismuthates and cuprates suggest that bismuthates should belong to conventional phonon-mediated superconductors while cuprates might be unconventional supercondutors.Comment: 9 pages, 5 figure

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette