Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by $g(x,t)=D(x)T(t)$, and the behaviors of probability distributions, for some specific functions of $D(x)$% , are analyzed. In particular, for $D(x)\sim | x| ^{-\theta /2}$, the physical solutions for the probability distribution in the Ito, Stratonovich and postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod

An increase in TcT_c under hydrostatic pressure in the superconducting doped topological insulator Nb0.25_{0.25}Bi2_2Se3_3

We report an unexpected positive hydrostatic pressure derivative of the superconducting transition temperature in the doped topological insulator \NBS via $dc$ SQUID magnetometry in pressures up to 0.6 GPa. This result is contrary to reports on the homologues \CBS and \SBS where smooth suppression of $T_c$ is observed. Our results are consistent with recent Ginzburg-Landau theory predictions of a pressure-induced enhancement of $T_c$ in the nematic multicomponent $E_u$ state proposed to explain observations of rotational symmetry breaking in doped Bi$_2$Se$_3$ superconductors.Comment: 5 pages, 5 figure

Signature of the matching field in Bose-glass melting of untwinned YBa_2Cu_3O_(7-δ) single crystals

We map out the phase boundary separating the Bose-glass and vortex-liquid phases in an irradiated twin-free YBa_2Cu_3O_(7-δ) single crystal. We take the phase boundary to be the temperature T_g and magnetic field H at which the crystal begins to screen a small ac magnetic field, h_(ac). There is a significant change in slope dT_g/dH of the phase boundary at the matching field B_Φ (≃0.5 T) indicating that interstitial vortices significantly weaken pinning in the Bose-glass state. There is also a pronounced peak in the slope dT_g/dH just below B_Φ at higher h_(ac). Both features disappear when the field is tilted away from the columns

Bose glass melting and the transverse Meissner effect in YBa_2Cu_3O_(7-δ) single crystals

We map out the phase boundary separating the vortex solid and liquid phases in YBa_2Cu_3O_(7-δ) (YBCO) single crystals with irradiation-induced columnar defects. These randomly distributed, extended defects are expected to localize vortices into a "Bose glass" phase. The transition from the vortex liquid into the Bose glass is predicted to exhibit two fundamental signatures: a vanishing of the linear resistivity and, concomitantly, a screening of de magnetic fields applied perpendicular to the defect axis, the transverse Meissner effect. We have investigated both aspects by systematic measurements on two YBCO single crystals with different defect densities (matching fields of 0.25 and 0.5 T), as well as on an unirradiated control sample. The melting line determined by the temperature, T_m, of vanishing resistance undergoes a 30% decrease in slope as the magnetic field is ramped through the matching field. This is evidence that interstitial vortices are pinned much more weakly than originally thought. If we associate the melting temperature with the Bose glass transition temperature, we obtain static critical exponents of ν⊥=1.7±0.2 and ν⊥=1.9±0.1 for the crystals with matching fields of 0.25 and 0.5 T, respectively. Simultaneously, we use a ten-element, linear array of microfabricated Hall probe magnetometers to observe directly the flux screening associated with the transverse Meissner state. We find the temperature above which the Meissner state breaks down, T_s, to decrease linearly as the magnetic field applied perpendicular to the columnar defect axis increases. This linear trend, found in both irradiated crystals to cover a range of at least 40 K in T_s, is closely in line with the current theoretical expectation ν⊥≃1. However, already for angles as small as one degree, T_s(H⊥) falls below T_m(H⊥) by more than 10 K. Thus, between Ts(H⊥) and T_m(H⊥) we observe a large regime characterized by zero resistivity in the absence of a transverse Meissner effect: vortices remain effectively localized even when rotated off the columnar defects

Ground-state fidelity of Luttinger liquids: A wave functional approach

We use a wave functional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground-state wave functionals are discussed using both the Schrodinger (functional differential equation) formulation and a path integral formulation. The fidelity between Luttinger liquids with Luttinger parameters K and K' is found to decay exponentially with system size, and to obey the symmetry F(K,K')=F(1/K,1/K') as a consequence of a duality in the bosonization description of Luttinger liquids.Comment: 13 pages, IOP single-column format. Sec. 3 expanded with discussion of short-distance cut-off. Some typos corrected. Ref. 44 in v2 is now footnote 2 (moved by copy editor). Published versio

Focusing Capillary Optics for Use in Solution Small-Angle X-Ray Scattering

Measurements of the global conformation of macromolecules can be carried out using small-angle X-ray scattering (SAXS). Glass focusing capillaries, manufactured at the Cornell High Energy Synchrotron Source (CHESS), have been successfully employed for SAXS measurements on the heme protein cytochrome c. These capillaries provide high X-ray flux into a spot size of tens of micrometres, permitting short exposures of small-volume samples. Such a capability is ideal for use in conjunction with microfluidic mixers, where time resolution may be determined by beam size and sample volumes are kept small to facilitate mixing and conserve material