Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.Comment: 58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published versio

Tunable ohmic environment using Josephson junction chains

We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical SQUIDs, with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in-situ the SQUIDs' inductance, the double chain can operate as tunable ohmic resistor in a frequency band spanning up to one GHz, with a resistance that can be swept through values comparable to the resistance quantum R_q = (h/4e^2) ~ 6.5 k{\Omega}. We argue that the circuit complexity is within reach using current Josephson junction technology.Comment: 11 pages, 9 figure

Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance and a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate, elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to terminal/boundary value or obstacle problems for the parabolic Heston operator correspond to value functions for American-style options on the underlying asset.Comment: 47 pages; to appear in Transactions of the American Mathematical Societ

Baryon anomaly and strong color fields in Pb+Pb collisions at 2.76A TeV at the CERN Large Hadron Collider

With the HIJING/BBbar v2.0 heavy ion event generator, we explore the phenomenological consequences of several high parton density dynamical effects predicted in central Pb+Pb collisions at the Large Hadron Collider (LHC) energies. These include (1) jet quenching due to parton energy loss (dE/dx), (2) strangeness and hyperon enhancement due to strong longitudinal color field (SCF), and (3) enhancement of baryon-to-meson ratios due to baryon-anti-baryon junctions (JJbar) loops and SCF effects. The saturation/minijet cutoff scale p0(s)and effective string tension kappa(s,A) are constrained by our previous analysis of LHC p+p data and recent data on the charged multiplicity for Pb+Pb collisions reported by the ALICE collaboration. We predict the hadron flavor dependence (mesons and baryons) of the nuclear modification factor RAA(pT)$ and emphasize the possibility that the baryon anomaly could persist at the LHC up to pT=10 GeV, well beyond the range observed in central Au+Au collisions at RHIC energies.Comment: 25 pages, 8 figures, revtex4, text modifications, added references, accepted for publication Phys. Rev. C (2011

Soft Open Charm Production in Heavy-Ion Collisions

Effects of strong longitudinal color electric fields (SCF) on the open charm production in nucleus-nucleus (A + A) collisions at 200A GeV are investigated within the framework of the HIJING-BBbar v2.0 model. A three fold increase of the effective string tension due to in medium effects in A + A collisions, results in a sizeable (60-70 percents) enhancement of the total charm production cross sections. The nuclear modification factors show a suppression at moderate transverse momentum consistent with RHIC data. At Large Hadron Collider energies the model predicts an increase of total charm production cross sections by approximately an order of magnitude.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let