Continuous measurements of two qubits

We develop a theory of coherent quantum oscillations in two, in general interacting, qubits measured continuously by a mesoscopic detector with arbitrary non-linearity and discuss an example of SQUID magnetometer that can operate as such a detector. Calculated spectra of the detector output show that the detector non-linearity should lead to mixing of the oscillations of the two qubits. For non-interacting qubits oscillating with frequencies $\Omega_1$ and $\Omega_2$, the mixing manifests itself as spectral peaks at the combination frequencies $\Omega_1\pm \Omega_2$. Additional nonlinearity introduced by the qubit-qubit interaction shifts all the frequencies. In particular, for identical qubits, the interaction splits coherent superposition of the single-qubit peaks at $\Omega_1=\Omega_2$. Quantum mechanics of the measurement imposes limitations on the height of the spectral peaks.Comment: 14 pages, 6 figure

Reheating in the Presence of Inhomogeneous Noise

Explosive particle production due to parametric resonance is a crucial feature of reheating in an inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter and gravitational fluctuations and often induce a parametric resonance instability. In a previous paper (hep-ph/9709273) it was shown that homogeneous (i.e. space independent) noise leads to an increase of the generalized Floquet exponent for all modes, at least if the noise is temporally uncorrelated. Here we extend the results to the physically more realistic case of spatially inhomogeneous noise. We demonstrate - modulo some mathematical fine points which are addressed in a companion paper - that the Floquet exponent is a non- decreasing function of the amplitude of the noise. We provide numerical evidence for an even stronger statement, namely that in the presence of inhomogeneous noise, the Floquet exponent of each mode is larger than the maximal Floquet exponent of the system in the absence of noise.Comment: 21 pages, 4 figure

Decoherence of a two-qubit system with a variable bath coupling operator

We examine the decoherence of an asymmetric two-qubit system that is coupled via a tunable interaction term to a common bath or two individual baths of harmonic oscillators. The dissipative dynamics are evaluated using the Bloch-Redfield formalism. It is shown that the behaviour of the decoherence effects is affected mostly by different symmetries between the qubit operator which is coupled to the environment and temperature, whereas the differences between the two bath configurations are very small. Moreover, it is elaborated that small imperfections of the qubit parameters do not lead to a drastic enhancement of the decoherence rates.Comment: 10 pages, 5 figure

Determination of the primary structure and carboxyl pKAs of heparin-derived oligosaccharides by band-selective homonuclear-decoupled two-dimensional 1H NMR

Determination of the structure of heparin-derived oligosaccharides by 1H NMR is challenging because resonances for all but the anomeric protons cover less than 2 ppm. By taking advantage of increased dispersion of resonances for the anomeric H1 protons at low pD and the superior resolution of band-selective, homonuclear-decoupled (BASHD) two-dimensional 1H NMR, the primary structure of the heparin-derived octasaccharide ∆UA(2S)-[(1 → 4)-GlcNS(6S)-(1 → 4)-IdoA(2S)-]3-(1 → 4)-GlcNS(6S) has been determined, where ∆UA(2S) is 2-O-sulfated ∆4,5-unsaturated uronic acid, GlcNS(6S) is 6-O-sulfated, N-sulfated β-d-glucosamine and IdoA(2S) is 2-O-sulfated α-l-iduronic acid. The spectrum was assigned, and the sites of N- and O-sulfation and the conformation of each uronic acid residue were established, with chemical shift data obtained from BASHD-TOCSY spectra, while the sequence of the monosaccharide residues in the octasaccharide was determined from inter-residue NOEs in BASHD-NOESY spectra. Acid dissociation constants were determined for each carboxylic acid group of the octasaccharide, as well as for related tetra- and hexasaccharides, from chemical shift–pD titration curves. Chemical shift–pD titration curves were obtained for each carboxylic acid group from sub-spectra taken from BASHD-TOCSY spectra that were measured as a function of pD. The pKAs of the carboxylic acid groups of the ∆UA(2S) residues are less than those of the IdoA(2S) residues, and the pKAs of the carboxylic acid groups of the IdoA(2S) residues for a given oligosaccharide are similar in magnitude. Relative acidities of the carboxylic acid groups of each oligosaccharide were calculated from chemical shift data by a pH-independent method

Residual dipolar coupling investigation of a heparin tetrasaccharide confirms the limited effect of flexibility of the iduronic acid on the molecular shape of heparin

The solution conformation of a fully sulfated heparin-derived tetrasaccharide, I, was studied in the presence of a 4-fold excess of Ca2+. Proton–proton and proton–carbon residual dipolar couplings (RDCs) were measured in a neutral aligning medium. The order parameters of two rigid hexosamine rings of I were determined separately using singular value decomposition and ab initio structures of disaccharide fragments of I. The order parameters were very similar implying that a common order tensor can be used to analyze the structure of I. Using one order tensor, RDCs of both hexosamine rings were used as restraints in molecular dynamics simulations. RDCs of the inner iduronic acid were calculated for every point of the molecular dynamics trajectory. The fitting of the calculated RDCs of the two forms of the iduronic acid to the experimental values yielded a population of 1C4 and 2So conformers of iduronic acid that agreed well with the analysis based on proton–proton scalar coupling constants. The glycosidic linkage torsion angles in RDC-restrained molecular dynamics (MD) structures of I are consistent with the interglycosidic three-bond proton–carbon coupling constants. These structures also show that the shape of heparin is not affected dramatically by the conformational flexibility of the iduronic acid ring. This is in line with conclusions of previous studies based on MD simulations and the analysis of 1H-1H NOEs. Our work therefore demonstrates the effectiveness of RDCs in the conformational analysis of glycosaminoglycans

Predictors of complications after endoscopic retrograde cholangiopancreatography: a prognostic model for early discharge

Background: Several studies have evaluated predictors for complications of endoscopic retrograde cholangiopancreatography (ERCP), but their relative importance is unknown. In addition, currently used blood tests to detect post-ERCP pancreatitis are inconsistent. The aim of this study was to determine predictors of post-ERCP complications that could discriminate between patients at highest and lowest risk of post-ERCP complications and to develop a model that is able to identify patients that can safely be discharged shortly after ERCP. Methods: In a single-center, retrospective analysis over the period 2002-2007, predictors of post-ERCP complications were evaluated in a multivariable analysis and compared with those identified from a literature review. A prognostic model was developed based on these risk factors, which was further evaluated in a prospective patient population. Results: From our retrospective analysis and literature review, we selected the eight most important risk factors for post-ERCP pancreatitis and cholangitis. In the prognostic model, the risk factors (precut) sphincterotomy, sphincter of Oddi dysfunction, younger age, female gender, history of pancreatitis, p