Arithmetic correlations over large finite fields

The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M\"obius function and the divisor function, are the subject of classical problems in analytic number theory. The function field analogues of these problems have recently been resolved in the limit of large finite field size $q$. However, in this limit the correlations disappear: the arithmetic functions become uncorrelated. We compute averages of terms of lower order in $q$ which detect correlations. Our results show that there is considerable cancellation in the averaging and have implications for the rate at which correlations disappear when $q \rightarrow\infty$; in particular one cannot expect remainder terms that are of the order of the square-root of the main term in this context.Comment: The paper has been accepted by IMR

Trapping state restoration in the randomly-driven Jaynes-Cummings model by conditional measurements

We propose a scheme which can effectively restore fixed points in the quantum dynamics of repeated Jaynes-Cummings interactions followed by atomic state measurements, when the interaction times fluctuate randomly. It is based on selection of superposed atomic states whose phase correlations tend to suppress the phase fluctuations of each separate state. One suggested realization involves the convergence of the cavity field distribution to a single Fock state by conditional measurements performed on two-level atoms with fluctuating velocities after they cross the cavity. Another realization involves a trapped ion whose internal-motional state coupling fluctuates randomly. Its motional state is made to converge to a Fock state by conditional measurements of the internal state of the ion.Comment: RevTeX, 5 pages, four (EPS) figures automatically included through epsfig. Physical Review A 1998 (accepted for publication) Two references added to Ref. [8]. No other change. Final version which will appear in Physical Review

Observation of the rare decay B+ -> K+π0π0 and measurement of the quasi-two-body contributions B+ -> K*(892)+π0, B+ -> f0(980)K+, and B+ -> χc0K+

We report an analysis of charmless hadronic decays of charged B mesons to the final state K(+) pi(0)pi(0), using a data sample of (470.9 +/- 2.8) x 10(6) B (B) over bar events collected with the BABAR detector at the Y(4S) resonance. We observe an excess of signal events, with a significance above 10 standard deviations including systematic uncertainties, and measure the branching fraction and CP asymmetry to be B(B(+) -> K(+) pi(0)pi(0)) = (16.2 +/- 1.2 +/- 1.5) x 10(-6) and A(CP)(B(+) -> K(+) pi(0)pi(0)) = -0.06 +/- 0.06 +/- 0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B(+) -> K*(892)(+) pi(0), B(+) -> f(0)(980)K(+), and B(+) -> chi(c0)K(+) quasi-two-body decays. We report the world's best measurements of the branching fraction and CP asymmetry of the B(+) -> K(+) pi(0)pi(0) and B(+) -> K(+)(892)(+) pi(0) channels

Optimal Dynamical Decoherence Control of a Qubit

A theory of dynamical control by modulation for optimal decoherence reduction is developed. It is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.Comment: 6 pages, including 2 figures and an appendi

Scalable solid-state quantum processor using subradiant two-atom states

We propose a realization of a scalable, high-performance quantum processor whose qubits are represented by the ground and subradiant states of effective dimers formed by pairs of two-level systems coupled by resonant dipole-dipole interaction. The dimers are implanted in low-temperature solid host material at controllable nanoscale separations. The two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.Comment: 4 pages, 3 figure

First observation of Bs0 → D*s2+Xμ-ν decays

Using data collected with the LHCb detector in proton–proton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays B0s→D+sXμ−ν and B0s→D0K+Xμ−ν are detected. Two structures are observed in the D0K+ mass spectrum at masses consistent with the known Ds1(2536)+ and D∗s22573)+ mesons. The measured branching fractions relative to the total B0s semileptonic rate are B(B0s→D∗+s2Xμ−ν)/B(B0s→Xμ−ν) = (3.3±1.0±0.4)%, and B(B0s→D+s1Xμ−ν)/B(B0s→Xμ−ν) = (5.4±1.2±0.5)%, where the first uncertainty is statistical and the second is systematic. This is the first observation of the D∗+s2 state in B0s decays; we also measure its mass and width

Variance of sums in arithmetic progressions of arithmetic functions associated with higher degree <i>0</i>-functions in F_<i>q</i>[<i>t</i>]

We compute the variances of sums in arithmetic progressions of generalised -divisor functions related to certain -functions in q[], in the limit as q → ∞. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when q → ∞, in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual -divisor function, when the -function in question has degree one. They illustrate the role played by the degree of the -functions; in particular, we find qualitatively new behaviour when the degree exceeds one. Our calculations apply, for example, to elliptic curves defined over q[], and we illustrate them by examining in some detail the generalised -divisor functions associated with the Legendre curve

First determination of the CPCP content of D→π+π−π+π−D \to \pi^+\pi^-\pi^+\pi^- and updated determination of the CPCP contents of D→π+π−π0D \to \pi^+\pi^-\pi^0 and D→K+K−π0D \to K^+K^-\pi^0

Quantum-correlated $\psi(3770) \to D\bar{D}$ decays collected by the CLEO-c experiment are used to perform a first measurement of $F_+^{4\pi}$, the fractional $CP$-even content of the self-conjugate decay $D \to \pi^+\pi^-\pi^+\pi^-$, obtaining a value of $0.737 \pm 0.028$. An important input to the measurement comes from the use of $D \to K^0_{\rm S}\pi^+\pi^-$ and $D \to K^0_{\rm L}\pi^+\pi^-$ decays to tag the signal mode. This same technique is applied to the channels $D \to\pi^+\pi^-\pi^0$ and $D \to K^+K^-\pi^0$, yielding $F_+^{\pi\pi\pi^0} = 1.014 \pm 0.045 \pm 0.022$ and $F_+^{KK\pi^0} = 0.734 \pm 0.106 \pm 0.054$, where the first uncertainty is statistical and the second systematic. These measurements are consistent with those of an earlier analysis, based on $CP$-eigenstate tags, and can be combined to give values of $F_+^{\pi\pi\pi^0} = 0.973 \pm 0.017$ and $F_+^{KK\pi^0} = 0.732 \pm 0.055$. The results will enable the three modes to be included in a model-independent manner in measurements of the unitarity triangle angle $\gamma$ using $B^\mp \to DK^\mp$ decays, and in time-dependent studies of $CP$ violation and mixing in the $D\bar{D}$ system.Comment: Minor revisions following journal acceptanc