7,589 research outputs found
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 . However, in this limit the correlations disappear: the arithmetic
functions become uncorrelated. We compute averages of terms of lower order in
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 ; 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+Ļ0Ļ0 and measurement of the quasi-two-body contributions B+ -> K*(892)+Ļ0, B+ -> f0(980)K+, and B+ -> Ļc0K+
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 ā D*s2+XĪ¼-Ī½ decays
Using data collected with the LHCb detector in protonāproton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays B0sāD+sXĪ¼āĪ½ and B0sāD0K+XĪ¼āĪ½ are detected. Two structures are observed in the D0K+ mass spectrum at masses consistent with the known Ds1(2536)+ and Dās22573)+ mesons. The measured branching fractions relative to the total B0s semileptonic rate are B(B0sāDā+s2XĪ¼āĪ½)/B(B0sāXĪ¼āĪ½) = (3.3Ā±1.0Ā±0.4)%, and B(B0sāD+s1XĪ¼āĪ½)/B(B0sāXĪ¼āĪ½) = (5.4Ā±1.2Ā±0.5)%, where the ļ¬rst uncertainty is statistical and the second is systematic. This is the ļ¬rst observation of the Dā+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<sub><i>q</i></sub>[<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 ā ā. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when q ā ā, 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 content of and updated determination of the contents of and
Quantum-correlated decays collected by the CLEO-c
experiment are used to perform a first measurement of , the
fractional -even content of the self-conjugate decay , obtaining a value of . An important
input to the measurement comes from the use of
and decays to tag the signal mode. This same
technique is applied to the channels and , yielding and
, where the first uncertainty is
statistical and the second systematic. These measurements are consistent with
those of an earlier analysis, based on -eigenstate tags, and can be
combined to give values of and
. The results will enable the three modes to
be included in a model-independent manner in measurements of the unitarity
triangle angle using decays, and in time-dependent
studies of violation and mixing in the system.Comment: Minor revisions following journal acceptanc
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