On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Quantum measurement of a mesoscopic spin ensemble

We describe a method for precise estimation of the polarization of a mesoscopic spin ensemble by using its coupling to a single two-level system. Our approach requires a minimal number of measurements on the two-level system for a given measurement precision. We consider the application of this method to the case of nuclear spin ensemble defined by a single electron-charged quantum dot: we show that decreasing the electron spin dephasing due to nuclei and increasing the fidelity of nuclear-spin-based quantum memory could be within the reach of present day experiments.Comment: 8 pages, 2 figures; minor changes, published versio

Symbolic Dynamics Analysis of the Lorenz Equations

Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor by numerical work alone. By constructing symbolic dynamics of 1D and 2D maps from the Poincare sections all unstable periodic orbits up to a given length at a fixed parameter set may be located and all stable periodic orbits up to a given length may be found in a wide parameter range. This knowledge, in turn, tells much about the nature of the chaotic limits. Applied to the Lorenz equations, this approach has led to a nomenclature, i.e., absolute periods and symbolic names, of stable and unstable periodic orbits for an autonomous system. Symmetry breakings and restorations as well as coexistence of different regimes are also analyzed by using symbolic dynamics.Comment: 35 pages, LaTeX, 13 Postscript figures, uses psfig.tex. The revision concerns a bug at the end of hlzfig12.ps which prevented the printing of the whole .ps file from page 2

Nitrate, sulphate and chloride contents in public drinking water supplies in Sicily, Italy

Water samples collected from public drinking water supplies in Sicily were analysed for electric conductivity and for their chloride, sulphate and nitrate contents. The samples were collected as uniformly as possible from throughout the Sicilian territory, with an average sampling density of about one sample for every 7,600 inhabitants. Chloride contents that ranged from 5.53 to 1,302 mg/l were correlated strongly with electric conductivity, a parameter used as a proxy for water salinity. The highest values are attributable to seawater contamination along the coasts of the island. High chloride and sulphate values attributable to evaporitic rock dissolution were found in the central part of Sicily. The nitrate concentrations ranged from 0.05 to 296 mg/l, with 31 samples (4.7% of the total) exceeding the maximum admissible concentration of 50 mg/l. Anomalous samples always came from areas of intensive agricultural usage, indicating a clear anthropogenic origin. The same parameters were also measured in bottled water sold in Sicily, and they all were within the ranges for public drinking water supplies. The calculated mean nitrate intake from consuming public water supplies (16.1 mg/l) did not differ significantly from that of bottled water (15.2 mg/l). Although the quality of public water supplies needs to be improved by eliminating those that do not comply with the current drinking water limits, at present it does not justify the high consumption of bottled water (at least for nitrate contents)

Time-optimal rotation of a spin 1/2: application to the NV center spin in diamond

We study the applicability of the time optimal bang-bang control designed for spin-1/2 [U. Boscain and P. Mason, J. Math. Phys. {\bf 47}, 062101 (2006)] to the rotation of the electron spin of a nitrogen-vacancy (NV) center in diamond. The spin of the NV center is a three-level system, with two levels forming a relevant qubit subspace where the time-varying magnetic control field performs rotation, and the third level being idle. We find that the bang-bang control protocol decreases the rotation time by 20--25% in comparison with the traditional oscillating sinusoidal driving. We also find that for most values of the bias field the leakage to the idle level is very small, so that the NV center is a suitable testbed for experimental study of the time-optimal protocols. For some special values of the bias field, however, the unwanted leakage is greatly increased. We demonstrate that this is caused by the resonance with higher-order Fourier harmonics of the bang-bang driving field.Comment: 6 pages, 4 figure

Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls

Dynamically corrected gates were recently introduced [Khodjasteh and Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, confirming the expected fidelity performance in a wide parameter range. Robutness against a class of systematic control errors is automatically incorporated in the perturbative error regime.Comment: 21 pages, 7 figures (errors fixed, figures added, text updated

CaloCube: a novel calorimeter for high-energy cosmic rays in space

In order to extend the direct observation of high-energy cosmic rays up to the PeV region, highly performing calorimeters with large geometrical acceptance and high energy resolution are required. Within the constraint of the total mass of the apparatus, crucial for a space mission, the calorimeters must be optimized with respect to their geometrical acceptance, granularity and absorption depth. CaloCube is a homogeneous calorimeter with cubic geometry, to maximise the acceptance being sensitive to particles from every direction in space; granularity is obtained by relying on small cubic scintillating crystals as active elements. Different scintillating materials have been studied. The crystal sizes and spacing among them have been optimized with respect to the energy resolution. A prototype, based on CsI(Tl) cubic crystals, has been constructed and tested with particle beams. Some results of tests with different beams at CERN are presented.Comment: Seven pages, seven pictures. Proceedings of INSTR17 Novosibirs

Quantum control theory for coupled 2-electron dynamics in quantum dots

We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrodinger equation is solved nonperturbatively in conjunction with several quantum control strategies. This results in optimized electric pulses in the THz regime which can populate combinations of states with very short transition times. The speedup compared to intuitively constructed pulses is an order of magnitude. We furthermore make use of optimized pulse control in the simulation of an experimental preparation of the molecular quantum dot system. It is shown that exclusive population of certain excited states leads to a complete suppression of spin dephasing, as was indicated in Nepstad et al. [Phys. Rev. B 77, 125315 (2008)].Comment: 24 pages, 9 figure

On equations over sets of integers

Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition S+T=\makeset{m+n}{m \in S, \: n \in T} and with ultimately periodic constants is exactly the class of hyper-arithmetical sets. Equations using addition only can represent every hyper-arithmetical set under a simple encoding. All hyper-arithmetical sets can also be represented by equations over sets of natural numbers equipped with union, addition and subtraction S \dotminus T=\makeset{m-n}{m \in S, \: n \in T, \: m \geqslant n}. Testing whether a given system has a solution is $\Sigma^1_1$-complete for each model. These results, in particular, settle the expressive power of the most general types of language equations, as well as equations over subsets of free groups.Comment: 12 apges, 0 figure

21 years of Timing PSR B1509-58

We present an updated timing solution for the young, energetic pulsar PSR B1509-58 based on 21.3 years of radio timing data and 7.6 years of X-ray timing data. No glitches have occurred in this time span, in contrast to other well-studied young pulsars, which show frequent glitches. We report a measurement of the third frequency derivative of (-1.28+/-0.21)x10^(-31) s^(-4). This value is 1.65 standard deviations from, i.e. consistent with, that predicted by the simple constant magnetic dipole model of pulsar spin-down. We measured the braking index to be n=2.839+/-0.003 and show that it varies by 1.5% over 21.3 yr due to contamination from timing noise. Results of a low-resolution power spectral analysis of the significant noise apparent in the data yield a spectral index of alpha=-4.6+/-1.0 for the red noise component.Comment: 21 pages, 4 figures, 2 tables. Accepted by Ap