Theory of the coplanar-waveguide Penning trap

A novel planar Penning trap is presented, which results from the projection of the well-known three-dimensional cylindrical trap onto the surface of a chip. The introduced trap is also a coplanar-waveguide cavity, similar to those used in circuit quantum electrodynamics experiments with superconducting two-level systems. It opens up the possibility of integrating a single trapped electron, or geonium atom, into quantum circuits. The trap is an elliptical Penning trap, with the magnetic field parallel to the chip's surface. A design procedure is described, which permits the compensation of electric anharmonicities up to sixth order. This should render possible the observation of a single trapped electron and the accurate measurement of its eigenfrequencies, a sine qua non requirement for a useful planar geonium technology

Randomly Spread CDMA: Asymptotics via Statistical Physics

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear MMSE detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio suffers a degradation due to the multiple-access interference. The uncoded error performance (e.g., symbol-error-rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems.Comment: To be published in IEEE Transactions on Information Theor

A statistical theory of polymer network degradation

A statistical theory was proposed for the degradation (random scission of chains) of a network having f-functional nodes in the case where all chains contain equireactive groups and a chain scission event does not create new groups or suppress more than one group. Closedform relations were established between the conversion ratio of the degradation process and the crosslink density. Emphasis was put on the value of the conversion ratio for which the gel disappears. Some limited cases already considered in the literature were recovered, but a general solution was proposed for networks having any number of reactive groups per chain, be it uniform or not, and for conversion ratios up to the degelation point. The results were applied successfully to recent experiments regarding the hydrolysis of a polyester

WHEN CHEAPER IS BETTER: FEE DETERMINATION IN THE MARKET FOR EQUITY MUTUAL FUNDS

In this paper, we develop a model of the market for equity mutual funds that captures three key characteristics of this market. First, there is competition among funds. Second, fund managers' ability is not observed by investors before making their investment decisions. And third, some investors do not make optimal use of all available information. The main results of the paper are that 1) price competition is compatible with positive mark-ups in equilibrium; and 2) worse-performing funds set fees that are greater or equal than those set by better-performing funds. These predictions are supported by available empirical evidence.

The Noncoherent Rician Fading Channel -- Part II : Spectral Efficiency in the Low-Power Regime

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. The spectral-efficiency/bit-energy tradeoff in the low-power regime is examined when the input has limited peakedness. It is shown that if a fourth moment input constraint is imposed or the input peak-to-average power ratio is limited, then in contrast to the behavior observed in average power limited channels, the minimum bit energy is not always achieved at zero spectral efficiency. The low-power performance is also characterized when there is a fixed peak limit that does not vary with the average power. A new signaling scheme that overlays phase-shift keying on on-off keying is proposed and shown to be optimally efficient in the low-power regime.Comment: To appear in the IEEE Transactions on Wireless Communication

Support Recovery with Sparsely Sampled Free Random Matrices

Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with X_i \sim \Cc\Nc(0,\Pc_x) and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random matrix \Um, and a randomly chosen subset, of average size $n p$, $p \in [0,1]$, of the resulting vector components is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where \Um is typically %A16 the identity or a matrix with iid components, to allow \Um satisfying a certain freeness condition. This class of matrices encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verd\'u, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate in the limit of $n \to \infty$. We also extend the scope of the large deviation approach of Rangan, Fletcher and Goyal and characterize the performance of a class of estimators encompassing thresholded linear MMSE and $\ell_1$ relaxation

Co-oxidation kinetic model for the thermal oxidation of polyethylene-unsaturated substrate systems

The thermal oxidation of polyethylene (PE) impregnated by the methyl esters of unsaturated fatty acids (UFEs) was studied using chemiluminescence, and infra-red spectrophotometry. It was shown that the presence of UFEs accelerates the PE aging process. This can be interpreted as a co-oxidation phenomenon. In this study, the previously established models for PE and UFEs self-oxidation have been coupled in order to develop a co-oxidation model. Using the existing rate constants for the PE and UFEs selfoxidations, this model can simulate the complex shape of the kinetic curves of PE-UFE co-oxidatio

The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. First the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire SNR range when there is only a peak power constraint. The Rician fading with phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average power limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.Comment: To appear in the IEEE Transactions on Wireless Communication