Random walks generated by Ewens distribution on the symmetric group

This paper studies Markov chains on the symmetric group $S_n$ where the transition probabilities are given by Ewens distribution with parameter $\theta>0$. The eigenvalues are identified to be content polynomials of partitions divided by n$th$ rising factorial of $\theta.$ The mixing time analysis is carried out for two cases: If $\theta$ is a constant integer, the chain is fast enough that the mixing time does not depend on $n.$ If $\theta=n$, the chain exhibits a total variation cutoff at $\frac{\log n}{\log 2}$ steps.Comment: 24 pages, 2 figure

Random decompositions of Eulerian statistics

This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of descents in random involutions and in random derangements are asymptotically normal with a rate of convergence of order $n^{-1/2}$ and $n^{-1/3}$ respectively.Comment: 28 page

Observation of quantum interference in the plasmonic Hong-Ou-Mandel effect

We report direct evidence of the bosonic nature of surface plasmon polaritons (SPPs) in a scattering-based beamsplitter. A parametric down-conversion source is used to produce two indistinguishable photons, each of which is converted into a SPP on a metal-stripe waveguide and then made to interact through a semi-transparent Bragg mirror. In this plasmonic analog of the Hong-Ou-Mandel experiment, we measure a coincidence dip with a visibility of 72%, a key signature that SPPs are bosons and that quantum interference is clearly involved.Comment: 5 pages, 3 figure

Pulse-mode quantum projection synthesis: Effects of mode mismatch on optical state truncation and preparation

Quantum projection synthesis can be used for phase-probability-distribution measurement, optical-state truncation and preparation. The method relies on interfering optical lights, which is a major challenge in experiments performed by pulsed light sources. In the pulsed regime, the time frequency overlap of the interfering lights plays a crucial role on the efficiency of the method when they have different mode structures. In this paper, the pulsed mode projection synthesis is developed, the mode structure of interfering lights are characterized and the effect of this overlap (or mode match) on the fidelity of optical-state truncation and preparation is investigated. By introducing the positive-operator-valued measure (POVM) for the detection events in the scheme, the effect of mode mismatch between the photon-counting detectors and the incident lights are also presented.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Exact metric around a wiggly cosmic string

The exact metric around a wiggly cosmic string is found by modifying the energy momentum-tensor of a straight infinitely thin cosmic string to include an electric current along the symmetry axis.Comment: 5 page

Thermoluminescence study of Mn doped lithium tetraborate powder and pellet samples synthesized by solution combustion synthesis

In this paper, the thermoluminescence (TL) dosimetric characteristics under beta-ray, x-ray and gamma-ray excitations of powder and pellet Mn-doped lithium tetraborates (LTB) which were produced by solution combustion synthesis technique were investigated, and the results were compared with that of TLD-100 chips. The chemical composition and morphologies of the obtained LTB and Mn-doped LTB (LTB:Mn) were confirmed by X-ray diffraction (XRD), Fourier Transform Infrared (FTIR) and scanning electron microscopy (SEM) with EDX. LTB:Mn was studied using luminescence spectroscopy. In addition, the effects of sintering and annealing temperatures and times on the thermoluminescence (TL) properties of LTB:Mn were investigated. The glow curves of powder samples as well as pellet samples exposed to different beta doses exhibited a low temperature peak at about 100 °C followed by an intense principal high temperature peak at about 260 °C. The kinetic parameters (E, b, s) associated with the prominent glow peaks were estimated using Tm-Tstop, initial rise (IR) and computerized glow curve deconvolution (CGCD) methods. The TL response of integral TL output increased linearly with increasing the dose in the range of 0.1-10 Gy and was followed by a superlinearity up to 100 Gy both for powder and pellet samples using beta-rays. Powder and pellet LTB:Mn were irradiated to a known dose by a linear accelerator with 6 and 18 MV photon beams, 6-15 MeV electron beams and a traceable 137Cs beam to investigate energy response. Further, TL sensitivity, fading properties and recycling effects related with beta exposure of LTB:Mn phosphor were evaluated and its relative energy response was also compared with that of TLD-100 chips. The comparison of the results showed that the obtained phosphors have good TL dose response with adequate sensitivity and linearity for the measurement of medical doses

Nuclear Spins in a Nanoscale Device for Quantum Information Processing

Coherent oscillations between any two levels from four nuclear spin states of I=3/2 have been demonstrated in a nanometre-scale NMR semiconductor device, where nuclear spins are all-electrically controlled. Using this device, we discuss quantum logic operations on two fictitious qubits of the I=3/2 system, and propose a quantum state tomography scheme based on the measurement of longitudinal magnetization, $M_z$.Comment: 5 pages, 4 figure

On-machine fabrication of PCD and WC micro end mills using micro electro discharge machining

Micro electro discharge machining (μ -EDM) process can be used to fabricate micro-milling tools of different geometries from tungsten carbide (WC) and polycrystalline diamond (PCD). The non-contact nature of EDM process makes micro tool fabrication a challenging task while offering the advantage of eliminating tool run out and clamping errors since micro tools fabricated on-machine. The tools are fabricated and used on the same spindle. In this study, a combination of block-EDM and wire electro discharge grinding (WEDG) techniques are used to fabricate micro end mills of different geometries. The influences of EDM process parameters on material erosion rate and surface roughness are examined. The performance of the fabricated micro-tools in ductile mode machining of fused silica has been investigated. It is found that micro end mills can be used to fabricate prototypes of microfluidics chips with acceptable quality. © 2014 Inderscience Enterprises Ltd