Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur

Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3_3Bi and GdPtBi

In the Dirac/Weyl semimetal, the chiral anomaly appears as an "axial" current arising from charge-pumping between the lowest (chiral) Landau levels of the Weyl nodes, when an electric field is applied parallel to a magnetic field $\bf B$. Evidence for the chiral anomaly was obtained from the longitudinal magnetoresistance (LMR) in Na$_3$Bi and GdPtBi. However, current jetting effects (focussing of the current density $\bf J$) have raised general concerns about LMR experiments. Here we implement a litmus test that allows the intrinsic LMR in Na$_3$Bi and GdPtBi to be sharply distinguished from pure current jetting effects (in pure Bi). Current jetting enhances $J$ along the mid-ridge (spine) of the sample while decreasing it at the edge. We measure the distortion by comparing the local voltage drop at the spine (expressed as the resistance $R_{spine}$) with that at the edge ($R_{edge}$). In Bi, $R_{spine}$ sharply increases with $B$ but $R_{edge}$ decreases (jetting effects are dominant). However, in Na$_3$Bi and GdPtBi, both $R_{spine}$ and $R_{edge}$ decrease (jetting effects are subdominant). A numerical simulation allows the jetting distortions to be removed entirely. We find that the intrinsic longitudinal resistivity $\rho_{xx}(B)$ in Na$_3$Bi decreases by a factor of 10.9 between $B$ = 0 and 10 T. A second litmus test is obtained from the parametric plot of the planar angular magnetoresistance. These results strenghthen considerably the evidence for the intrinsic nature of the chiral-anomaly induced LMR. We briefly discuss how the squeeze test may be extended to test ZrTe$_5$.Comment: 17 pages, 8 figures, new co-authors added, new Fig. 6a added. In press, PR

Large magnetic penetration depth and thermal fluctuations in a Ca10_{10}(Pt3_{3}As8_{8})[(Fe1−x_{1-x}Ptx_{x})2_{2}As2_{2}]5_{5} (x=0.097) single crystal

We have measured the temperature dependence of the absolute value of the magnetic penetration depth $\lambda(T)$ in a Ca$_{10}$(Pt$_{3}$As$_{8}$)[(Fe$_{1-x}$Pt$_{x}$)$_{2}$As$_{2}$]$_{5}$ (x=0.097) single crystal using a low-temperature magnetic force microscope (MFM). We obtain $\lambda_{ab}$(0)$\approx$1000 nm via extrapolating the data to $T = 0$. This large $\lambda$ and pronounced anisotropy in this system are responsible for large thermal fluctuations and the presence of a liquid vortex phase in this low-temperature superconductor with critical temperature of 11 K, consistent with the interpretation of the electrical transport data. The superconducting parameters obtained from $\lambda$ and coherence length $\xi$ place this compound in the extreme type \MakeUppercase{\romannumeral 2} regime. Meissner responses (via MFM) at different locations across the sample are similar to each other, indicating good homogeneity of the superconducting state on a sub-micron scale

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur

Building a 3.5 m prototype interferometer for the Q & A vacuum birefringence experiment and high precision ellipsometry

We have built and tested a 3.5 m high-finesse Fabry-Perot prototype inteferometer with a precision ellipsometer for the QED test and axion search (Q & A) experiment. We use X-pendulum-double-pendulum suspension designs and automatic control schemes developed by the gravitational-wave detection community. Verdet constant and Cotton-Mouton constant of the air are measured as a test. Double modulation with polarization modulation 100 Hz and magnetic-field modulation 0.05 Hz gives 10^{-7} rad phase noise for a 44-minute integration.Comment: This draft has been presented in the 5th Edoardo Amaldi Conference on Gravitational Wave

Growth to early adulthood following extremely preterm birth: the EPICure study.

OBJECTIVE: To investigate growth trajectories from age 2.5 to 19 years in individuals born before 26 weeks of gestation (extremely preterm; EP) compared with term-born controls. METHODS: Multilevel modelling of growth data from the EPICure study, a prospective 1995 birth cohort of 315 EP participants born in the UK and Ireland and 160 term-born controls recruited at school age. Height, weight, head circumference and body mass index (BMI) z-scores were derived from UK standards at ages 2.5, 6, 11 and 19 years. RESULTS: 129 (42%) EP children were assessed at 19 years. EP individuals were on average 4.0 cm shorter and 6.8 kg lighter with a 1.5 cm smaller head circumference relative to controls at 19 years. Relative to controls, EP participants grew faster in weight by 0.06 SD per year (95% CI 0.05 to 0.07), in head circumference by 0.04 SD (95% CI 0.03 to 0.05), but with no catch-up in height. For the EP group, because of weight catch-up between 6 and 19 years, BMI was significantly elevated at 19 years to +0.32 SD; 23.4% had BMI >25 kg/m2 and 6.3% >30 kg/m2 but these proportions were similar to those in control subjects. EP and control participants showed similar pubertal development in early adolescence, which was not associated with height at 19 years in either study group. Growth through childhood was related to birth characteristics and to neonatal feeding practices. CONCLUSIONS: EP participants remained shorter and lighter and had smaller head circumferences than reference data or controls in adulthood but had elevated BMI

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update

Controlling the Momentum Current of an Off-resonant Ratchet

We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein Condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. \textbf{11}, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.Comment: arXiv admin note: substantial text overlap with arXiv:1210.565