Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states.Comment: 22 pages; published in J. Phys. A: Math. Theo

An improved diameter bound for finite simple groups of Lie type

© 2019 London Mathematical Society For a finite group (Formula presented.), let (Formula presented.) denote the maximum diameter of a connected Cayley graph of (Formula presented.). A well-known conjecture of Babai states that (Formula presented.) is bounded by (Formula presented.) in case (Formula presented.) is a non-abelian finite simple group. Let (Formula presented.) be a finite simple group of Lie type of Lie rank (Formula presented.) over the field (Formula presented.). Babai's conjecture has been verified in case (Formula presented.) is bounded, but it is wide open in case (Formula presented.) is unbounded. Recently, Biswas and Yang proved that (Formula presented.) is bounded by (Formula presented.). We show that in fact (Formula presented.) holds. Note that our bound is significantly smaller than the order of (Formula presented.) for (Formula presented.) large, even if (Formula presented.) is large. As an application, we show that more generally (Formula presented.) holds for any subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a vector space of dimension (Formula presented.) defined over the field (Formula presented.)

Singular Effects of Spin-Flip Scattering on Gapped Dirac Fermions

We investigate the effects of spin-flip scattering on the Hall transport and spectral properties of gapped Dirac fermions. We find that in the weak scattering regime, the Berry curvature distribution is dramatically compressed in the electronic energy spectrum, becoming singular at band edges. As a result the Hall conductivity has a sudden jump (or drop) of $e^2/2h$ when the Fermi energy sweeps across the band edges, and otherwise is a constant quantized in units of $e^2/2h$. In parallel, spectral properties such as the density of states and spin polarization are also greatly enhanced at band edges. Possible experimental methods to detect these effects are discussed

Directed electron transport through ballistic quantum dot under microwave radiation

Rectification of microwave radiation by asymmetric, ballistic quantum dot is observed. The directed transport is studied at different frequency (1-40 GHz) temperatures (0.3K-6K)and magnetic field. Dramatic reduction of the rectification is found in magnetic fields at which the cyclotron (Larmor) radius of the electron orbits at Fermi level is smaller than the size of the quantum dot. It strongly suggests the ballistic nature of the observed nonlinear phenomena. Both symmetric and anti-symmetric with respect to the magnetic field contributions to the directed transport are presented. We have found that the behavior of the symmetric part of the rectified voltage with the magnetic field is different significantly for microwaves with different frequencies. A ballistic model of the directed transport is proposed.Comment: 5 pages, 3 figure

Analysis of Y(4660) and related bound states with QCD sum rules

In this article, we take the vector charmonium-like state Y(4660) as a $\psi'f_0(980)$ bound state (irrespective of the hadro-charmonium and the molecular state) tentatively, study its mass using the QCD sum rules, the numerical value $M_Y=4.71\pm0.26 \rm{GeV}$ is consistent with the experimental data. Considering the SU(3) symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states $\psi'\sigma(400-1200)$, $\Upsilon'"f_0(980)$ and $\Upsilon"'\sigma(400-1200)$ with the QCD sum rules, and make reasonable predictions for their masses.Comment: 18 pages, 32 figures, revised versio

Negative order KdV equation with both solitons and kink wave solutions

In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is $(\frac{-u_{xx}}{u})_{t}=2uu_{x}$, which actually comes from the negative KdV hierarchy and could be transformed to the Camassa-Holm equation through a gauge transform. The Lax pair of the equation is derived to guarantee its integrability, and furthermore the equation is shown to have classical solitons, periodic soliton and kink solutions

On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.Comment: to appear in Journal of Mathematical Physics, 17 pages, Late

Trends in cancer incidence and mortality in Scotland: description and possible explanations.

Secular and cohort trends in mortality from cancer in Scotland during 1953-93, and incidence during 1960-90, were analysed using individual records from the national mortality and registration files. For certain cancer sites, the secular analyses of mortality were extended back to 1911 by use of published data. Mortality from cancer at older ages in Scotland has increased over the last 40 years. In each sex, this trend has been dominated by the effects of smoking: all-cancer rates and rates of lung cancer, now the most common fatal cancer in men and in women in Scotland, reached a peak in the cohort of men born at the turn of the century and the cohort of women born in the 1920s. For much of the period, the Scottish all-age rates of lung cancer were the highest reported in the world; they are now decreasing on a secular basis in men, but are still increasing in women. There have also been large increases at older ages in the incidence and mortality rates for cancer of the prostate in recent years. bladder cancer, nervous system cancer, non-Hodgkin's lymphoma, myeloma and leukaemia; for each there is likely to be a considerable artefactual element to the increase, with differing degrees of possibility that there may in addition be an element of real increase. Substantial decreases in mortality at all ages have occurred for stomach and colorectal cancers and substantial increases at all ages for pleural cancer and melanoma. Rates of mortality from breast cancer, the most common cancer in women in Scotland, have generally increased over the past 80 years; a temporary cessation in this upward trend occurred in the years during and after the Second World War, and recently rates have turned downward, probably at least in part because of better treatment. Mortality from ovarian cancer, the second most common reproductive-related female tumour in Scotland, has also increased at older ages. At younger ages, mortality from cancer in Scotland has decreased, especially in men, whereas incidence has not. This divergence, which has been a consequence of better treatment, has occurred especially for cancers of the testis and ovary, Hodgkin's disease and leukaemia. There have been increases at young adult ages, however, in both mortality from and incidence of oral and pharyngeal, oesophageal and laryngeal cancers in men, and melanoma and non-Hodgkin's lymphoma in each sex. Cervical cancer rates at young ages also increased, but this trend has reversed for incidence in the most recent birth cohorts. Incidence rates have also increased for testicular cancer in young adults and leukaemia in children. With the possible exceptions of non-Hodgkin's lymphoma and childhood leukaemia, the increasing rates are likely largely to reflect real rises in incidence, and they highlight the need for investigation of the causes of these cancers, and, when causes are known, for preventive action

Cancer incidence in the Falkland Islands

Cancer incidence in the Falkland Islands, 1989–2000, was compared with rates in England and Wales, from which most Islanders originate. Colon and rectum cancer incidence was significantly raised 1989–93 but greatly reduced after 1994, when colonoscopic screening in high-risk families and sigmoidoscopic screening in the general population were introduced. http://www.bjcancer.com © 2001 Cancer Research Campaig