Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.Comment: 5 pages, 4 figure

Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma(v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma)/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.Comment: 12 page

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Mott Transition and Spin Structures of Spin-1 Bosons in Two-Dimensional Optical Lattice at Unit Filling

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic ($U_2>0$) and ferromagnetic ($U_2<0$) couplings, respectively.Comment: 5 pages, 5 figures, to appear in Journal of the Physical Society of Japa

Variational Monte Carlo analysis of the Hubbard model with a confining potential: one-dimensional fermionic optical lattice systems

We investigate the one-dimensional Hubbard model with a confining potential, which may describe cold fermionic atoms trapped in an optical lattice. Combining the variational Monte Carlo simulations with the new stochastic reconfiguration scheme proposed by Sorella, we present an efficient method to systematically treat the ground state properties of the confined system with a site-dependent potential. By taking into account intersite correlations as well as site-dependent on-site correlations, we are able to describe the coexistence of the metallic and Mott insulating regions, which is consistent with other numerical results. Several possible improvements of the trial states are also addressed.Comment: 7 pages, 15 figures; removed unnecessary graphs (p.8-p.32 in the old version are removed

The Loop Algorithm

A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion (SSE). It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal ones. The method has been applied successfully to a variety of models for spin and charge degrees of freedom, including Heisenberg and XYZ spin models, hard-core bosons, Hubbard, and tJ-models. Due to the improved efficiency, precise calculations of asymptotic behavior and of quantum critical exponents have been possible.Comment: Third Edition, July 2002. (78 pages, 11 figures). To appear in Adv.Phys. Updated. New chapter on Operator Formulation, with continuous time and with SS

Hormone replacement therapy before breast cancer diagnosis significantly reduces the overall death rate compared with never-use among 984 breast cancer patients

Nine hundred and eighty-four breast cancer patients were interviewed regarding exogenous hormonal use. This represents a random sample of breast cancer patients in Southern Sweden referred to the Department of Oncology at Lund for treatment between 1978 and 1997 (excluding 1980 and 1981) with a 100% follow-up. Ever-use of hormone replacement therapy (HRT) prior to diagnosis was significantly associated with a longer overall survival in women with their breast cancer diagnosed at ages 45 and above, relative risk (RR) of dying 0.73 (95% confidence interval (CI) 0.62-0.87; P = 0.0005). Ever use of HRT prior to breast cancer diagnosis was significantly positively associated with overall longer survival after adjustment for T-stage, N-stage, M-stage, year of diagnosis and age at diagnosis, RR of dying 0.78 (95% CI 0.65-0.93; P = 0.006). Hormone replacement therapy use and oestrogen receptor positivity were independently significantly associated with overall longer survival, P = 0.005 and P < 0.0001, respectively, in one model. HRT use and progesterone receptor positivity were also independently significantly associated with longer overall survival, P = 0.003 and P = 0.0003, respectively, in another model. The mode of diagnosis was known in 705 women. Mammography screening was not more common among HRT users compared with never-users, where this information was available. Both mammography screening and HRT use were independently associated with longer survival, P = 0.002 and P = 0.038 respectively

Fitness, motor competence and body composition as correlates of adolescent neck/shoulder pain: an exploratory cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Adolescent neck/shoulder pain (NSP) is a common and sometimes debilitating problem. Several risk factors for this condition have been investigated, but no studies have previously evaluated associations between fitness, motor competence, body composition and adolescent NSP.</p> <p>Methods</p> <p>1608 males and females of mean age 14 years answered questions on their history of NSP (4 measures), and were tested for aerobic fitness, upper and lower limb power, trunk endurance, grip strength, shoulder flexibility, motor competence and anthropometric factors. Univariate and multivariate logistic regressions were used to test for associations between NSP and physical variables.</p> <p>Results</p> <p>There were significant gender differences for most physical and pain variables. After multivariate analysis, males had lower odds of NSP if they had reduced back endurance [OR: 0.66 (95% CI: 0.46–0.97)], reduced persistent control [0.42 (0.19–0.95], and increased muscle power [0.33 (0.12–0.94)], and higher odds of NSP if they had a higher basketball throw [2.47 (1.22–5.00)] and jump performance [3.47 (1.55–7.74)]. Females had lower odds for NSP if they had a reduced jump performance [0.61(0.41–0.92)], a better basketball throw [0.60(0.40–0.90)], lower shoulder flexibility [0.54 (0.30–0.98)] and a higher aerobic capacity [0.61 (0.40–0.93)], and higher odds for NSP if they had greater abdominal endurance [1.57(1.07–2.31)] and greater bimanual dexterity [1.77(1.18–2.65)]. Females showed a U shaped relationship between NSP and back endurance [low: 2.12 (1.20–3.74); high 2.12 (1.18–3.83)].</p> <p>Conclusion</p> <p>Adolescent NSP was associated with fitness and motor competence, although the associations varied with gender, and their strength was limited.</p