Mass Expansions of Screened Perturbation Theory

The thermodynamics of massless phi^4-theory is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the Lagrangian. We analytically calculate the pressure and entropy to three-loop order and the screening mass to two-loop order, expanding in powers of m/T. The truncated m/T-expansion results are compared with numerical SPT results for the pressure, entropy and screening mass which are accurate to all orders in m/T. It is shown that the m/T-expansion converges quickly and provides an accurate description of the thermodynamic functions for large values of the coupling constant.Comment: 22 pages, 10 figure

Influence of seating styles on head and pelvic vertical movement symmetry in horses ridden at trot

Detailed knowledge of how a rider’s seating style and riding on a circle influences the movement symmetry of the horse’s head and pelvis may aid rider and trainer in an early recognition of low grade lameness. Such knowledge is also important during both subjective and objective lameness evaluations in the ridden horse in a clinical setting. In this study, inertial sensors were used to assess how different rider seating styles may influence head and pelvic movement symmetry in horses trotting in a straight line and on the circle in both directions. A total of 26 horses were subjected to 15 different conditions at trot: three unridden conditions and 12 ridden conditions where the rider performed three different seating styles (rising trot, sitting trot and two point seat). Rising trot induced systematic changes in movement symmetry of the horses. The most prominent effect was decreased pelvic rise that occurred as the rider was actively rising up in the stirrups, thus creating a downward momentum counteracting the horses push off. This mimics a push off lameness in the hindlimb that is in stance when the rider sits down in the saddle during the rising trot. On the circle, the asymmetries induced by rising trot on the correct diagonal counteracted the circle induced asymmetries, rendering the horse more symmetrical. This finding offers an explanation to the equestrian tradition of rising on the ‘correct diagonal.’ In horses with small pre-existing movement asymmetries, the asymmetry induced by rising trot, as well as the circular track, attenuated or reduced the horse’s baseline asymmetry, depending on the sitting diagonal and direction on the circle. A push off hindlimb lameness would be expected to increase when the rider sits during the lame hindlimb stance whereas an impact hindlimb lameness would be expected to decrease. These findings suggest that the rising trot may be useful for identifying the type of lameness during subjective lameness assessment of hindlimb lameness. This theory needs to be studied further in clinically lame horses

Screened Perturbation Theory to Three Loops

The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.Comment: 30 pages, 10 figure

Chiral Susceptibility in Hard Thermal Loop Approximation

The static and dynamic chiral susceptibilities in the quark-gluon plasma are calculated within the lowest order perturbative QCD at finite temperature and the Hard Thermal Loop resummation technique using an effective quark propagator. After regularisation of ultraviolet divergences, the Hard Thermal Loop results are compared to QCD lattice simulations.Comment: 12 pages, 4 figures, revised version, to be published in Phys. Rev.

Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries

Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H unequal 1/2, x(t) is a non-Markovian process. Here we study x(t) in presence of an absorbing boundary at the origin and focus on the probability density P(x,t) for the process to arrive at x at time t, starting near the origin at time 0, given that it has never crossed the origin. It has a scaling form P(x,t) ~ R(x/t^H)/t^H. Our objective is to compute the scaling function R(y), which up to now was only known for the Markov case H=1/2. We develop a systematic perturbation theory around this limit, setting H = 1/2 + epsilon, to calculate the scaling function R(y) to first order in epsilon. We find that R(y) behaves as R(y) ~ y^phi as y -> 0 (near the absorbing boundary), while R(y) ~ y^gamma exp(-y^2/2) as y -> oo, with phi = 1 - 4 epsilon + O(epsilon^2) and gamma = 1 - 2 epsilon + O(epsilon^2). Our epsilon-expansion result confirms the scaling relation phi = (1-H)/H proposed in Ref. [28]. We verify our findings via numerical simulations for H = 2/3. The tools developed here are versatile, powerful, and adaptable to different situations.Comment: 16 pages, 8 figures; revised version 2 adds discussion on spatial small-distance cutof

Radiative levitation: a likely explanation for pulsations in the unique hot O subdwarf star SDSS J160043.6+074802.9

Context. SDSS J160043.6+074802.9 (J1600+0748 for short) is the only hot sdO star for which unambiguous multiperiodic luminosity variations have been reported so far. These rapid variations, with periods in the range from ~60 s to ~120 s, are best qualitatively explained in terms of pulsational instabilities, but the exact nature of the driving mechanism has remained a puzzle. Aims. Our primary goal is to examine quantitatively how pulsation modes can be excited in an object such as J1600+0748. Given the failure of uniform-metallicity models as well documented in the recent Ph.D. thesis of C. Rodríguez-López, we consider the effects of radiative levitation on iron as a means to boost the efficiency of the opacity-driving mechanism in models of J1600+0748. Methods. We combine high sensitivity time-averaged optical spectroscopy and full nonadiabatic calculations to carry out our study. In the first instance, this is used to estimate the location of J1600+0748 in the log $g-T_{\rm eff}$ plane. Given this essential input, we pulsate stellar models consistent with these atmospheric parameters. We construct both uniform-metallicity models and structures in which the iron abundance is specified by the condition of diffusive equilibrium between gravitational settling and radiative levitation. Results. On the basis of NTLE H/He synthetic spectra, we find that the target star has the following atmospheric parameters: log g = 5.93 $\pm$ 0.11, $T_{\rm eff}$ = 71 070 $\pm$ 2725 K, and log N(He)/N(H) = -0.85 $\pm$ 0.08. This takes into account our deconvolution of the spectrum of J1600+0748 as it is polluted by the light of a main sequence companion. We confirm that uniform-metallicity stellar models with Z in the range from 0.02 to 0.10 cannot excite pulsation modes of the kind observed. On the other hand, we find that the inclusion of radiative levitation, as we implemented it, leads to pulsational instabilities in a period range that overlaps with, although it is narrower than, the observed range in J1600+0748. The excited modes correspond to low-order, low-degree p-modes. Conclusions. We infer that radiative levitation is a likely essential ingredient in the excitation physics at work in J1600+0748

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order (NNLO). The resulting thermodynamic potential enables us to evaluate different thermodynamic quantities including pressure and various quark number susceptibilities (QNS). Comparison between our analytic results for those thermodynamic quantities with the available lattice data shows a good agreement.Comment: 5 pages, 6 figures, conference proceedings of XXI DAE-BRNS HEP Symposium, IIT Guwahati, December 2014; to appear in 'Springer Proceedings in Physics Series

Half Semimetallic Antiferromagnetism in the Sr2_2CrTO6_6 System, T=Os, Ru

Double perovskite Sr$_2$CrOsO$_6$ is (or is very close to) a realization of a spin-asymmetric semimetallic compensated ferrimagnet, according to first principles calculations. This type of near-half metallic antiferromagnet is an unusual occurrence, and more so in this compound because the zero gap is accidental rather than being symmetry determined. The large spin-orbit coupling (SOC) of osmium upsets the spin balance (no net spin moment without SOC): it reduces the Os spin moment by 0.27 $\mu_B$ and induces an Os orbital moment of 0.17 $\mu_B$ in the opposite direction. The effects combine (with small oxygen contributions) to give a net total moment of 0.54 $\mu_B$ per cell in \scoo, reflecting a large impact of SOC in this compound. This value is in moderately good agreement with the measured saturation moment of 0.75 $\mu_B$. The value of the net moment on the Os ion obtained from neutron diffraction (0.73 $\mu_B$ at low temperature) differs from the calculated value (1.14 $\mu_B$). Rather surprisingly, in isovalent Sr$_2$CrRuO$_6$ the smaller SOC-induced spin changes and orbital moments (mostly on Ru) almost exactly cancel. This makes Sr$_2$CrRuO$_6$ a "half (semi)metallic antiferromagnet" (practically vanishing net total moment) even when SOC is included, with the metallic channel being a small-band-overlap semimetal. Fixed spin moment (FSM) calculations are presented for each compound, illustrating how they provide different information than in the case of a nonmagnetic material. These FSM results indicate that the Cr moment is an order of magnitude stiffer against longitudinal fluctuations than is the Os moment.Comment: 6 page