QCD Thermodynamics at Intermediate Coupling

The weak-coupling expansion of the QCD free energy is known to order g_s^6log{g_s}, however, the resulting series is poorly convergent at phenomenologically relevant temperatures. In this proceedings, I discuss hard-thermal-loop perturbation theory (HTLpt) which is a gauge-invariant reorganization of the perturbative expansion for gauge theories. I review a recent NNLO HTLpt calculation of QCD thermodynamic functions. I show that the NNLO HTLpt results are consistent with lattice data down to temperatures T~2T_c.Comment: 3 pages, 2 figures; talk given at the conference "Quark Confinement and the Hadron Spectrum IX", August 30 - September 3, 2010, Madrid, Spain; to appear in the AIP proceeding

A brief overview of hard-thermal-loop perturbation theory

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.Comment: 20 pages, 11 figures; Review article for the program on "AdS/CFT and Novel Approaches to Hadron and Heavy Ion Physics", October 11 - December 3, 2010, Kavli Institute for Theoretical Physics China (KITPC), Chinese Academy of Sciences (CAS), Beijing, China. Published version in Communications in Theoretical Physic

The quark mass gap in strong magnetic fields

Quarks in strong magnetic fields (|eB|>>Lambda_QCD^2 ~ 0.04 GeV^2) acquire enhanced infrared phase space proportional to |eB|. Accordingly they provide larger chiral condensates and stronger backreactions to the gluon dynamics. Confronting theories with lattice data at various values of |eB|, one can test theoretical ideas as well as validity of various approximations, domain of applicability of the effective models, and so on. The particularly interesting findings on the lattice are inverse magnetic catalysis and linear growth of the chiral condensate as a function of |eB|, which pose theoretical challenges. In this talk we propose a scenario to explain both phenomena, claiming that the quark mass gap should stay at around ~ Lambda_QCD, instead of ~|eB|^{1/2} which has been supposed from dimensional arguments and/or effective model calculations. The contrast between infrared and ultraviolet behaviors of the interaction is a key ingredient to obtain the mass gap of ~Lambda_QCD.Comment: 4 pages, proceedings of the XXIV Quark Matter conference, May 19-24 2014, Darmstadt (Germany

Massless Mode and Positivity Violation in Hot QCD

We calculate the quark self-energy at one-loop level at high temperature, taking into account contributions from both the (chromo)electric scale $gT$ and the (chromo)magnetic scale $g^2T$. While reproducing standard massive excitations due to the electric scale, we uncover a novel massless excitation ascribable to the magnetic scale. The residue of this massless excitation is nonpositive at all temperatures, which consequently gives rise to positivity violation in the quark spectral functions. This demonstrates the profound impact of confinement effects on thermal quark collective excitations, which manifest genuine long-range correlations in the system.Comment: 5 pages, 2 figures; v3 - published versio

QED Thermodynamics at Intermediate Coupling

We discuss reorganizing finite temperature perturbation theory using hard-thermal-loop (HTL) perturbation theory in order to improve the convergence of successive perturbative approximations to the free energy of a gauge theory. We briefly review the history of the technique and present new results for the three-loop HTL-improved approximation for the free energy of QED. We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at intermediate coupling, e ~ 2. The reorganization is gauge invariant by construction, and due to cancellation among various contributions, one can obtain a completely analytic result for the resummed thermodynamic potential at three loops.Comment: 8 pages, 3 figures, Proceedings contribution to "Three Days of Strong Interactions", Wroclaw (Poland), July 200

New Results in Multivariate Time Series with Applications

This dissertation presents some new results in stationary multivariate time series. The asymptotic properties of the sample autocovariance are established, that is, we derive a multivariate version of Bartlett\u27s Classic Formula. The estimation of the autocovariance function plays a crucial role in time series analysis, in particular for the identification problem. Explicit formula for vector autoregressive $(p)$ and vector moving average $(q)$ processes are presented as examples. We also address linear processes driven by non-independent errors, a feature that permits consideration of multivariate GARCH processes. We next compare several techniques to discriminate two multivariate stationary signals. The compared methods include Gaussian likelihood ratio variance/covariance matrix tests and spectral-based tests gauging equality of the autocovariance function of the two signals. A simulation study is presented that illuminates the various properties of the methods. An analysis of experimentally collected gearbox data is also presented

Decentralized control of large flexible structures by joint decoupling

A decentralized control design method is presented for large complex flexible structures by using the idea of joint decoupling. The derivation is based on a coupled substructure state-space model, which is obtained from enforcing conditions of interface compatibility and equilibrium to the substructure state-space models. It is shown that by restricting the control law to be localized state feedback and by setting the joint actuator input commands to decouple joint 'degrees of freedom' (dof) from interior dof, the global structure control design problem can be decomposed into several substructure control design problems. The substructure control gains and substructure observers are designed based on modified substructure state-space models. The controllers produced by the proposed method can operate successfully at the individual substructure level as well as at the global structure level. Therefore, not only control design but also control implementation is decentralized. Stability and performance requirement of the closed-loop system can be achieved by using any existing state feedback control design method. A two-component mass-spring damper system and a three-truss structure are used as examples to demonstrate the proposed method

The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $\alpha$.Comment: 13 pages, 13 figure