Regularization schemes and the multiplicative anomaly

Elizalde, Vanzo, and Zerbini have shown that the effective action of two free Euclidean scalar fields in flat space contains a `multiplicative anomaly' when zeta-function regularization is used. This is related to the Wodzicki residue. I show that there is no anomaly when using a wide range of other regularization schemes and further that this anomaly can be removed by an unusual choice of renormalisation scales. I define new types of anomalies and show that they have similar properties. Thus multiplicative anomalies encode no novel physics. They merely illustrate some dangerous aspects of zeta-function and Schwinger proper time regularization schemes.Comment: 11 pages, LaTeX2e, major revision 15th December 1998 with focus now on renormalisation scales. Appendix and a few minor comments included which are not in Phys.Lett.B. published versio

Non-perturbative calculations of a global U(1) theory at finite density and temperature

We use an optimised hopping parameter expansion for the free energy (linear delta expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first order as the chemical potential increases.Comment: 24 pages, 11 figure

Representation of nonequilibrium steady states in large mechanical systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.Comment: 27 pages, 3 figure

Gender and race distribution of dental graduates (1985 - 2004) and first year dental students (2000 - 2005) in South Africa

This paper, written at the close of a decade of democracy in South Africa, sets out to analyse the demographic profile of dental graduates from 1985-2004 at the five Faculties/Schools of Dentistry in South Africa. A comparison of the profiles for the pre-democracy (1985-1994) and post-apartheid (1995-2004) periods has been made. The demographic profile of first year dental students from 2000-2005 is also presented. From 1985-1994, most dental graduates were male (79%), but this changed substantially from 1995-2004, with females comprising 46% of those graduating. In the pre-democracy period, more than three-quarters of all graduates were White (78%), decreasing to 46% in the post-apartheid period under review. Black graduates increased from 6% to 24% across the two study periods. Amongst the first year dental student intake from 2000- 2005, females comprised 57%. There was an almost equal distribution across the White, Black and Asian groups. Dental faculties/schools have made important strides in transforming the demographic profile of their students. The percentage of Black graduates, however, needs to be significantly increased if it is to reflect the national population. Faculties/schools must further ensure that able students from working class background are identified and considered for acceptance into the undergraduate dental programme, and should then be offered the necessary academic and mentoring support to enable success

Thermal Green Functions at Zero Energy

The thermal expectation values of all possible bosonic generalised retarded functions evaluated at zero energy are studied. The relationship of such functions to calculational schemes, technical problems and physical applications is outlined. It is then shown that all generalised retarded functions constructed from any one set of bosonic fields are equal at zero energy. This is done completely generally and is not limited to any approximation scheme such as perturbation theory.Comment: 16 pages, LaTeX (no figures), available through anonymous ftp as LaTeX from ftp://euclid.tp.ph.ic.ac.uk/papers/94-5_26.tex or as LaTeX or postscript at http://euclid.tp.ph.ic.ac.uk/Papers/index.htm

Wick's Theorem at Finite Temperature

We consider Wick's Theorem for finite temperature and finite volume systems. Working at an operator level with a path ordered approach, we show that contrary to claims in the literature, expectation values of normal ordered products can be chosen to be zero and that results obtained are independent of volume. Thus the path integral and operator approaches to finite temperature and finite volume quantum field theories are indeed seen to be identical. The conditions under which normal ordered products have simple symmetry properties are also considered.Comment: 15 pages, LaTeX (no figures), available through anonymous ftp as LaTeX from ftp://euclid.tp.ph.ic.ac.uk/papers/95-6_18.tex or as LaTeX or postscript at http://euclid.tp.ph.ic.ac.uk/Papers/index.htm

The Emergence of Leadership in Social Networks

We study a networked version of the minority game in which agents can choose to follow the choices made by a neighbouring agent in a social network. We show that for a wide variety of networks a leadership structure always emerges, with most agents following the choice made by a few agents. We find a suitable parameterisation which highlights the universal aspects of the behaviour and which also indicates where results depend on the type of social network.Comment: 22 pages (as in Physica A but with a few extra references to supplementary material) plus 11 pages of supplementary material not in Physica A versio

A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.Comment: 34 pages, Revte

Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which "heat" is replaced by the "excess heat", is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komtatsu et al.Comment: 19 pages, 2 figure

Identity of the imaginary-time and real-time thermal propagators for scalar bound states in a one-generation Nambu-Jona-Lasinio model

By rigorous reanalysis of the results, we have proven that the propagators at finite temperature for scalar bound states in one-generation fermion condensate scheme of electroweak symmetry breaking are in fact identical in the imaginary-time and the real-time formalism. This dismisses the doubt about possible discrepancy between the two formalisms in this problem. Identity of the derived thermal transformation matrices of the real-time matrix propagators for scalar bound states without and with chemical potential and the ones for corresponding elementary scalar particles shows similarity of thermodynamic property between the two types of particles. Only one former inference is modified, i.e. when the two flavors of fermions have unequal nonzero masses, the amplitude of the composite Higgs particle will decay instead grow in time.Comment: 5 pages, revtex4, no figure