The 3-graviton vertex function in thermal quantum gravity

The high temperature limit of the 3-graviton vertex function is studied in thermal quantum gravity, to one loop order. The leading ($T^4$) contributions arising from internal gravitons are calculated and shown to be twice the ones associated with internal scalar particles, in correspondence with the two helicity states of the graviton. The gauge invariance of this result follows in consequence of the Ward and Weyl identities obeyed by the thermal loops, which are verified explicitly.Comment: 19 pages, plain TeX, IFUSP/P-100

A general theory of DNA-mediated and other valence-limited interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure

Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

Nonlinear interaction between electromagnetic fields at high temperature

The electron-positron `box' diagram produces an effective action which is fourth order in the electromagnetic field. We examine the behaviour of this effective action at high-temperature (in analytically continued imaginary-time thermal perturbation theory). We argue that there is a finite, nonzero limit as $T\rightarrow \infty$ (where $T$ is the temperature). We calculate this limit in the nonrelativistic static case, and in the long-wavelength limit. We also briefly discuss the self-energy in 2-dimensional QED, which is similar in some respects.Comment: 13 pages, DAMTP 94/3

Non-linear electromagnetic interactions in thermal QED

We examine the behavior of the non-linear interactions between electromagnetic fields at high temperature. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T tends to infinity. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.Comment: 7 pages, IFUSP/P-111

On the Infrared Behavior of the Pressure in Thermal Field Theories

We study non-perturbatively, via the Schwinger-Dyson equations, the leading infrared behavior of the pressure in the ladder approximation. This problem is discussed firstly in the context of a thermal scalar field theory, and the analysis is then extended to the Yang-Mills theory at high temperatures. Using the Feynman gauge, we find a system of two coupled integral equations for the gluon and ghost self-energies, which is solved analytically. The solutions of these equations show that the contributions to the pressure, when calculated in the ladder approximation, are finite in the infrared domain.Comment: 20 pages plus 4 figures available by request, IFUSP/P-100

Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids

The traditional view that the physical properties of a simple liquid are determined primarily by its repulsive forces was recently challenged by Berthier and Tarjus, who showed that in some cases ignoring the attractions leads to large errors in the dynamics [L. Berthier and G. Tarjus, Phys. Rev. Lett. 103, 170601 (2009); J. Chem. Phys. 134, 214503 (2011)]. We present simulations of the standard Lennard-Jones liquid at several condensed-fluid state points, including a fairly low density state and a very high density state, as well as simulations of the Kob-Andersen binary Lennard-Jones mixture at several temperatures. By varying the range of the forces, results for the thermodynamics, dynamics, and structure show that the determining factor for getting the correct statics and dynamics is not whether or not the attractive forces {\it per se} are included in the simulations. What matters is whether or not interactions are included from all particles within the first coordination shell (FCS) - the attractive forces can thus be ignored, but only at extremely high densities. The recognition of the importance of a local shell in condensed fluids goes back to van der Waals; our results confirm this idea and thereby the basic picture of the old hole- and cell theories for simple condensed fluids

The Dirac Sea

We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard Fock space construction.Comment: 7 page

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.Comment: 19 pages, 13 figure