Point Particle Case Research Articles

Effective field theory for binary cosmic strings

We extend the effective field theory (EFT) formalism for gravitational radiation from a binary system of compact objects to the case of extended objects. In particular, we study the EFT for a binary system consisting of two infinitely-long cosmic strings with small velocity and small spatial substructure, or "wiggles". The complexity of the system requires the introduction of two perturbative expansion parameters, constructed from the velocity and size of the wiggles, in contrast with the point particle case, for which a single parameter is sufficient. This further requires us to assign new power counting rules in the system. We integrate out the modes corresponding to potential gravitons, yielding an effective action for the radiation gravitons. We show that this action describes a changing quadrupole, sourced by the bending modes of the string, which in turn generates gravitational waves. We study the ultraviolet divergences in this description, and use them to obtain the classical renormalization group flow of the string tension in such a setting.

Surprisingly large uncertainties in temperature extraction from thermal fits to hadron yield data at LHC

The conventional hadron-resonance gas (HRG) model with the Particle Data Group hadron input, full chemical equilibrium, and the hadron-type dependent eigenvolume interactions, is employed to fit the hadron midrapidity yield data of the ALICE collaboration for the most central Pb+Pb collisions. For the case of point-like hadrons, the well-known fit result is reproduced. However, the situation changes if the hadrons have different eigenvolumes. In the case when all the mesons are point-like while all the baryons have an effective hardcore radius of 0.3 fm, the temperature dependence of has a broad minimum in the temperature range of 155−210 MeV, with a fit quality comparable to the minimum in the point-particle case. A very similar result is obtained when only baryon–baryon eigenvolume interactions are considered, with the eigenvolume parameter taken from the previous fit to the ground state of nuclear matter. Finally, when we apply the eigenvolume corrections with a mass-proportional eigenvolume , fixed to a particular hardcore proton radius rp, we observe a second minimum in the temperature dependence of , located at significantly higher temperatures. For instance, at rp = 0.5 fm, the fit quality is better than in the point-particle HRG case in a very wide temperature range of 170−320 MeV, which creates uncertainty in the temperature determination from the fit to the data of 150 MeV. These results show that thermal fits to the heavy-ion hadron yield data are very sensitive to the modeling of the short-range repulsion eigenvolume between hadrons, and that the chemical freeze-out temperature can only be extracted from the LHC hadron yield data with sizable uncertainty.

Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs.

Smearing effect due to the spread of a probe particle on the Brownian motion near a perfectly reflecting boundary

Quantum fluctuations of electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time-direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$-component, $ < \D v_{z}^{2}>$, for the wave-packet case is quite different from the test point-particle case ($z$ is the coordinate normal to the plate). The result for the wave-packet is $<\D v_{z}^{2} > \sim 1/\t^2$ in the late time ($\t$ is the measuring time), in stead of the reported late-time behavior $<\D v_{z}^{2} > \sim 1/z^2$ for a point-particle probe. This result can be quite significant for further investigations on the measurement of vacuum fluctuations.

Onset of diffusive behavior in confined transport systems

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size, modeling simple microporous membranes. It is well established that the point-particle case displays anomalous transport, because of slow correlation decay in the absence of defocusing collisions. We investigate which features of point-particle transport survive in the case of finite-sized particles (which undergo defocusing collisions). A similar question was investigated by Lansel, Porter, and Bunimovich [Chaos 16, 013129 (2006)], who found that certain integrals of motion and multiple ergodic components, characteristic of the point-particle case, remain in "mushroom"-like systems with few finite-sized particles. We quantify the time scales over which the transport of disks shows features typical of the point particles, or is driven toward diffusive behavior. In particular, we find that interparticle collisions drive the system toward diffusive behavior more strongly than defocusing boundary collisions. We illustrate how, and at what stage, typical thermodynamic behavior (consistent with kinetic theory) is observed, as particle numbers grow and mean free paths diminish. These results have both applied (e.g., nanotechnological) and theoretical interest.

Null strings in Schwarzschild spacetime

The null string equations of motion and constraints in Schwarzschild spacetime are given. The solutions are those of the null geodesics of general relativity appended by a null string constraint in which the ``constants of motion'' depend on the world-sheet spatial coordinate. Because of the extended nature of a string, the physical interpretation of the solutions is completely different from the point particle case. In particular, a null string is generally not propagating in a plane through the origin, although each of its individual points is. Some special solutions are obtained and their physical interpretation is given. Especially, the solution for a null string with a constant radial coordinate $r$ moving vertically from the south pole to the north pole around the photon sphere is presented. A general discussion of classical null or tensile strings as compared to massless or massive particles is given. For instance, tensile circular solutions with a constant radial coordinate $r$ do not exist at all. The results are discussed in relation to the previous literature on the subject.

Ion–ion correlations in polyelectrolyte solutions: Hard sphere counterions

The intimately related mechanisms of macroion screening and ion–ion correlations in electrolyte solutions are investigated with the aim to explore the simplest theoretical estimations of the latter on the former. The Poisson–Boltzmann theory of macroion screening in electrolyte solutions was developed under two important assumptions. Specifically, the correlated motion of the mobile ions is ignored by identifying the mean field electrostatic potential with the potential of average force and, moreover, only point charges are considered so that finite size effects are not accounted for. Utilizing the generalized van der Waals free energy density functional formulation for inhomogeneous fluids, we obtain simple corrections to the Poisson–Boltzmann result where both these mechanisms are treated in local and nonlocal approximations. By incorporating a somewhat more realistic short range repulsive interaction, the asymptotic instability encountered in the point particle case is avoided and self-consistent density profiles can be computed. Nonlocal approximations are shown to be thermodynamically consistent in terms of the contact theorem for the osmotic pressure, and excellent agreement with Monte Carlo simulation is achieved even at high electrostatic coupling and with large particles.

TOPOLOGICAL SPIN-STATISTICS THEOREMS FOR STRINGS

Recently, a topological proof of the spin-statistics theorem has been proposed for a system of point particles. It does not require relativity or field theory, but assumes the existence of antiparticles. We extend this proof to a system of string loops in three space dimensions and show that by assuming the existence of antistring loops, one can prove a spin-statistics theorem for these string loops. According to this theorem, all unparametrized strings (such as flux tubes in superconductors and cosmic strings) should be quantized as bosons. Also, as in the point particle case, we find that the theorem excludes non-Abelian statistics.

Bilinear Hydrodynamics and the Stokes-Einstein Law

The autocorrelation function of the density of a tagged particle is studied using the Mori formalism. The variables used are the collective conserved variables, the tagged-particle density, and bilinear products thereof. The case of point particles is considered in two dimensions, and, in three dimensions, self-diffusion by a particle of arbitrary size is treated. It is found that the bilinear-hydrodynamic approach automatically separates the self-diffusion coefficient of the tagged particle into a nonhydrodynamic part, and a hydrodynamic part which resembles the Stokes-Einstein law. In two dimensions, it is found that the mean-square displacement of a particle increases as $t\mathrm{ln}t$, and that certain natural redefinitions of the diffusion and friction coefficients leave Einstein's law invariant. In three dimensions, for a large particle, the Stokes-Einstein law is reproduced. The relation between the well-known ${t}^{(\frac{\ensuremath{-}3}{2})}$ "tails" on correlation functions, and the Stokes-Einstein law, is discussed.