Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {stackrel {lambda_0}{rightarrow}}~ 3 V;$ and $V {stackrel {mu}{rightarrow}}~P$, $U {stackrel { u}{ri
ghtarrow}}~ Q$, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces $n rightarrow n$ molecular interaction processes with $n geq 4$, where $n$ is the number of molecules participating of type $U$ or $V$. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state $sigma = phi_u phi_v^2$, where $phi_i$ corresponds to the fields representing the densities of $U$ and $V$. Finally, we discuss the difference between representing $sigma$ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension we find that while they show markedly different behavior in the short spatio-temporal scale, high momentum (UV) limit, they are formally equivalent in the large spatio-temporal scale, low momentum (IR) regime. On the other hand in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite $sigma$. Thus in this regime $sigma$ behave as an entity unto itself suggesting that it can be effectively treated as an independent chemical species.
We give a first principles derivation of the stochastic partial differential equations that describe the chemical reactions of the Gray-Scott model (GS): $U+2V {stackrel {lambda}{rightarrow}} 3 V;$ and $V {stackrel {mu}{rightarrow}} P$, $U {stackrel
{ u}{rightarrow}} Q$, with a constant feed rate for $U$. We find that the conservation of probability ensured by the chemical master equation leads to a modification of the usual differential equations for the GS model which now involves two composite fields and also intrinsic noise terms. One of the composites is $psi_1 = phi_v^2$, where $ < phi_v >_{eta} = v$ is the concentration of the species $V$ and the averaging is over the internal noise $eta_{u,v,psi_1}$. The second composite field is the product of three fields $ chi = lambda phi_u phi_v^2$ and requires a noise source to ensure probability conservation. A third composite $psi_2 = phi_{u} phi_{v}$ can be also be identified from the noise-induced reactions. The Hamiltonian that governs the time evolution of the many-body wave function, associated with the master equation, has a broken U(1) symmetry related to particle number conservation. By expanding around the (broken symmetry) zero energy solution of the Hamiltonian (by performing a Doi shift) one obtains from our path integral formulation the usual reaction diffusion equation, at the classical level. The Langevin equations that are derived from the chemical master equation have multiplicative noise sources for the density fields $phi_u, phi_v, chi$ that induce higher order processes such as $n rightarrow n$ scattering for $n > 3$. The amplitude of the noise acting on $ phi_v$ is itself stochastic in nature.
We discuss the mean-field theories obtained from the leading order in a large-$N$ approximation for one- and two- component dilute Bose gases. For a one-component Bose gas this approximation has the following properties: the Bose-Einstein condensatio
n (BEC) phase transition is second order but the critical temperature $T_c$ is not shifted from the non-interacting gas value $T_0$. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intra- species interactions and focus on the stability of the mixture state above $T_c$. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the inter-species interaction strength to the intra-species interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.
LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this paper we calculate the cross sections for top quark production
from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, higgs or supersymmetry) at the LHC may be an useful signature for black hole production.
We consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to other func
tions which are pre-factors and post-factors when the domain of integration of the argument of that function is from -infty to +infty. This shift theorem is useful to perform certain integrals and path integrals involving the exponential of sum of two non-commuting operators.
We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter alpha. We determine the transverse mom
entum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter alpha used to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter alpha independent.
If the fundamental Planck scale is near a TeV, then we should expect to see TeV scale black holes at the LHC. Similarly, if the scale of supersymmetry breaking is sufficiently low, then we might expect to see light supersymmetric particles in the nex
t generation of colliders. If the mass of the supersymmetric particle is of order a TeV and is comparable to the temperature of a typical TeV scale black hole, then such sparticles will be copiously produced via Hawking radiation: The black hole will act as a resonance for sparticles, among other things. In this paper we compared various signatures for SUSY production at LHC, and we contrasted the situation where the sparticles are produced directly via parton fusion processes with the situation where they are produced indirectly through black hole resonances. We found that black hole resonances provide a larger source for heavy mass SUSY (squark and gluino) production than the direct pQCD-SUSY production via parton fusion processes depending on the values of the Planck mass and blackhole mass. Hence black hole production at LHC may indirectly act as a dominant channel for SUSY production. We also found that the differential cross section dsigma/dp_t for SUSY production increases as a function of the p_t (up to p_t equal to about 1 TeV or more) of the SUSY particles (squarks and gluinos), which is in sharp contrast with the pQCD predictions where the differential cross section dsigma/dp_t decreases as p_t increases for high p_t about 1 TeV or higher. This is a feature for any particle emission from TeV scale blackhole as long as the temperature of the blackhole is very high (~ TeV). Hence measurement of increase of dsigma/dp_t with p_t for p_t up to about 1 TeV or higher for final state particles might be a useful signature for blackhole production at LHC.
If the fundamental Planck scale is near a TeV, then parton collisions with high enough center-of-mass energy should produce black holes. The production rate for such black holes has been extensively studied for the case of a proton-proton collision a
t sqrt s = 14 TeV and for a lead-lead collision at sqrt s = 5.5 TeV at LHC. As the parton energy density is much higher at lead-lead collisions than in pp collisions at LHC, one natural question is whether the produced black holes will be able to absorb the partons formed in the lead-lead collisions and eventually `eat the quark-gluon plasma formed at LHC. In this paper, we make a quantitative analysis of this possibility and find that since the energy density of partons formed in lead-lead collisions at LHC is about 500 GeV/fm^3, the rate of absorption for one of these black holes is much smaller than the rate of evaporation. Hence, we argue that black holes formed in such collisions will decay very quickly, and will not absorb very many nearby partons. More precisely, we show that for the black hole mass to increase via parton absorption at the LHC the typical energy density of quarks and gluons should be of the order of 10^{10} GeV/fm^3. As LHC will not be able to produce such a high energy density partonic system, the black hole will not be able to absorb a sufficient number of nearby partons before it decays. The typical life time of the black hole formed at LHC is found to be a small fraction of a fm/c.
The phase diagram of the Gross-Neveu (G-N) model in 2+1 dimensions as a function of chemical potential and temperature has a simple curve separating the broken symmetry and unbroken symmetry phases, with chiral symmetry being restored both at high te
mperature and high density. We study, in leading order in the 1/N expansion, the dynamics of the chiral phase transition for an expanding plasma of quarks in the Gross-Neveu model in 2+1 dimensions assuming boost invariant kinematics. We compare the time evolution of the order parameter (mass of the fermion) for evolutions starting in the unbroken and broken phases. The proper time evolution of the order parameter resembles previous results in the 1+1 dimensional G-N model in the same approximation. The time needed to traverse the transition is insensitive to mu.
