The effect of initial spatial correlations on late time kinetics of bimolecular irreversible reactions

We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional dispersion equation. As has been previously shown, we demonstrate that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We do so in a fully analytical manner using moment equations. In particular the novel aspect of this work is that we focus on the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. We focus on short range and long (power law) range correlations and demonstrate how long range correlations can give rise to different late time scalings than one would expect purely from the underlying transport model. For the short range correlations the late time scalings deviate from the well mixed t⁻¹$t^{-1}$ and scale like t^−1/2α$t^{-1/2\alpha }$, where 1<α≤2$1<\alpha \le 2$ is the fractional dispersion exponent, in agreement with previous studies. For the long range correlation case it scales like t^−β/2α$t^{-\beta /2\alpha }$, where 0<β<1$0<\beta <1$ is the power law correlation exponent.     

Quantum critical Hall exponents

We investigate a finite size “double scaling” hypothesis using data from an experiment on a quantum Hall system with short range disorder ,  and . For Hall bars of width w at temperature T   the scaling form is w^−μT^−κ$w^{-\mu }{T}^{-\kappa }$, where the critical exponent μ≈0.23$\mu \approx 0.23$ we extract from the data is comparable to the multi-fractal exponent _α0−2${\alpha }_0-2$ obtained from the Chalker–Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal σ-model with m matter fields [5]. The value _ν8=2.60513…${\nu }_8=2.60513\dots$ of the localisation exponent obtained from the m=8$m=8$ model is in excellent agreement with the best available numerical value _νnum=2.607±0.004${\nu }_{\mathrm{num}}=2.607\pm 0.004$ derived from the CC-model [6]. Existing experimental data appear to favour the m=9$m=9$ model, suggesting that the quantum Hall system is not in the same universality class as the CC-model. We discuss the reason this may not be the case, and propose experimental tests to distinguish between the two possibilities.     

On hydrogen transport in the first wall material of fusion devices in the presence of a broadband distribution of traps over the trapping energy

The dynamics of hydrogen dissolved in a sample with continuous distribution of traps over trapping energy φ(ε)∝exp(−αε)$\phi (\epsilon )\propto \exp (-\alpha \epsilon )$ (ε=E/T$\epsilon =E/T$ is the ratio of trapping energy E to the sample's temperature T  ) is considered. Assuming that the hydrogen density is smaller than the trap density and the most of hydrogen is trapped, we found that the dynamics of hydrogen transport can be described by either sub-diffusion or non-linear diffusion equations. Analysis of the outgassing of the sample homogeneously loaded with hydrogen gives, in the most important cases, both power-law, _ΓH∝t^−p${\Gamma }_{\mathrm{H}}\propto t^{-p}$ (p≥1/2$p\ge 1/2$) and exponential, ln(_ΓH)∝−t^α$\ln ({\Gamma }_{\mathrm{H}})\propto -t^{\alpha }$, time dependencies of the outgassing flux, _ΓH(t)${\Gamma }_{\mathrm{H}}(t)$.     

Qubit disentanglement in local squeezed reservoirs

We consider the influence of the local squeezed vacuum fields on two initially entangled two-qubit system. By considering the upper bound of entanglement under time evolution, we find that the decay of the quantum entanglement shows different behavior for different time scales (t?max{(2βA)⁻¹,(2βB)⁻¹}$t?\max \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$ and t?min{(2βA)⁻¹,(2βB)⁻¹}$t?\min \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$). The relative phase of the squeezing environment can also affect the entanglement dynamics profoundly.     

Post-breakthrough scaling in reservoir field simulation

We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group  ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡_μoil/_μwater$m\equiv {\mu }_{oil}/{\mu }_{water}$) and the inter-well (injector-producer) distance r$r$ on the oil production rate C(t)$C\left(t\right)$ and the breakthrough time _tbr$t_{br}$ are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m$m$ and r$r$, _tbr∝r^αm^β$t_{br}\propto r^{\alpha }{m}^{\beta }$, with α=1.8$\alpha =1.8$ and β=−0.25$\beta =-0.25$ for the random porosity type, and α=1.0$\alpha =1.0$ and β=−0.2$\beta =-0.2$ for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝t^γ$P\left(t\right)\propto t^{\gamma }$, with γ=−1.81$\gamma =-1.81$, where P(t)$P\left(t\right)$ is the time derivative of C(t)$C\left(t\right)$. The curves related to different values of m$m$ and r$r$ may be collapsed suggesting a universal behavior for the oil production rate.     

Dynamical properties for a mixed Fermi accelerator model

The behavior of the decay of velocity in a semi-dissipative one-dimensional Fermi accelerator model is considered. Two different kinds of dissipative forces were considered: (i) F∝−v$F\propto -v$ and; (ii) F∝−v²$F\propto -v^2$. We prove the decay of velocity is linear for (i) and exponential for (ii). During the decay, the particles move along specific corridors which are constructed by the borders of the stable manifolds of saddle points. These corridors organize themselves in a very complicated way in the phase space leading the basin of attraction of the sinks to be seemingly of fractal type.     

Statistical anisotropy from vector curvaton in D-brane inflation

We investigate the possibility of embedding the vector curvaton paradigm in D-brane models of inflation in type IIB string theory in a simple toy model. The vector curvaton is identified with the U(1)$U(1)$ gauge field that lives on the world volume of a D3-brane, which may be stationary or undergoing general motion in the internal space. The dilaton is considered as a spectator field which modulates the evolution of the vector field. In this set-up, the vector curvaton is able to generate measurable statistical anisotropy in the spectrum and bispectrum of the curvature perturbation assuming that the dilaton evolves as e^−?∝a²$e^{-?}\propto a^2$ where a(t)$a(t)$ is the scale factor. Our work constitutes a first step towards exploring how such distinctive features may arise from the presence of several light fields that naturally appear in string theory models of cosmology.     

Fisher information,Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |_λc−λ|^−1/4${|{\lambda }_c-\lambda |}^{-1/4}$ around the critical value of the coupling strength _λc${\lambda }_c$ for any value of the parameter β$\beta$.     

Emergence of helicity ±2 modes (gravitons) from qubit models

We construct two quantum qubit models (or quantum spin models) on three-dimensional lattice in space, L-type model and N-type model. We show that, under a controlled approximation, all   the low energy excitations of the L-type model are described by one set of helicity ±2 modes with ω∝k³$\omega \propto k^3$ dispersion. We also argue that all   the low energy excitations of the N-type model are described by one set of helicity ±2 modes with ω∝k$\omega \propto k$ dispersion. In both model, the low energy helicity ±2 modes can be described by a symmetric tensor field _hμν$h_{\mu \nu }$ in continuum limit, and the gaplessness of the helicity ±2 modes is protected by an emergent linearized diffeomorphism gauge symmetry _hμν→_hμν+_∂μfν+_∂νfμ$h_{\mu \nu }\to h_{\mu \nu }+{\partial }_{\mu }{f}_{\nu }+{\partial }_{\nu }{f}_{\mu }$ at low energies. Thus the linearized quantum gravity emerge from our lattice models  . It turns out that the low energy effective Lagrangian density of the L-type model is invariant under the linearized diffeomorphism gauge transformation. Such a property protects the gapless ω∝k³$\omega \propto k^3$ helicity ±2 modes. In contrast, the low energy effective Lagrangian of the N-type model changes by a boundary term under the linearized diffeomorphism gauge transformation. Such a property protects the gapless ω∝k$\omega \propto k$ helicity ±2 modes. From many-body physics point of view, the ground states of the our two qubit model represent new states of quantum matter, whose low energy excitations are all described by one set of gapless helicity ±2 modes.     

Scattering rates for leptogenesis: Damping of lepton flavour coherence and production of singlet neutrinos

Using the Closed Time Path (CTP) approach, we perform a systematic leading order calculation of the relaxation rate of flavour correlations of left-handed Standard Model leptons. This quantity is of pivotal relevance for flavoured leptogenesis in the Early Universe, and we find it to be 5.19×10⁻³T$5.19\times {10}^{-3}T$ at T=10⁷ GeV$T={10}^7\text{GeV}$ and 4.83×10⁻³T$4.83\times {10}^{-3}T$ at T=10¹³ GeV$T={10}^{13}\text{GeV}$, in substantial agreement with estimates used in previous phenomenological analyses. These values apply to the Standard Model with a Higgs-boson mass of 125 GeV$125\text{GeV}$. The dependence of the numerical coefficient on the temperature T is due to the renormalisation group running. The leading linear and logarithmic dependencies of the flavour relaxation rate on the gauge and top-quark couplings are extracted, such that the results presented in this work can readily be applied to extensions of the Standard Model. We also derive the production rate of light (compared to the temperature) sterile right-handed neutrinos, a calculation that relies on the same methods. We confirm most details of earlier results, but find a substantially larger contribution from the t-channel exchange of fermions.     

Uncertainty relations in quantum optics. Is the photon intelligent?

The Robertson–Schrödinger, Heisenberg–Robertson and Trifonov uncertainty relations for arbitrary two functions f₁$f_1$ and f₂$f_2$ depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties (Δf₁)²⋅(Δf₂)²${\left(\Delta f_1\right)}^2\cdot {\left(\Delta f_2\right)}^2$ or the sum (Δf₁)²+(Δf₂)²${\left(\Delta f_1\right)}^2+{\left(\Delta f_2\right)}^2$ are investigated for the cases f₁=?,exp(i?),exp(−i?),cos?,sin?$f_1=?,exp\left(i?\right),exp(-i?),cos?,sin?$ and f₂=n$f_2=n$.     

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.     

Jack polynomial fractional quantum Hall states and their generalizations

In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=−(r−1)/(k+1)$\alpha =-(r-1)/(k+1)$, (r−1)$(r-1)$ and (k+1)$(k+1)$ relatively prime, and with partition given in terms of its frequencies by [n₀^0(r−1)sk^0r−1k^0r−1k?^0r−1m]$[n_0{0}^{(r-1)s}k{0}^{r-1}k{0}^{r-1}k?0^{r-1}m]$ satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.     

Generalized Weyl quantization on the cylinder and the quantum phase

Generalized Weyl quantization formalism for the cylindrical phase space S¹×R¹$S^1\times {\mathbb{R}}^1$ is developed. It is shown that the quantum observables relevant to the phase of the linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space L²(S¹)$L^2\left(S^1\right)$.     

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F∝−v^γ$F\propto -v^{\gamma }$. The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton’s second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for γ=1$\gamma =1$; (ii) exponential for γ=2$\gamma =2$; and (iii) second-degree polynomial type for γ=1.5$\gamma =1.5$. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.     

Dark matter annihilation in the Galactic Center as seen by the Fermi Gamma Ray Space Telescope

We analyze the first two years of data from the Fermi Gamma Ray Space Telescope from the direction of the inner 10° around the Galactic Center with the intention of constraining, or finding evidence of, annihilating dark matter. We find that the morphology and spectrum of the emission between 1.25° and 10° from the Galactic Center is well described by the processes of decaying pions produced in cosmic ray collisions with gas, and the inverse Compton scattering of cosmic ray electrons in both the disk and bulge of the Inner Galaxy, along with gamma rays from known points sources in the region. The observed spectrum and morphology of the emission within approximately 1.25° (∼175 parsecs) of the Galactic Center, in contrast, departs from the expectations for by these processes. Instead, we find an additional component of gamma ray emission that is highly concentrated around the Galactic Center. The observed morphology of this component is consistent with that predicted from annihilating dark matter with a cusped (and possibly adiabatically contracted) halo distribution (ρ∝r−γ$\rho \propto r^{-\gamma }$, with γ=1.18$\gamma =1.18$ to 1.33). The observed spectrum of this component, which peaks at energies between 1–4 GeV (in E²$E^2$ units), can be well fit by a 7–10 GeV dark matter particle annihilating primarily to tau leptons with a cross section in the range of 〈σv〉=4.6×¹⁰⁻²⁷$〈\sigma v〉=4.6\times {10}^{-27}$ to 5.3×¹⁰⁻²⁶ cm³/s$5.3\times {10}^{-26}{\text{cm}}^3/\text{s}$, depending on how the dark matter distribution is normalized. We also discuss other sources for this emission, including the possibility that much of it originates from the Milky Way?s supermassive black hole.     

Constraints on sub-GeV hidden sector gauge bosons from a search for heavy neutrino decays

Several models of dark matter motivate the concept of hidden sectors consisting of SU_(3)C×SU_(2)L×U_(1)Y$\mathit{SU}{(3)}_C\times \mathit{SU}{(2)}_L\times U{(1)}_Y$ singlet fields. The interaction between our and hidden matter could be transmitted by new abelian U^′(1)$U^{\prime }(1)$ gauge bosons A^′$A^{\prime }$ mixing with ordinary photons. If such A^′$A^{\prime }$?s with the mass in the sub-GeV range exist, they would be produced through mixing with photons emitted in decays of η   and η^′${\eta }^{\prime }$ neutral mesons generated by the high energy proton beam in a neutrino target. The A^′$A^{\prime }$?s would then penetrate the downstream shielding and be observed in a neutrino detector via their A^′→e⁺e⁻$A^{\prime }\to e^{+}{e}^{-}$ decays. Using bounds from the CHARM neutrino experiment at CERN that searched for an excess of e⁺e⁻$e^{+}{e}^{-}$ pairs from heavy neutrino decays, the area excluding the γ−A^′$\gamma -A^{\prime }$ mixing range 10⁻⁷???10⁻⁴${10}^{-7}???{10}^{-4}$ for the A^′$A^{\prime }$ mass region 1?_MA′?500 MeV$1?M_{A^{\prime }}?500\text{MeV}$ is derived. The obtained results are also used to constrain models, where a new gauge boson X   interacts with quarks and leptons. New upper limits on the branching ratio as small as Br(η→γX)?10⁻¹⁴$\mathrm{Br}(\eta \to \gamma X)?{10}^{-14}$ and Br(η^′→γX)?10⁻¹²$\mathrm{Br}({\eta }^{\prime }\to \gamma X)?{10}^{-12}$ are obtained, which are several orders of magnitude more restrictive than the previous bounds from the Crystal Barrel experiment.     

Short-time quantum propagator and Bohmian trajectories

We begin by giving correct expressions for the short-time action following the work Makri–Miller. We use these estimates to derive an accurate expression modulo Δt²$\mathrm{\Delta }{t}^2$ for the quantum propagator and we show that the quantum potential is negligible modulo Δt²$\mathrm{\Delta }{t}^2$ for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.     

Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold

We use Monte Carlo to investigate the Berezinskii–Kosterlitz–Thouless transition close to the site percolation threshold in a square lattice. Several thermodynamic quantities are calculated for lattice sizes L×L$L\times L$, from 16<L<640$16<L<640$. Our results are consistent with an infinite order transition for any value of the concentration of magnetic sites. We found that close to the critical percolation concentration, _pc$p_c$ (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as _TBKT∝(p−_pc)^0.908$T_{\mathit{BKT}}\propto {(p-p_c)}^{0.908}$ and the specific heat behaves as _Tsh∝p^1.133$T_{sh}\propto p^{1.133}$.