Gluon transport equations,plasma oscillations,and screening

The gluon transport equations (Phys. Lett. 177B (1986) 402) are reconsidered to derive a consistent semiclassical limit. Introducing the color current of gluon fluctuations around a classical mean field, we calculate the color permeability function of a collisionless gluon plasma in linear response approximation. The dispersion relations and electric screening length agree with one-loop high temperature QCD results. We find no magnetic screening atO(g ²) and predict transverse magnetic plasma oscillations similar to electric ones. The extension to include particle production by a mean color field is shortly described.     

Estimate of the cosmic ray background in an interferometric antenna for gravitational wave detection

The effect of the cosmic ray interaction in the masses of an interferometric antenna for gravitational wave (GW) detection is evaluated. In a 3 km antenna this background, mainly due to muons gives a limit, for 1 ms GW pulses, of h∼8.5×10^-23 with a frequency of 2×10^-1 events/year and 8.5×10^-26 with 4.1×10^-6 events/year. For GW having frequency>10 Hz the sensitivity limit is h∼1.7×10^-31. This background seems to allow unshielded operation of the interferometer test masses.     

Plasmons in semiconductors and insulators: A simple formula

Based on the dielectric function of an excitonic system, a simple model dielectric function is constructed. The high energy zero of this function yields the plasma frequency, and is given by: (hω_x)² = (hω_f)² + E_x² where ω_f is the free electron plasma frequency and E_x the lowest exciton energy. It is argued that this formula is valid for both, Frenkel and Wannier excitons, and comparison is made with experiments on a variety of crystals, ranging from InSb to Ar. In all cases, surprisingly good agreement is found.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.     

Small x behaviour of the chirally-odd parton distribution h 1(x,Q 2)

The small x behaviour of the structure function h ₁ (x, Q ²) is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small x. The leading one behaves like (1/x)⁰ i.e. it is just a constant in this limit. The second contribution, suppressed by one power of x, includes the terms summed by the GLAP equation. Thus for h ₁ (x, Q ²) the GLAP asymptotics and Regge asymptotics are completely different, making h ₁(x, Q ²) quite an interesting quantity for the study of small x physics.     

The classical field limit of nonrelativistic bosons. I. Borel summability for bounded potentials

We study the classical field limit as $\text{h}\text{?}\text{→ 0}$ of nonrelativistic many-boson systems with two-body interaction in the neighborhood of a fixed ?-independent solution of the classical evolution equation (namely, the Hartree equation). The unitary group describing the evolution of the quantum system, after multiplication from both sides by suitable ?-dependent Weyl operators which somehow subtract out the classical motion, has an expansion in power series of $\text{h}\text{?}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, the zeroth-order term of which describes the quantum fluctuations of the system around the classical motion. We prove that for bounded two-body interaction potentials and small time intervals, this series is strongly Borel summable; namely, it yields a power series which is Borel summable in vector norm when applied to fixed ?-independent vectors taken from a suitable dense set.     

Statistical mechanics characterization of spatio-compositional inhomogeneity

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: (i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), (ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conserved, an upper limit for a pillar height h_max occurs. If due to a further constraint there is the more demanding limit h?h^∗<h_max, the exact number of restricted compositions can be then obtained only through the generating function. However, at least for systems with exclusive composition degrees of freedom, we show that neglecting the h^∗ is not destructive yet for a nice correlation of the h^∗-constrained entropic measure and its less demanding counterpart, which is much easier to compute. Given examples illustrate a broad applicability of the measure and its ability to quantify some of the subtleties of a fractional Brownian motion, time evolution of a quasipattern [A.M. Rucklidge, M. Silber, SIAM J. Appl. Dyn. Syst. 8 (2009) 298 http://www.maths.leeds.ac.uk/~alastair/papers/RS_qp_siads_abs.html; A.M. Rucklidge, M. Silber, Phys. Rev. E 75 (2007) 055203] and reconstruction of a laser-speckle pattern [Y. Jiao, F.H. Stillinger, S. Torquato, Phys. Rev. E 77 031135, (the II part) (2008); Phys. Rev. E 76 031110 (the I part) (2007)], which are hard to discern.     

Deep inelastic lepton-hadron scattering in massive vector gauge models

A class of strong interaction models in which the interactions between fractionally charged colored quarks are mediated by massive neutral vector gluons is considered. All the vector gluons acquire masses via the usual Higgs mechanism. The effective coupling constants $\text{g}$ (gauge coupling) and $\text{h}$ (quartic self-coupling) are supposed to approach a limit cycle in the limit of large space-like momenta. The large Q² behavior of the moments of the deep inelastic lepton-hadron structure functions is analysed using this hypothesis. It is shown that Bjorken scaling is violated by power terms of Q² multiplied by an oscillating function of Q².     

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r ⁶ at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh ⁴ on, also decay as 1/r ⁶. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r ⁶, while the charge correlation decays faster, as 1/r ¹⁰. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.     

Surface-induced finite-size effects for first-order phase transitions

We consider classical lattice models describing first-order phase transitions, and study the finite-size scaling of the magnetization and susceptibility. In order to model the effects of an actual surface in systems such as small magnetic clusters, we consider models with free boundary conditions. For a field-driven transition with two coexisting phases at the infinite-volume transition pointh=h _t , we prove that the low-temperature, finite-volume magnetizationm _free(L, h) per site in a cubic volume of sizeL ^d behaves like $$m_{free} (L,h) = \frac{{m_ + + m_ - }}{2} + \frac{{m_ + - m_ - }}{2}tanh\left[ {\frac{{m_ + - m_ - }}{2}L^d (h - h_\chi (L))} \right] + O\left( {\frac{1}{L}} \right)$$ whereh _x (L) is the position of the maximum of the (finite-volume) susceptibility andm _± are the infinite-volume magnetizations ath=h _t +0 andh=h _t ?0, respectively. We show thath _x (L) is shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t provided the surface free energies of the two phases at the transition point are different. This should be compared with the shift for periodic boundary conditions, which for an asymmetric transition with two coexisting phases is proportional only to 1/L ^2d . One can consider also other definitions of finite-volume transition points, for example, the positionh _U (L) of the maximum of the so-called Binder cumulantU _free(L,h). Whileh _U (L) is again shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t , its shift with respect toh _χ (L) is of the much smaller order 1/L ^2d . We give explicit formulas for the proportionality factors, and show that, in the leading 1/L ^2d term, the relative shift is the same as that for periodic boundary conditions.     

Limit cycle in a bound exciton recombination model in non-equilibrium semiconductors

A non-equilibrium semiconductor model involving the processes of photogeneration of electron-hole pairs (e-h) (rate G), stimulated creation of excitons from e-h (rate constant C) and decay of excitons on recombination centres (rate constant k) is analyzed in this paper for steady states and limit cycle behaviour. Considering the exciton decay to be similar to enzymatic processes in chemical reactions obeying a Michaelis-Menten law, and choosing units such that k = 1 = N, where N is the concentration of recombination centres, the model represents a 2-parameter (C and G) 2-dimensional (exciton and electron-hole concentrations x, n) dynamical system with a unique steady state (x₀,n₀) which is unstable in the region (l ? G)³?4C, the equality sign corresponding to the bifurcation curve in parameter space. In the region (l ? G)³ > 4C the system displays a unique stable limit cycle which is obtained in analytical form by employing a two-time-scales method for parameters in the neighbourhood of the bifurcation curve. The limit cycles are tilted ellipses with angular frequency $\text{}\text{?}$gw of the order of 10⁶ s^?1. In a realistic semiconductor situation G$\text{\$}\text{?}$10^?3.     

Theory of laser-induced gas ionization

The mechanism of laser-induced gas ionization is analyzed in the context of the theories presently available, namely multiphoton and cascade theory, and their predictions are shown to be in serious divergence from experimentation. A novel hypothesis is then formulated which considers the classical photon energy expression ε=hν as the limit of a general expression ε=hν/[1?β_ν f(I)],f(I) being a function of light intensity and β_ν a coefficient such that β_ν f(I) significantly differs from zero only for high-intensity laser light. Starting from the new formulation of the photon energy expression, a theory is developed for the laser ionization phenomenon and a few simple relations are found. The successful use of these relations in the verification of the experimental results suggests that the new photon energy expression has a real physical meaning rather than an empirical significance, and some considerations on the physical meaning are presented.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

The K = 2 band in 24Mg and the point symmetry of the alpha-cluster model state

The failure of previous constrained alpha-cluster model calculations to reproduce the proper symmetry for the K = 2 band in ²⁴M is overcome by an unconstrained variation. The resulting cluster centers have D_2h symmetry but differ from the classical alpha-particle model.     

Q-Operator and Fusion Relations for U q (C (2)(2))

The construction of the Q-operator for twisted affine superalgebra U _q (C ⁽²⁾(2)) is given. It is shown that the corresponding prefundamental representations give rise to evaluation modules some of which do not have a classical limit, which nevertheless appear to be a necessary part of fusion relations.     

An Inverse Problem for Trapping Point Resonances

We consider semi-classical Schrödinger operator P(h) = ? h ²Δ + V(x) in ${{\mathbb R}^n}$ such that the analytic potential V has a non-degenerate critical point x ₀ = 0 with critical value E ₀ and we can define resonances in some fixed neighborhood of E ₀ when h > 0 is small enough. If the eigenvalues of the Hessian are ${\mathbb Z}$ -independent the resonances in h ^δ-neighborhood of E ₀ (δ > 0) can be calculated explicitly as the eigenvalues of the semi-classical Birkhoff normal form. Assuming that potential is symmetric with respect to reflections about the coordinate axes we show that the classical Birkhoff normal form determines the Taylor series of the potential at x ₀. As a consequence, the resonances in a h ^δ-neighborhood of E ₀ determine the first N terms in the Taylor series of V at x ₀. The proof uses the recent inverse spectral results of V. Guillemin and A. Uribe.     

Generation of a dense electron beam in a thin film using an ultraintense femtosecond laser pulse

Electron dynamics in a thin target irradiated with femtosecond laser pulses at an intensity of 10²⁰ W/cm² is studied in the framework of the kinetic theory of laser plasma based on the construction of propagators (in classical limit) for electron and ion distribution functions in plasma. The calculations are performed for real densities and charges of plasma ions. Electrons are partly ejected from the target. The laser pulse energy is predominantly absorbed by electrons, and the electrons are accelerated to relatively high energies.     

A variance formula related to a quantum conductance problem

Let t be a block of an Haar-invariant orthogonal (β=1), unitary (β=2) or symplectic (β=4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for Var(tr(t^∗t)). The case for β=2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit ⁻¹(8β) for β=1,2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.