Four particle harmonic-oscillator transformation brackets and their simplifications for special values of the mass-ratio parameters

We present a new independent scheme of SO(3) group transformations suitable for the N particle system, composed of N − 1 and 1 particle subsystems, where N − 1 particles have their own intrinsic clusterization. The simple expressions for corresponding four-particle harmonic-oscillator transformation brackets are presented, as well as their simplifications for the special values of mass ratio parameters d = 0, d → ∞ and d ₁ = 0, d ₁ → ∞.     

Exponents and logarithms of the Potts model through a 1D quantum hamiltonian

Exact solution of the one-dimensional quantumq-state Potts model for finite chains and subsequent finite-size analysis yields values for the thermal critical exponenty=1/v forq=3 andq=4. By taking into account the shift of the critical point due to the finite size we obtainy=1.48±0.01 forq=4 in good agreement with they=3/2 conjectured by den Nijs. Using the conjecture of den Nijs we find evidence for a logarithmic factor forq=4 but not forq=3.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Effect of variations in peptide parameters and charges on the unperturbed dimensions of polypeptide chains

The net charges on various atoms of poly (l-alanine), polyglycine, poly (N-methyl-l-alanine) and poly (N-methylglycine) were computed using the MOLCAO method of Del Re forσ charges and the Hückel MO method forπ charges. The characteristic ratiosC _∞ were computed for all the above polypeptide chains, with different sets of parameters for the peptide unit. The calculated values ofC _∞ are found to be very sensitive to the input peptide geometry. The calculated value of 2·2 forC _∞ of poly (N-methylglycine) obtained with set-3 parameters (derived from a crystal structure containing prolyl residue) is closer to the experimental value of 1·8±0·2 than the value of 2·7 obtained with set 1 (Pauling-Corey parameters), suggesting that the peptide parameters of N-substituted aminoacids have close similarity to set 3 rather than to set 1. The calculated values ofC _∞ of the polypeptide chains show no correlation with the number of allowed conformations, suggesting that the ratio ofC _∞/C _f need not always provide information about the flexibility or freedom of rotation of chain units. Contribution No. 57 from the Molecular Biophysics Unit, Indian Institute of Science, Bangalore 560012, INDIA.     

The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams

By using the second-order moment of the power density, the beam width, far-field divergence angle and M² factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M² factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w₀/λ. The far-field divergence angle approaches an asymptotic value of θ_max=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.     

Anomalous dynamics in reaction-diffusion systems

Summary We review recent developments in the study of the diffusion reaction systems of the type A+B→C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space atx>0 andx<0, respectively. We find that whereas ford≥2 the mean-field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We also presented analytical and numerical results for the reaction rate on fractals and percolation systems. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Study of resonant two-photon absorption in the tetragonal modification of CdP2

Kinetic, spectral, intensity, angular, and polarization studies of resonant two-photon absorption (RTPA) in β-CdP₂ have been carried out. RTPA was observed with 2.60 eV total energy of the two quanta. It was found that RTPA occurs through a real intermediated level which lies in the forbidden band at a depthE=0.86 eV. The transverse electron relaxation time during RTPA, the cross section for absorption of laser radiation quanta ind ₃→C transitions, the equilibrium population of thed centers forn type doped samples, and the RTPA constant were determined to be 4.3 · 10¹⁴ sec, 1.25 · 10⁻¹⁷ cm, 0.95, and 0.028 cm/MW respectively. Ukrainian State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 1, pp. 21–26, January, 1999.     

Effect of the dimension of the phonon spectrum on the stability of condensed media states

The effect of dimension index d _f of the phonon spectrum, which is a structural characteristic in continual models, on the stability of states of condensed media is considered in the Einstein and Debye approximations. The estimate of the phase state stability is based on the Lindemann criterion generalized to arbitrary values of 0 ≤ d _f ≤ ∞. The problem of variation of physical characteristic of a substance by controlling the structure of its phonon spectrum is considered by analyzing the possibility of obtaining molecular hydrogen in the superfluid state. The Einstein and Debye models as applied to the problem on the dynamics of atomic oscillations are compared, and the divergence of the latter model for fractal dimensions d _f < 2 of the phonon spectrum is demonstrated, as well as the incompatibility of the Debye model at high temperatures and the model of a classical oscillator for all dimensions except d _f → ∞.     

Re-evaluation of the LHC potential for the measurement of <Emphasis Type="Italic">m</Emphasis><Subscript><Emphasis Type="Italic">W</Emphasis></Subscript>

We present a study of the LHC sensitivity to the W boson mass based on simulation studies. We find that both experimental and phenomenological sources of systematic uncertainties can be strongly constrained with Z measurements: the lineshape, dσ _Z /dm, is robustly predicted, and its analysis provides an accurate measurement of the detector resolution and absolute scale, while the differential cross-section analysis, d² σ _Z /dydp _T , absorbs the strong interaction uncertainties. A sensitivity δ m _W ∼7 MeV for each decay channel (W→e ν, W→μ ν), and for an integrated luminosity of 10 fb⁻¹, appears as a reasonable goal.     

The Controlled Teleportation of an Arbitrary Two-Atom Entangled State in Driven Cavity QED

In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state |φ〉₁₂=a|gg〉₁₂+b|ge〉₁₂+c|eg〉₁₂+d|ee〉₁₂ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.     

On ergodic properties for harmonic crystals

We consider the dynamics of a harmonic crystal in n dimensions with d components, where d and n are arbitrary, d, n ⩾ 1. The initial data are given by a random function with finite mean energy density which also satisfies a Rosenblatt-or Ibragimov-type mixing condition. The random function is close to diverse space-homogeneous processes as x _n → ±∞, with the distributions μ±. We prove that the phase flow is mixing with respect to the limit measure of statistical solutions. Partially supported by RFBR under grant no. 06-01-00096.     

Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d _S , ∞)–summable, the summability exponent d _S coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d _S -energy functional which is shown to be a self-similar conformal invariant. Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group.     

Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type

Let Σ _A be a finitely primitive subshift of finite type over a countable alphabet. For suitable potentials f : Σ _A → ℝ we can associate an invariant Gibbs equilibrium state μ _tf to the potential tf for each t ≥ 1. In this note, we show that the entropy h(μ _tf ) converges in the limit t→ ∞ to the maximum entropy of those invariant measures which maximize ∫ f dμ. We further show that every weak-* accumulation point of the family of measures μ _tf has entropy equal to this value. This answers a pair of questions posed by O. Jenkinson, R. D. Mauldin and M. Urbański.     

Infinite Volume Limit for the Stationary Distribution of Abelian Sandpile Models

We study the stationary distribution of the standard Abelian sandpile model in the box Λ_n = [-n, n] ^d ∩ ℤ ^d for d≥ 2. We show that as n→ ∞, the finite volume stationary distributions weakly converge to a translation invariant measure on allowed sandpile configurations in ℤ ^d . This allows us to define infinite volume versions of the avalanche-size distribution and related quantities. The proof is based on a mapping of the sandpile model to the uniform spanning tree due to Majumdar and Dhar, and the existence of the wired uniform spanning forest measure on ℤ ^d . In the case d > 4, we also make use of Wilson’s method. An erratum to this article is available at .     

Calculations of derivatives of porphin and porphyrazine with an annulated five-membered heteroaromatic ring using a modified INDO method

Quantum-chemical calculations for series of porphin (H₂P) and porphyrazine (H₂PA) derivatives whose molecules contain a 3,4-annulated five-membered heteroaromatic ring of pyrrole, furan, and thiophene as well as 1,2,5-triazole, 1,2,5-oxadiazole, and 1,2,5-thiadiazole have been carried out by the AM1 and INDO/Sm methods (m means “modified parametrization”). As follows from the unrestricted Hartree-Fock AM1 calculations, the ground state energy of the a isomer is lower than that of the b isomers for all compounds, the a and b isomers being NH isomers with the additional five-membered ring fused to a pyrrolenine or pyrrole ring, respectively. Condensation of the five-membered ring for the b isomers of the H₂P derivatives is shown to extend the main conjugation path from 18-membered to 21-membered cyclopolyene. However, the 18-membered cyclopolyene for the a isomers of the H₂P derivatives and 16-membered cyclopolyene for both isomers of the H₂PA derivatives prove to be isolated from the five-membered ring carrying six π-electrons. Based on INDO/Sm computations of electronic absorption spectra of the H₂P and H₂PA derivatives, it is shown that the Q_x level of the a isomers is sensitive to the nature of the annulated ring whereas the Q_y level is practically not shifted. On the contrary, the Q_x level of the b isomers is relatively insensitive to the nature of the annulated ring while the Q_y level decreases monotonously in the H₂P and H₂PA series, being the first excited state level for the majority of the derivatives (X is along the NH-HN axis; Y, perpendicular to it). The electronic absorption spectra at the border of the visible and near-UV regions are determined mainly by two high-intensity G → B_x and G → B_y transitions for the H₂P derivatives. However, four intense G → B_x, G → B_y, G → N_x, and G → N_y transitions are characteristic of the spectra of the H₂PA derivatives. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 606–622, September–October, 2008.     

Entropic Repulsion for the High Dimensional Gaussian Lattice Field Between Two Walls

The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝ^λ _N , λ _N = [−N, N] ^d ∩ ℤ ^d and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ _N where L is large enough but finite. We also study the same problem for two layered interfaces case.     

Renormalization group specific heat and magnetization of the Ising ferromagnet in cubic and hypercubic lattices

A real space renormalization group approach with two-terminal clusters is proposed for the calculation of the specific heat and spontaneous magnetization (for all temperatures) of the nearest-neighbour spin –1/2 Ising ferromagnet in simple cubic and hypercubic lattices. For arbitrary temperatures only small clusters (renormalization expansion factorb=2,3 ford=3 andb=2 ford=4) are considered: they lead to reasonable values for the critical points, exponents and amplitudes, to a thermal behaviour of the spontaneous magnetization which is already quite close to what is expected (from series results for example) but to a thermal behaviour of the specific heat which is not yet very close to what is expected. The global results improve whenb increases from 2 to 3. The drastic effect (on the specific heat) of an apparently innocuous approximation is exhibited. The discussion of theT0 andT limits is performed and theexact behaviours of the free and internal energies and the specific heat are obtained for sufficiently large values ofb andall dimensionalities.On leave of absence from Laboratorio de Física Teórica. Departamento de Física, Universidad Nactional de La Plata, CC No. 67 (1900), La Plata, Argentina.     

The corrections to scaling within Mazenko’s theory in the limit of low and high dimensions

We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low (d → 1) and high (d → ∞) dimensions. The corrections to scaling considered here follows from the departures of the initial condition from the scaling morphology. Including corrections to scaling, the equal time correlation function has the form: C(r, t) = f ₀(r/L)+L ^−ω f ₁(r/L)+…, where L is a characteristic length scale (i.e. domain size). The correction-to-scaling exponent ω and the correction-to-scaling functions f ₁(x) are calculated for both low and high dimensions. In both dimensions the value of ω is found to be ω = 4 similar to 1D Glauber model and OJK theory (the theory developed by Ohta, Jasnow and Kawasaki).     

Noncommutative electromagnetism as a large <Emphasis Type="Italic">N</Emphasis> gauge theory

We map noncommutative (NC) U(1) gauge theory on ℝ _C ^d ×ℝ _NC ²ⁿ to U(N→∞) Yang–Mills theory on ℝ _C ^d , where ℝ _C ^d is a d-dimensional commutative spacetime while ℝ _NC ²ⁿ is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ _C ^d is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ _C ^d . We show that the gauge-Higgs system (A _μ ,Φ ^a ) in the U(N→∞) Yang–Mills theory on ℝ _C ^d leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A _μ ,Φ ^a ) in half-BPS configurations describes self-dual Einstein gravity.