Block persistence

We define a block persistence probability p _l (t) as the probability that the order parameter integrated on a block of linear size l has never changed sign since the initial time in a phase-ordering process at finite temperature T<T _c . We argue that in the scaling limit of large blocks, where z is the growth exponent (), is the global (magnetization) persistence exponent and f(x) decays with the local (single spin) exponent for large x. This scaling is demonstrated at zero temperature for the diffusion equation and the large-n model, and generically it can be used to determine easily from simulations of coarsening models. We also argue that and the scaling function do not depend on temperature, leading to a definition of at finite temperature, whereas the local persistence probability decays exponentially due to thermal fluctuations. These ideas are applied to the study of persistence for conserved models. We illustrate our discussions by extensive numerical results. We also comment on the relation between this method and an alternative definition of at finite temperature recently introduced by Derrida [Phys. Rev. E 55, 3705 (1997)]. Received: 25 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Anomalous dynamical light scattering in soft glassy gels

We compute the dynamical structure factor S(q,τ) of an elastic medium where force dipoles appear at random in space and in time, due to “micro-collapses” of the structure. Various regimes are found, depending on the wave vector q and the collapse time θ. In an early-time regime, the logarithm of the structure factor behaves as (qτ)^3/2, as predicted in L. Cipelletti, S. Manley, R.C. Ball, D.A. Weitz, Phys. Rev. Lett. 84, 2275 (2000) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (qτ)^5/4 behaviour. Finally, the asymptotic long-time regime is found to behave as q ^3/2τ. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t _w, quasi-exponentially at first, and then as t _w ^4/5 with logarithmic corrections. Received 23 July 2001     

Quasi-Stable Configurations of Torus Vortex Knots and Links

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.

     

Self organized criticality in a modified Olami-Feder-Christensen model

A modified version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of the adding parameter p _{a d d} of the model. The probability density functions of the avalanche size differences at consecutive time steps (defined as returns) appear to be well approached, in the thermodynamic limit, by q-Gaussian shape with appropriate q values which can be obtained a priori from the avalanche size exponent τ. For small system sizes, however, return distributions are found to be consistent with the crossover formulas proposed recently in Tsallis and Tirnakli [J. Phys. Conf. Ser. 201, 012001 (2010)]. Our results strengthen recent findings of Caruso et al. [Phys. Rev. E 75, 055101(R) (2007)] on the real earthquake data which support the hypothesis that knowing the magnitude of previous earthquakes does not make the magnitude of the next earthquake predictable.     

Anomalous dynamical light scattering in soft glassy gels

We compute the dynamical structure factor S(q,τ) of an elastic medium where force dipoles appear at random in space and in time, due to “micro-collapses” of the structure. Various regimes are found, depending on the wave vector q and the collapse time θ. In an early time regime, the logarithm of the structure factor behaves as (qτ)^3/2, as predicted in (L. Cipelletti et al., Phys. Rev Lett. 84, 2275 (2000)) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (qτ)^5/4 behaviour. Finally, the asymptotic long-time regime is found to behave as q ^3/2τ. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t_w, quasi-exponentially at first, and then as t _w ^4/5 with logarithmic corrections. Received 15 April 2002     

Circular-like maps: sensitivity to the initial conditions, multifractality and nonextensivity

Dissipative one-dimensional maps may exhibit special points (e.g., chaos threshold) at which the Lyapunov exponent vanishes. Consistently, the sensitivity to the initial conditions has a power-law time dependence, instead of the usual exponential one. The associated exponent can be identified with 1/(1-q), where q characterizes the nonextensivity of a generalized entropic form currently used to extend standard, Boltzmann-Gibbs statistical mechanics in order to cover a variety of anomalous situations. It has been recently proposed (Lyra and Tsallis, Phys. Rev. Lett. 80, 53 (1998)) for such maps the scaling law , where and are the extreme values appearing in the multifractal function. We generalize herein the usual circular map by considering inflexions of arbitrary power z, and verify that the scaling law holds for a large range of z. Since, for this family of maps, the Hausdorff dimension d_f equals unity for all z in contrast with q which does depend on z, it becomes clear that d_f plays no major role in the sensitivity to the initial conditions. Received 5 February 1999     

Parabolic drift towards homogeneity in large-scale structures of galaxies

To describe the progressive transition in large-scale structures of galaxies from a seemingly fractal behavior at small scales to a homogeneous distribution at large scales, we use a new geometrical framework called entropic-skins geometry which is based on a diffusion equation of scale entropy through scale space. In the case of an equipartition of scale entropy losses in scale space, it is shown that fractal dimension (varying from 0 to 3) depends linearly on the logarithm of scale from the average size l_c of galaxies until a characteristic length scale l₀ beyond which distribution becomes homogeneous. A simple parabolic expression for correlation function can be derived: ln(1+ξ_i)=(β/2)ln²(l_o/l_i) with β=3/ln(l₀/l_c)≈0.32 and . This law has been verified using correlation functions measured on several redshift surveys.     

Critical dynamics of φ2n with random fields in the tree approximation

In the tree approximation, the critical relaxational dynamics of ²ⁿ with quenched random fields is calculated by renormalization near the upper critical dimensiond _u=4+2/(n–1). Although the relation between the characteristic frequency _c q and the wave-numberq is as usual,unusual results are obtained for the asymptotic decay of the order-parameter correlation functionS(q,t).Dedicated to Prof. Dr. W. Döring on the occasion of his 75th birthday     

Scaling and universality in models of step bunching: the “C<Superscript>+</Superscript>–C<Superscript>-</Superscript>” model

We recently introduced a novel model of step flow crystal growth – the so-called “C⁺–C^-” model [B. Ranguelov et al., C.R. Acad. Bulgare Sci. 60, 389 (2007)]. In this paper we aim to develop a complete picture of the model’s behaviour in the framework of the notion of universality classes. The basic assumption of the model is that the reference (“equilibrium”) densities used to compute the supersaturation might be different on either side of a step, so C_L/C_R ≠ 1 (L/R stands for left/right in a step train descending from left to right), and that this will eventually cause destabilization of the regular step train. Linear stability analysis considering perturbation of the whole step train shows that the vicinal is always unstable when the condition C_L /C_R >1 is fulfilled. Numerical integration of the equations of step motion combined with an original monitoring scheme(s) results in obtaining the exact size- and time- scaling of the step bunches in the limit of long times (including the numerical prefactors). Over a broad range of parameters the surface morphology is characterized by the appearance of the minimal interstep distance at the beginning of the bunches (at the trailing edge of the bunch) and may be described by a single universality class, different from those already generated by continuum theories [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002), J. Krug et al., Phys. Rev. B 71, 045412 (2005)]. In particular, the scaling of the minimal interstep distance l_min in the new universality class is shown to be l_min = (S_n /N)^1/(n+1), where N is the number of steps in the bunch, n is the exponent in the step-step repulsion law U ~ 1/d₀ ⁿ for two steps placed a distance d₀ apart and S_n is a combination of the model parameters. It is also shown that N scales with time with universal exponent 1/2 independent of n. For the regime of slow diffusion it is obtained for the first time that the time scaling depends only on the destabilization parameter C_L/C_R. The bunching outside the parameter region where the above scaling exists cannot be assigned to a specific universality class and thus should be considered non-universal.     

Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence

We provide a simple physical picture of the loss of coherence between two coherently split one-dimensional Bose-Einstein condensates. The source of the dephasing is identified with nonlinear corrections to the elementary excitation energies in either of the two independent condensates. We retrieve the result by Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on the subexponential decay of the coherence ∝exp [-(t/t₀)^2/3] for the large time t, however, the scaling of t₀ differs.     

Inhomogeneous Tsallis distributions in the HMF model

We study the maximization of the Tsallis functional at fixed mass and energy in the Hamiltonian Mean Field (HMF) model. We give a thermodynamical and a dynamical interpretation of this variational principle. This leads to q-distributions known as stellar polytropes in astrophysics. We study phase transitions between spatially homogeneous and spatially inhomogeneous equilibrium states. We show that there exists a particular index q _c = 3 playing the role of a canonical tricritical point separating first and second order phase transitions in the canonical ensemble and marking the occurence of a negative specific heat region in the microcanonical ensemble. We apply our results to the situation considered by Antoni and Ruffo [Phys. Rev. E 52, 2361 (1995)] and show that the anomaly displayed on their caloric curve can be explained naturally by assuming that, in this region, the QSSs are polytropes with critical index q _c = 3. We qualitatively justify the occurrence of polytropic (Tsallis) distributions with compact support in terms of incomplete relaxation and inefficient mixing (non-ergodicity). Our paper provides an exhaustive study of polytropic distributions in the HMF model and the first plausible explanation of the surprising result observed numerically by Antoni and Ruffo (1995). In the course of our analysis, we also report an interesting situation where the caloric curve presents both microcanonical first and second order phase transitions.     

On the operator equivalents and the crystal-field and spin Hamiltonian parameters

Operator equivalents used in magnetic resonance (electron paramagnetic resonance [EPR], electron-nuclear double resonance, nuclear magnetic resonance, etc.) are considered. The known non-Hermitian tensor operators O _±q ^(k) (0 ≤ q ≤ k) defined by D. Smith and J. H. M. Thornley (Proc. Phys. Soc. 89, 779–781, 1966) after H. A. Buckmaster (Can. J. Phys. 40, 1670–1677, 1962) are expressed in terms of Hermitian cosine and sine operators O _kq ^c and O _kq ^s. These new normalized operators are related to the nonnormalized extended Stevens operators O _k ^q and O _k ^−q ≡ Ω _k ^q defined by C. Rudowicz (J. Phys. C.: Solid State Phys. 18, 1415–1430, 1985), which are commonly used in EPR of transition ions. The relations between O _kq ^c,s and some other normalized operators occurring in the literature are also given. New crystal-field or spin Hamiltonian parameters B _kq ^c and B _kq ^s associated with the corresponding operators O _kq ^c and O _kq ^s are discussed.     

Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I

Explicit expressions for the fourth-order susceptibility (⁴), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T _c ⁽⁴⁾ = 2k _B ^–1 J/ln{1+2/[(z–1)^3/4–1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk _B is the Boltzmann constant. The temperatures at which ⁽⁴⁾ and the ordinary susceptibility (²) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.     

A Strict Inequality for the Random Triangle Model

The random triangle model on a graph G, is a random graph model where the usual i.i.d. measure is perturbed by a factor q ^t(), where q1 is a constant, and t() is the number of triangles in the random subgraph . Here we consider the case where G is the usual two-dimensional triangular lattice, for which there exists a percolation threshold p _c (q) such that the probability of getting an infinite connected component of retained edges is 0 for p<p _c (q), and 1 for p>p _c (q). It has previously been shown that p _c (q) is a decreasing function of q. Here we strengthen this by showing that p _c (q) is strictly decreasing. This confirms a conjecture by Häggström and Jonasson.     

A travelling cluster approximation for lattice fermions strongly coupled to classical degrees of freedom

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τ_N ∼N⁴. This limits achievable sizes to N ∼100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size N_c, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τ_N,Nc ∼NN_c³. Our results are obviously exact when N_c=N, and converge quickly to this asymptote with increasing N_c, particularly in the presence of disorder. We provide detailed benchmarks on the Holstein model and the double exchange model. The `locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control. This method forms the basis of our studies in Europhys. Lett. 68, 564 (2004), Phys. Rev. Lett. 94, 136601 (2005), and Phys. Rev. Lett. 96, 016602 (2006).     

High-resolution spectroscopy on the c1Π ← a1Δ transition in NH

The spectrum of the c¹Π, v = 0 ← a¹Δ, v = 0 band of the NH molecule at λ = 324 nm has been investigated under high resolution by laser-induced fluorescence in a molecular beam. From an analysis of the spectra we obtained: the magnetic dipole interaction constants a_N,H and the electric quadrupole constants eQq_1,2 for both electronic states, the improved values for the Λ-doubling constants q_π, q_π^D, and q_π^H for the c¹Π state, and rotational constants for both electronic states up to a third-order centrifugal distortion. Also, the Λ-doubling in the a¹Δ state could be determined.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.     

Uncertainty Inequality for the Entanglement of Both Two-rebits and Two-qubits States

We assume that both the concurrence C_r of a two-rebits state and the concurrence C_q of the usual two-qubits states are represented by hermitian operators (observables). We calculate the respective uncertainty ΔC_r and the uncertainty ΔC_q measured both as the standard deviation . We make the strictly mathematical assumption that there exists a canonical conjugate variable (called ξ) to the concurrence (C) such that both quantities satisfy a Robertson’s [1] uncertainty inequality of the form \( {\left(\Delta A\right)}^2{\left(\Delta B\right)}^2>{\left|\frac{1}{2}\left\langle \right[A,B\left]\right\rangle \right|}^2 \). From such inequality we impose bounds for both uncertainties Δξ_r and Δξ_q.

     

Spontaneous emission in dielectric nanoparticles

An analytical expression is obtained for the radiative-decay rate of an excited optical center in an ellipsoidal dielectric nanoparticle (with sizes much less than the wavelength) surrounded by a dielectric medium. It is found that the ratio of the decay rate A _nano of an excited optical center in the nanoparticle to the decay rate A _bulk of an excited optical center in the bulk sample is independent of the local-field correction and, therefore, of the adopted local-field model. Moreover, the expression implies that the ratio A _nano/A _bulk for oblate and prolate ellipsoids depends strongly on the orientation of the dipole moment of the transition with respect to the ellipsoid axes. In the case of spherical nanoparticles, a formula relating the decay rate A _nano and the dielectric parameters of the nanocomposite and the volumetric content c of these particles in the nanocomposite is derived. This formula reduces to a known expression for spherical nanoparticles in the limit c ≪ 1, while the ratio A _nano/A _bulk approaches unity as c tends to unity. The analysis shows that the approach used in a number of papers {H. P. Christensen, D. R. Gabbe, and H. P. Jenssen, Phys. Rev. B 25, 1467 (1982); R. S. Meltzer, S. P. Feofilov, B. Tissue, and H. B. Yuan, Phys. Rev. B 60, R14012 (1999); R. I. Zakharchenya, A. A. Kaplyanskii, A. B. Kulinkin, et al., Fiz. Tverd. Tela 45, 2104 (2003) [Phys. Solid State 45, 2209 (2003)]; G. Manoj Kumar, D. Narayana Rao, and G. S. Agarwal, Phys. Rev. Lett. 91, 203903 (2003); Chang-Kui Duan, Michael F. Reid, and Zhongqing Wang, Phys. Lett. A 343, 474 (2005); K. Dolgaleva, R. W. Boyd, and P. W. Milonni, J. Opt. Soc. Am. B 24, 516 (2007)}, for which the formula for A _nano is derived merely by substituting the bulk refractive index by the effective refractive index of the nanocomposite must be revised, because the resulting ratio A _nano/A _bulk turns out to depend on the local-field model. The formulas for the emission and absorption cross sections σ_nano for nanoparticles are derived. It is shown that the ratios σ_nano/σ_bulk and A _nano/A _bulk are not equal in general, which can be used to improve the lasing parameters. The experimentally determined and theoretically evaluated decay times of metastable states of dopant rare-earth ions in crystalline YAG and Y₂O₃ nanoparticles are compared with the corresponding values for bulk crystals of the same structure. Original Russian Text ? K.K. Pukhov, T.T. Basiev, Yu.V. Orlovskii, 2008, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 88, No. 1, pp. 14–20.     

Resonance method for IR sensing

A highly sensitive method for infrared radiation detection based on thermal resonance in an active bolometer is set forth. An active bolometer is a self-oscillating system consisting of an IR-sensitive cell in a feedback circuit of an adjustable proportional controller. The analysis of an active bolometer autonomous (dark) dynamics reveals that with a generalized gain factor A variation the system evolves from relaxation type towards oscillating and self-oscillating type. When A=A_c, where A_c is a critical value of the generalized gain factor A, the steady state loses stability through self-excited thermal oscillations. The resonance in a system weakly perturbed by IR radiation modulated at self-oscillation frequency q₀[1+exp(iω_ct)] is considered. It is shown that in a small precritical vicinity =(A−A_c)/A_c of the gain factor the amplitude of forced thermal oscillations is proportional to q₀/A_c. The D^* calculation reveals that the detection power of a passive (A=0) bolometer increases with feedback introduction by a factor of 1/||. The detection powers of feasible versions of an active bolometer are compared.