On the longitudinal magnetic susceptibility of fractal ferrodielectrics

The longitudinal component of the magnetic susceptibility tensor χ _zz of a fractal ferrodielectric with dimension d _F = 3 − ɛ, where ɛ > 0, is calculated. The magnon dispersion in this case is shown to be a strongly anisotropic function of the parameter ɛ which, in turn, leads to nontrivial frequency dependences of χ _zz .     

Dynamical entanglement as a signature of chaos in the semiclassical limit

The relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ _eff. Our findings indicate that as ℏ _eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system.     

Effect of infrared radiation on the plasticity of solid hydrogen

This paper reports on the first results obtained from the investigation of the effect of IR radiation on the low-temperature (1.8 ≤ T ≤ 4.2 K) plasticity of solid hydrogen. It has been found that, when the samples are exposed to IR radiation, a drastic increment Δɛ_IR of the elongation per unit length ɛ (which was preliminarily achieved under a continuously applied mechanical stress σ = const) occurs without an increase in the temperature of the samples. It has been revealed that the effect observed both in the case of normal hydrogen (n-H₂, 75% o-H₂) and in the case of parahydrogen (p-H₂, ∼0.2% o-H₂) only for a sufficiently high power of the IR radiation source has a threshold character. The reverse deformation of solid hydrogen is observed after the irradiation with a flux of IR photons is completed: the quantity ɛ rapidly decreases to values provided only by the applied load. The appearance of jumps in the increment of deformation Δɛ_IR ⁱ is interpreted as a consequence of the existence of the fundamental IR absorption band for solid hydrogens. It has been established that, depending on the time t of exposure of the samples to IR radiation, the change in the quantity Δɛ_IR ⁱ (t) obeys the logarithmic law, which is characteristic of the dislocation creep and observed in the case of unirradiated hydrogen. It has also been found that, under multiple relatively long-term exposure to IR radiation, the constant α of the logarithmic creep of n-H₂ abruptly decreases, whereas the strength of both the n-H₂ and p-H₂ samples increases significantly, which indicates their explicit hardening (instead of the expected “superplastic” behavior due to the exposure to IR irradiation).     

Soliton switching in twin-core fibers with gain and loss

Soliton propagation and switching in twin-core nonlinear fibers with gain and loss have been investigated based on a pair of coupled nonlinear Schr?dinger equations. We have found the fiber with equal amount of gain in both cores has the minimum ascending energy Δɛ of 1.5K, while the fiber with a certain amount of gain in one core and the same amount of loss in the other core has the minimum switching thresholdɛ _th of 2.05K. A new vector field is defined and its potential function is derived, which explains the switching behavior of the minimumɛ _th switch satisfactorily.     

Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

We showed in Part I that the Hopf algebra ℋ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at ɛ= 0 the holomorphic part γ₊(ɛ) of the Riemann–Hilbert decomposition γ₋(ɛ)^{− 1}γ₊(ɛ) of the loop γ(ɛ)∈G provided by dimensional regularization. We show in this paper that the group G acts naturally on the complex space X of dimensionless coupling constants of the theory. More precisely, the formula g ₀=gZ ₁ Z ₃ ^−3/2 for the effective coupling constant, when viewed as a formal power series, does define a Hopf algebra homomorphism between the Hopf algebra of coordinates on the group of formal diffeomorphisms to the Hopf algebra ℋ. This allows first of all to read off directly, without using the group G, the bare coupling constant and the renormalized one from the Riemann–Hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms. This shows that renormalization is intimately related with the theory of non-linear complex bundles on the Riemann sphere of the dimensional regularization parameter ɛ. It also allows to lift both the renormalization group and the β-function as the asymptotic scaling in the group G. This exploits the full power of the Riemann–Hilbert decomposition together with the invariance of γ₋(ɛ) under a change of unit of mass. This not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group G for the full higher pole structure of minimal subtracted counterterms in terms of the residue. Received: 21 March 2000 / Accepted: 3 October 2000     

Renormalization Group Approach to Interacting Polymerised Manifolds

We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension D interacting via an exclusion condition with a fixed impurity in d-dimensional Euclidean space in which the manifold is embedded. In this paper we take D=1, but modify the underlying free Gaussian covariance (thereby changing the canonical scaling dimension of the Gaussian random field) so as to simulate a polymerised manifold with fractional dimension . The canonical dimension of the coupling constant is , where −β/2 is the canonical scaling dimension of the Gaussian embedding field. β is held strictly positive and sufficiently small. For ɛ>0, sufficiently small, we prove for this model that the iterations of Wilson's renormalisation group transformations converge to a non-Gaussian fixed point. Although ɛ is small, our analysis is non-perturbative in ɛ. A similar model was studied earlier [CM] in the hierarchical approximation. Received: 7 January 1999 / Accepted: 20 August 1999     

Effect of a bias field on the dielectric properties of NaNbO3 solid solutions in the range of the giant temperature hysteresis of a phase transition

The effect of a bias field E on the value and temperature dependence of permittivity ɛ of ceramic samples of solid solutions 0.6NaNbO₃-0.4 NaTaO₃ (I), and 0.97[0.9NaNbO₃-0.1Na_0.5Bi_0.5TiO₃]-0.03LiNbO₃ (II) possessing an anomalously large temperature hysteresis of ɛ(T) dependence is studied. The character of the dependences of both the height and the temperature of the ɛ(T) maximum on the field show that composition (I) has antiferroelectric properties, while composition (II) has ferroelectric properties. It is found that up to 8 kV/cm, the strength of the bias field has actually no effect on the width of the ɛ(T) temperature hysteresis of the compositions under study.     

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Influence of the misfit of the crystal chemical parameters of Na and Li cations on the dielectric properties of NaNbO<Subscript>3</Subscript>-LiNbO<Subscript>3</Subscript> solid solutions

It is established that the Curie-Weiss temperature of Na_{1 − x} Li _x NbO₃ solid solutions determined by extrapolation of linear portions of the temperature dependence of the reciprocal of the permittivity ɛ⁻¹ from the cubic phase sharply increases with x, although the temperature of the ɛ(T) maximum decreases. It is shown in terms of a simple theoretical model that the experimentally observed change in the dielectric properties of Na_{1 − x} Li _x NbO₃ is well explained under the assumption of formation of a dipole system due to the displacement of Li cations from the center of the cubooctahedral cavity because of the significant steric misfit between the Na and Li cations.     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Synthesis, structure, and dielectric properties of KH2PO4 fractal aggregates

Macroscopic fractal aggregates of KH₂PH₄ (KDP) measuring up to 500 μm have been obtained. The fractal structure forms as a result of the precipitation of KDP particles from a supersaturated aqueous solution in the presence of a temperature gradient followed by a diffusioncontrolled mechanism of aggregation. The electron-microscopic analysis performed has shown that the fractals are formed predominantly from crystallites of the tetragonal modification measuring ∼1 μm. The dielectric constant (ɛ) of fractal KH₂PO₄ has been measured in the temperature range 80–300 K. A characteristic anomaly has been discovered on the ɛ(T) curve in the vicinity of 122 K, which attests to a ferroelectric phase transition. The absolute value of ɛ is significantly smaller than the components ɛ ₁₁ and ɛ ₃₃ for KH₂PO₄. Fiz. Tverd. Tela (St. Petersburg) 41, 2059–2061 (November 1999)     

Central Limit Theorem¶for Stochastic Hamilton–Jacobi Equations

We study the asymptotic behavior of , where u solves the Hamilton–Jacobi equation u _t +H(x,u _x ) ≡ 0 with H a stationary ergodic process in the x-variable. It was shown in Rezakhanlou–Tarver [RT] that u ^ɛ converges to a deterministic function provided H(x,p) is convex in p and the convex conjugate of H in the p-variable satisfies certain growth conditions. In this article we establish a central limit theorem for the convergence by showing that for a class of examples, u ^ɛ(x,t) can be (stochastically) represented as , where Z(x,t) is a suitable random field. In particular we establish a central limit theorem when the dimension is one and , where ω is a random function that enjoys some mild regularity. Received: 15 February 1999 / Accepted: 14 December 1999     

Slow Motion of Charges¶Interacting Through the Maxwell Field

We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R _ϕ, the charges are a distance ɛ^-1 R _ϕ apart and have a velocity with ɛ a small dimensionless parameter. We follow the motion of the charges over times of the order ɛ^-3/2 R _ϕ/c and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order ɛ². The magnetic fields and first order retardation generate the Darwin correction of the order ɛ³. Radiation damping would be of the order ɛ^7/2. Received: 13 January 2000 / Accepted: 4 February 2000     

Energy and critical ionic-bond parameter of a 3D large-radius bipolaron

A theory of a strong-coupling large-radius bipolaron has been developed. The possibility of the formation of 3D bipolarons in high-temperature superconductors is discussed. For the bipolaron energy, the lowest variational estimate has been obtained at α > 8, where α is the electron-phonon coupling constant. The critical ionic-bond parameter η _c = ɛ_∞/ɛ₀, where ɛ_∞ and ɛ₀ are the high-frequency and static dielectric constants, has been found to be η _c = 0.2496.     

Dielectric spectroscopy of PbZr1 ? xTixO3 solid solutions (0.495 ≤ x ≤ 0.51) in a temperature range of 100–300 K at frequencies from 1 × 10?2 to 2 × 107 Hz

The behavior of the relative permittivity ɛ/ɛ₀ of PbZr_{1 − x} Ti _x O₃ (PZT) solid solutions (0.495 ≤ x ≤ 0.51) in the temperature range of 100–300 K at frequencies from 1 × 10⁻² to 2 × 10⁷ Hz was investigated. Diffuse, strongly relaxing maxima at T = 230−260 K (x = 0.495−0.505) and 150–160 K (x = 0.510) were observed in the PZT studied. The relaxation processes are well described by the Vogel-Fulcher law, and the dielectric spectra are approximated by the Cole-Cole formula.     

Effect of ionizing radiation on the dielectric characteristics of TlInSe<Subscript>2</Subscript> and TlGaTe<Subscript>2</Subscript> single crystals

The temperature dependences of the electrical conductivity and the permittivity of TlInSe₂ and TlGaTe₂ crystals unirradiated and irradiated with 4-MeV electrons at a doze of 10¹⁶ cm⁻² have been investigated. It has been established that electron irradiation leads to a decrease in the electrical conductivity σ and the permittivity ɛ over the entire temperature range under study (90–320 K). It has been revealed that the TlInSe₂ and TlGaTe₂ single crystals undergo a sequence of phase transitions characteristic of crystals of this type, which manifest themselves as anomalies in the temperature dependences σ = f(T) and ɛ = f(T). Electron irradiation at a doze of 10¹⁶ cm⁻² does not affect the phase transition temperatures of the crystals under investigation.     

Fluctuation Bounds for Chaos Plus Noise in Dynamical Systems

We are interested in time series of the form y _n =x _n +ξ _n where {x _n } is generated by a chaotic dynamical system and where ξ _n models observational noise. Using concentration inequalities, we derive fluctuation bounds for the auto-covariance function, the empirical measure, the kernel density estimator and the correlation dimension evaluated along y ₀,…,y _n , for all n. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters.     

Field localization and particle confinement effects on pair creation by Schwinger’s mechanism

Solutions of the Dirac equation in the presence of a static uniform electric fieldɛ in thez-direction and a linear confining potentialAz, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials forɛ >A/e. The eigenspectrum and corresponding localized eigenfunctions forɛ <A/e are obtained from the reflection coefficient and the continuum solutions respectively. The rate for the electric field to decay into pairs is derived from the transmission coefficient. Neglecting nonabelian effects in quantum chromodynamics we identify the fieldɛ with a colour electric field and the produced particles with a quark and an antiquark. By considering a cylindrical geometry, we thus obtain a generalization of Schwinger’s formula, for the fieldɛ in a finite spatial region with the quark (antiquark) being confined in thez direction by the linear potentialAz and in the perpendicular direction by the MIT bag boundary condition. The result is used to qualitatively study Schwinger’s mechanism of quark-gluon plasma (QGP) formation in ultrarelativistic heavy ion collisions. It is found that the critical strength of the field required to create pairs is enhanced,ɛ _c(A) >ɛ _c(A = 0). The rate of pair creation for constantɛ, decreases for non-zeroA, implying longer QGP formation times. Because ofɛ _c(A) >ɛ _c(0), QGP is predicted to be formed in the early stages of the nuclear collision. The finite size effects and the MIT bag boundary condition effects on QGP formation are also discussed.     

Thermoelectric power in quasi-two-dimensional systems with scattering of current carriers by phonons

The thermopower α in electron systems with a quasi-two-dimensional energy spectrum is investigated in the relaxation-time tensor approximation. The longitudinal and transverse components of the thermopower are calculated for scattering of the current carriers by different types of phonons. It is shown that the anisotropy of the thermopower in such systems is substantial. The dependence of a on the ratio of the Fermi level ɛ _F to the half-width ɛ ₀ of the one-dimensional conduction band is considered. For scattering by acoustical and nonpolar optical phonons, the thermopower changes sign: α becomes positive for ɛ _F<ɛ ₀. Comparison of the theory with published experimental data demonstrates good qualitative agreement. Fiz. Tverd. Tela (St. Petersburg) 39, 1857–1858 (October 1997)