Dielectric relaxations,magnetodielectric and magnetoelectric interactions in Bi0.6La0.4MnO3 ceramics

Complex permittivity ε*/ε₀ = ε′/ε₀–iε″/ε₀ of the bismuth–lanthanum manganite Bi_0.6La_0.4MnO₃ ceramics has been measured in the temperature range of 10–220 K at frequencies f = 20–10⁶ Hz and magnetic inductions B = 0–0.846 T. At a temperature of 80 K, the spectra ε′/ε₀(t) and ε″/ε₀(t) demonstrate the dielectric relaxation that is a superposition of contributions of several relaxation processes, each of which is dominant in its frequency range: I (f < 10³ Hz, II (10³ < f < 10⁵ Hz), and III (10⁵ < f < 10⁶ Hz). In the range of 10–120 K, anomalous behavior of ε′/ε₀(T) and ε″/ε₀(T) is observed near the temperature of the transition from the paramagnetic to ferromagnetic phase and is due to the Anderson localization of charge carrier on a spin disorder.     

直流偏置电场下BaTiO３基陶瓷介电常数非线性机理的研究

采用传统固相法制备了Ba_0.6Sr_0.4TiO_３(BST)和BaZr< sub>xTi_１-xO_３(x=0.25，0.3，0.35，0.4)（ＢＺＴ）陶瓷 ，并对其在直流偏置电场下的介电常数非线性行为进行了系统、详细的研究.结果表明，基 于Devonshire的宏观相变理论(phenomenological theory)提出的公式ε_r(app) ε_r(0)=1［1+αε^{３_{r(0)E２ ］1/3和ε(E)=ε1－ε2E2+ε3E4，均可定量地解释BST体系顺电相的介电常数非线性行为，其中εr (app)表示材料在电场下的介电常数，εr(0)表示不加电场即静态下材料 的介电常数，α是非谐性因子，E表示电场强度，ε(E)表示材料在电场下的介电常数，ε１，ε２，ε３分别表示线性、非线性和高阶介电常数. 而对于处于铁电相和居里温度附近的BST体系，则需要考虑铁电畴对介电常数非线性的贡献 ，这种贡献随着外加直流偏置电场强度的增大逐步减小.对于弛豫铁电体BZT体系，即使处于 顺电相，也必须考虑由极性微区的冻结与合并引起的介电常数的下降，极性微区对介电常数 非线性的贡献随着电场强度和温度的上升而有所下降. 关键词： BST x}Ti_１-xO_３')" href="#">BaZr_xTi_１-xO_３ 可调性 介电 常数非线性 直流偏置电场}     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Dielectric response of KCN crystal at ultra low frequencies

The dielectric response of pure KCN crystals (ε′, ε″ and tg σ) has been measured as a function of temperature in the frequency range 10⁻² Hz to 10⁴ Hz. In the antiferroelectric phase the width of the loss peak are found practically independent of temperature (1.4 decades) and close to a Debye behavior; the relaxation time of the CN⁻ dipoles is characterized by an Arrhenius behavior τ = τ₀ exp (U/KT) with τ₀ = 7.26 × 10⁻¹⁵s and U = 0, 147 eV confirming a classical temperature activated reorientation of the dipoles.     

Nonlinear stability analysis of the Lorenz model by Lyapunov's direct method

The preturbulent region of the Lorenz model is investigated with the aim to determine the attractive region around the stable fixed points as a function of the Rayleigh parameterr. Close to the turbulent threshold, i.e. for small deviations ?=r _T?r, the attractive region is a highly anisotropic ellipsoid in the phase space. Its volumeV obays the power lawV(ε)=const ?^α with the critical exponent α=5/2. A Landau type approximation, on the other hand, leads to α-3/2. The reason for this discrepancy is discussed. In addition we develop a series expression which allows to calculate the maximal domain of attraction also for large deviations ε. Numerical results from the two lowest terms of the series are represented for 0<ε?6.     

Effective hamiltonian of Bloch electrons in a homogeneous electrical field

In order to construct a band mechanics of Bloch electrons in a homogeneous electrical field E with the interband interaction taken into account, a method of determining the exact single-band Hamiltonian $$H_q = \varepsilon _q^F (\kappa ) + Fi\frac{\partial }{{\partial \kappa }}$$ is proposed, where ε _q ^F (κ) is the renormalized (effective) electron dispersion law for R = 0 and the q-th Bloch band,F= ¦e¦·E. The function ε _q ^F (κ) is expressed in terms of the interband element coordinates as well as in terms of periodic solutions of the system of ordinary differential equations which degenerateinto a common Riccati equation in a two-band approximation. A solution of the system and the form of ε _q ^F (κ), in agreement with the Wanhier result, is found in the quasiclassical approximation.     

On the optical absorption due to particle-hole excitations in thin metal films

We present here a qualitative discussion on the optical absorption due to particle-hole excitations in thin metal films. We show that in sufficiently thin films, such excitations yield resonant absorption, when P-polarized light is obliquely incident on the metal surface. For instance, for frequency ω #62; ε_F where ε_F is the Fermi-energy, such resonances occur whenever ω satisfies the condition ω/ε_F = (1 + nπ/dq_F)² - 1, where n = 1,3,5,…,q_F is the Fermi wave-vector and d is the thickness of the film. The experimental observability of this effect is also discussed.     

Maxwell–Wagner relaxation and magnetodielectric properties of Bi<Subscript>0.5</Subscript>La<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> ceramics

The complex permittivity ε = ε′–iε″ of manganite bismuth–lanthanum Bi_0.5La_0.5MnO₃ ceramics has been measured at temperature T = 78 K in the frequency range f = 200–10⁵ Hz and in the magnetic induction range B = 0–5 T. Dielectric relaxation and the pronounced magnetodielectric effect have been detected. The explanation based on the superposition of Maxwell–Wagner relaxation and the magnetoresistance effect has been proposed.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

One-dimensional hard rod caricature of hydrodynamics

We give here a rigorous deduction of the “hydrodynamic” equation which holds in the hydrodynamic limit, for a model system of one-dimensional identical hard rods interacting through elastic collisions. The equation should be considered as the analog of the Euler equation of real hydrodynamics. Owing to the degeneracy of the model, it is written in terms of a functiong(q, v, t) expressing the density of particles with velocityv at the pointq at timet. For this equation we prove an existence and uniqueness theorem in some natural class of functions. Our main result is the proof that if {^∈, ∈ >0} is a class of initial states which are homogeneous on a scale much less than ε^?1, and if the corresponding particle densities tend, asε→0, in the proper scale, to the initial hydrodynamic densityg _o (q,v), then, under some general assumptions on the states ∈^? and ong ₀, the particle densities of the evolved states at timeε ^?1 t, tend asε→0 to the unique solution of the hydrodynamic equation with initial conditiong ₀. The proof is completed by exhibiting a large class of initial families {^∈, ∈ >0} which possess the required properties.     

Poincaré subalgebras in so(4, 2) and sl(5, R)

Injective homomorphisms ε which map the Poincaré Lie algebra P into so(4, 2)=C are considered. Two mappings ε₁ and ε₂ are said to be Int-equivalent iff there exists an inner automorphism ρⁱⁿ_c> of C such that ε₁=ρⁱⁿ_cε₂. The set of all ε splits into four Int- equivalence classes. Mappings in different classes are equivalent with respect to non-inner automorphisms of C. A corresponding theorem holds for homomorphisms of P into sl (5, R). These algebraic properties give strong limitations for those integrable representations of P which can be found by restriction of integrable representations of so(4, 2) and of sl(5, R) to ε(P). Physical applications of the results are discussed.     

Finite-size crossover in systems with slab geometry

A renormalization group study of the finite-size (dimensional) crossover is carried out with the help pf ε = 4 − d and ε₀ = 3 − d expansion techniques. The finite-size crossover and the invariance relation for the length scale transformation are proven up to the two-loop approximation. The formal equivalence between the finite-size crossover in classical systems and the quantum-to-classical dimensional crossover in certain quantum statistical models is emphasized and exploited. The finite-size corrections to the fluctuation shift of the critical temperature and the width of the critical region are investigated. It is shown that the shift exponent λ describing the fractional rounding of the critical temperature obeys the relation λ = D − 2, where D is the dimensionality of the system.     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

The n-loop expansion of the Reggeon calculus

We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ³ Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σ_tot ≈ (1n s)^0.27 at infinity, close to the O(ε²) result.     

Dilation analyticity in constant electric field

The resolvent of the operatorH ₀(ε, θ)=?Δe ^-20+εx ₁ e ^θ is not analytic in θ for θ in a neighborhood of a real point, if the electric field ε is non-zero. (One manifestation of this singular behavior is that for 0<|Im θ|<π/3,H ₀(ε, θ) has no spectrum in the finite plane.) Nevertheless it is shown that the techniques of dilation analyticity still can be used to discuss the long-lived states (resonances) of a system described by a Hamiltonian of the formH=?Δ+εx ₁+V(x).     

Circular radiation heat shields with temperature dependent emissivities: transient and steady-state analyses

Radiation heat loss is an important type of heat loss in thermal systems. In this work, a numerical study of the transient response of two circular radiation heat shields inserted between two parallel and circular surfaces of emissivities ε₁ and ε₂ is presented. The same dimensions have been assumed for the two main radiating surfaces and the two radiation shields. The radiation shields are assumed to have different emissivities on their top (ε₃ and ε₅) and bottom ( ε₄ and ε₆) surfaces, and both are assumed to be different but linear functions of temperature. A specific configuration is investigated in detail to highlight the transient temperature and heat transfer characteristics of the system. Some new results for the transient temperature and heat transfer characteristics of the system such as the effect of shield location, shield emissivities, the temperature dependence of shield emissivities, system dimensions, temperatures of the hot and cold surfaces and emissivities of the hot and cold surfaces are presented for future references. It has been observed that increasing the temperature of the first radiation shield by changing a parameter such as surface emissivity or distance between the radiation shield or the temperature of the hot surface, will not necessarily decrease the temperature of the second radiation shield.     

违反标度定律的一种相变模型

本文准确地求得了一种三维八顶点模型(能量参数满足条件ε₁+ε₂=ε₃+ε₄)的全部临界指数:α=α′=0,β=1/4,δ=7,γ=1/2,γ′=3/2,ν=ν′=1,η=3/2。它们不满足标度定律,其原因是在相变时极化关联的范围发生了收缩(从晶面(1,1,1)和(1,1,1)收缩成晶轴[1,0,1]。     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.