Goos-Hänchen effect of spin electron beams in a parallel double <Emphasis Type="Italic">δ</Emphasis>-barrier magnetic nanostructure

In this paper, we study the effect of time-periodic coupling strength (TPCS) and network connection degree ⟨k⟩ on the temporal coherence of the chaotic bursting of the scale-free networks of thermo-sensitive neurons. It is found that the chaotic bursting becomes ordered and can exhibit coherence resonance (CR) when TPCS amplitude ε ₀ or the network connection degree ⟨k⟩ is varied. In particular, the neuronal bursting may exhibit multiple CR (MCR) behavior when TPCS frequency ω is varied. It is also found that, as ⟨k⟩ is increased, the value of ε ₀ for the MCR decreases, but the frequency for the MCR almost keeps unchanged. These results show that the chaotic bursting can be tamed and the bursting temporal coherence can be enhanced and even optimized by TPCS and network connection degree. Furthermore, TPCS can repetitively enhance and even optimize the temporal coherence of the neuronal bursting behavior. These findings may help to better understand the roles of TPCS and network connection degree for improving the time precision of the information processing in neuronal networks.     

Entanglement entropy fluctuations in quantum Ising chains

The behavior of Ising chains with the spin-spin interaction value λ in a transverse magnetic field of constant intensity (h = 1) is considered. For a chain of infinite length, exact analytical formulas are obtained for the second central moment (dispersion) of the entropy operator Ŝ = -lnρ with reduced density matrix ρ, which corresponds to a semi-infinite part of the model chain occurring in the ground state. In the vicinity of a critical point λ_c = 1, the entanglement entropy fluctuation ΔS (defined as the square root of dispersion) diverges as ΔS ∼ [ln(1/|1 − λ|)]^1/2. For the known behavior of the entanglement entropy S, this divergence results in that the relative fluctuation δS = ΔS/S vanishes at the critical point, that is, a state with almost nonfluctuating entanglement is attained.     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Size effect in spin-crossover systems investigated by FORC measurements,for surfacted [Fe(NH<Subscript>2</Subscript>-trz)<Subscript>3</Subscript>](Br)<Subscript>2</Subscript>·3H<Subscript>2</Subscript>O nanoparticles: reversible contributions and critical size

We investigated the thermal transition of coated nano-particles of the title compound, on a set of samples of average diameter ⟨d⟩ ~ 30, 50, 70, 110 nm, with rather broad size distributions. As expected, the width of the major hysteresis loop was an increasing function of ⟨d⟩. We recorded first-order reversal curves (FORC), the initial parts of which displayed a finite slope, revealing the presence of reversible contributions expected from particles smaller than the critical size d _C associated with the collapse of the hysteresis loop. Kinetic effects were also evidenced thanks to isothermal stages. Reversibility of the FORC curves at the vicinity of the reversal temperature was controlled. Thanks to the reversibility property we could determine the reversible contributions to the total response of all samples and derive the corresponding d _C values. Consistent results were obtained by accounting for an anhysteretic contribution from the large particles, leading to an accurate determination d _C  ~ 45−50 nm, much better than the width of the size distributions.     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨N _nc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.     

Relaxation to Equilibrium for Two Dimensional Disordered Ising Systems in the Griffiths Phase

We consider Glauber–type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder–averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder–average C(t) of time–autocorrelation function satisfies (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J ₀>0, our results apply even if the active bonds percolate and J ₀ is larger than the critical value J _c of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper bound is optimal. This implies the existence of a dynamical phase transition which occurs when J crosses J _c . Received:     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

Microwave energy channeling in plasma waveguides created by a high-power UV laser in the atmosphere

The grazing mode of microwave propagation in a hollow plasma waveguide formed by ionization of atmospheric air with a small easily ionized additive by strong UV pulses of the Garpun KrF laser (λ = 248 nm, the pulse duration and energy are ∼70 ns and ∼50 J) was experimentally demonstrated for the first time. The annular laser beam produced a hollow tube ∼10 cm in diameter with an electron density of ∼10¹² cm⁻³ in a plasma wall ∼1 cm thick, over whichmicrowave radiation with λ _mw ∼ 8 mm was transmitted to a distance of 60 m. Themicrowave signal transmitted by the waveguide was amplified by a factor of 6 in comparison with propagation in free space.     

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼K _f q ⁴ and ∼Qq ² terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A ₀)^−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A ₀, a flexural rigidity K _f , and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√K _f B(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli K _f and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus K _A , the equilibrium area per lipid A _t , and the chain order parameter S(θ). The text was submitted by the authors in English.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

Entanglement in the Extended XY Spin Model with Three Spin Interaction and External Field

We investigate the pairwise thermal entanglement of the extended XY model with three spin interactions and external filed on zig-zag lattice. The influences of three spin interactions J ₂ and external field λ on the thermal entanglement of the nearest neighbor (NN) and next nearest neighbor (NNN) spins are considered. It is found that J ₂ and λ suppress both the maximal value and the critical temperature of the NN entanglement C ₁₂. However, when it comes to the NNN entanglement C ₁₃, there exists a critical value of J ₂ above which both the maximal entanglement and the critical temperature can be enhanced by J ₂ for a fixed external field. With J ₂ fixed, the effect of λ on C ₁₃ are different for different values of J ₂. For J ₂<1, λ suppresses both T _C and the maximal values of C ₁₃. For J ₂≥1, λ enhances the maximal values of C ₁₃ while decreases the critical temperature. These results show that one is able to get the entanglement wanted by properly controlling the values of the three spin interactions J ₂ and the external field λ.     

Asymptotic and effective coarsening exponents in surface growth models

We consider a class of unstable surface growth models, ?_t z = -?_x J\partial_t z = -\partial_x {\cal J} , developing a mound structure of size λ and displaying a perpetual coarsening process, i.e. an endless increase in time of λ. The coarsening exponents n, defined by the growth law of the mound size λ with time, λ∼tⁿ, were previously found by numerical integration of the growth equations [A. Torcini, P. Politi, Eur. Phys. J. B 25, 519 (2002)]. Recent analytical work now allows to interpret such findings as finite time effective exponents. The asymptotic exponents are shown to appear at so large time that cannot be reached by direct integration of the growth equations. The reason for the appearance of effective exponents is clearly identified.     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Low-temperature properties of ferromagnetic Fibonacci superlattices

Theoretical analysis of the layered quasi-periodic Fibonacci structures (superlattices-sequence) is presented for the systems consisting of n_A and n_B ferromagnetically ordered planes within the layers with S_a and S_b spins, respectively, while the interfaces are coupled with bilinear and/or biquadratic exchange interaction, within the framework of localized spin model in the low-temperature limit. Transfer matrix method and direct diagonalization after the bosonization in Bloch's approximation resulted both in the same analytical expression for the magnon-excitation energy. The equivalence (at low-temperatures) of the transfer matrix (spin) and boson approach was discussed, as well as the role of the interlayer biquadratic coupling between different blocks constituting the Fibonacci sequences. Also, our approach allows the determination of the internal energy and calculation of the magnon contribution to the specific heat. It was clearly demonstrated that the magnon specific heat vanishes for T → 0. Our results are compared with the results of other authors.     

Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility χ(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of χ(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic–antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen. Supported in part by NSF Grant No. PHY 01-00.     

Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T ₁ and T _n . Let E J _n be the steady-state energy current across the chain, averaged over the masses. We prove that E J _n ~ (T ₁ − T _n )n ^−3/2 in the limit n → ∞, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999