Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Magnetoresistance of the semiconducting spinelide Cu0.625Ga0.375Cr2Se4 having a low-temperature long-range magnetic order-spin glass transition

A study is reported of the dependence of magnetoresistance Δρ/ρ on the square of magnetization σ ² of the semiconducting spinelide Cu_0.625Ga_0.375Cr₂Se₄, which exhibits a low-temperature transition from long-range magnetic order (LRMO) to the spin glass (SG) state in strong magnetic fields. It is shown that at the freezing temperature T _f the Δρ/ρ(σ ²) relations change their slope, and that below T _f this slope is about one half that for T>T f. This finding, together with the earlier observation that the freezing temperature does not depend on the frequency of the ac magnetic field in which it was measured, suggests that the spin-glass phase consists of spins of individual Cr³⁺ ions, and that the SG-LRMO crossover is a phase transition. Fiz. Tverd. Tela (St. Petersburg) 40, 315–317 (February 1998)     

CIDEP Created by the Quenching of Photo-Excited Tryptophan at Protein Surface: A Challenge to CIDEP Probing of Protein Structural Changes

Quenching of the triplet excited state of molecular tryptophan by nitroxide radical in 1,4-dioxane and water solutions was investigated by means of time-resolved electron paramagnetic resonance (EPR) and Fourier-transform (FT)-EPR. The chemically induced dynamic electron polarization (CIDEP) signals with net emissive phase were recorded at these quenching events and were analyzed through radical-triplet pair mechanism. The CIDEP time profiles were well reproduced by Bloch and kinetic equations, assuming radical-triplet pair mechanism with the appropriate quenching rate constants. From a comparison of the simulation and the experiment, CIDEP enhancement factor in 1,4-dioxane was determined to be −30 × P _eq, where P _eq is the spin polarization of nitroxide at thermal equilibrium. Net emissive CIDEP was also observed by FT-EPR measurements on the nitroxide quenching of the triplet excited state of tryptophan residue in α-lactalbumin. Magnitude of CIDEP created in α-lactalbumin/nitroxide system depends on the pH condition of α-lactalbumin solution, which is related to protein folding dynamics. We argue the CIDEP mechanism at the α-lactalbumin surface and propose a possibility of a novel CIDEP method to probe a protein surface and structural changes.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Dislocational kinetics in the intense deformation of fcc single crystals

The stability of the dislocational subsystem of fcc single crystals deformed in dynamic conditions is investigated. It is shown that, depending on the deformational conditions, the system may have one or two steady states, one of which is ρ _s ⁽¹⁾ . When the system has one trivial steady state, it may be stable or unstable. In some conditions, a second unstable point ρ _s ⁽²⁾ appears; in this case, ρ _s ⁽¹⁾ is stable. Tomsk State Architectural and Building Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 43–48, August, 1997.     

Bistability of quantum magnetotransport in a multilayer Ge/p-Ge1−x Six heterostructure with wide potential wells

Two metastable states of a multilayer Ge/p-Ge_1−x Si_x heterosystem with wide (∼ 35 nm) potential wells (Ge) are observed in strong magnetic fields B at low temperatures. In the first state, the Hall resistivity exhibits an inflection near the value ρ_xy=h/e ² scaled to one Ge layer. The longitudinal magnetoresistivity ρ_xx(B) possesses a minimum in the range of fields where this inflection occurs. The temperature evolution of the inflection in ρ_xy(B), the minimum of ρ _xx(B), and the value of ρ_xy at the inflection indicates a weakly expressed state of the quantum Hall effect with a uniform current distribution over the layers. In the second metastable state, an unusually wide plateau near h/2e ² with a very weak field dependence is observed in ρ_xy(B). Estimates show that in these samples the Fermi level lies below but close to the top of the inflection in the bottom of the well. For this reason, the second state can be explained by separation of a hole gas in the Ge layers into two sublayers, and the saturation of ρ_xy(B) near h/2e ² can be explained by the formation of a quantum Hall insulator state. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 290–297 (25 August 1999)     

Double spin asymmetry in exclusive ρ0 muoproduction at COMPASS

The longitudinal double spin asymmetry A₁ ^ρ for exclusive leptoproduction of ρ⁰ mesons, μ+N→μ+N+ρ, is studied using the COMPASS 2002 and 2003 data. The measured reaction is incoherent exclusive ρ⁰ production on polarised deuterons. The Q² and x dependence of A₁ ^ρ is presented in a wide kinematical range, 3×10^-3<Q²< 7 (GeV/c)² and 5×10^-5<x<0.05. The results presented are the first measurements of A₁ ^ρ at small Q² (Q²< 0.1 (GeV/c)²) and small x (x<3×10^-3). The asymmetry is in general compatible with zero in the whole kinematical range. PACS 13.60.Le; 13.88.+e     

AN-Type Dunkl Operators and New Spin Calogero–Sutherland Models

A new family of A _N -type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero–Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin Hamiltonians. Received: 17 February 2001 / Accepted: 8 March 2001     

Equilibrium low temperature heat capacity of the spin density wave compound (TMTTF)<Subscript>2</Subscript>Br: effect of a magnetic field

We have investigated the effect of the magnetic field (B) on the very low-temperature equilibrium heat capacity c_eq of the quasi-1 D organic compound (TMTTF)₂Br, characterized by a commensurate Spin Density Wave (SDW) ground state. Below 1 K, c_eq is dominated by a Schottky-like A_ST^-2 contribution, very sensitive to the experimental time scale, a property that we have previously measured in numerous DW compounds. Under applied field (in the range 0.2–7 T), the equilibrium dynamics, and hence c_eq extracted from the time constant, increases enormously. For B ≥ 2–3 T, c_eq varies like B², in agreement with a magnetic Zeeman coupling. Another specific property, common to other Charge/Spin density wave (DW) compounds, is the occurrence of metastable branches in c_eq, induced at very low temperature by the field exceeding a critical value. These effects are discussed within a generalization to SDWs in a magnetic field of the available Larkin-Ovchinnikov local model of strong pinning. A limitation of the model when compared to experiments is pointed out.     

q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

We study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r ^α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.      

Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =-Λ + w ₁ρ(a) + w ₂ a ^β + 0 and energy density ρ = Λ+ρ₀₁ a ^-3(1+w) +ρ₀₂ a ^α +ρ₀₃ a ^-3, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Ω_m,0 ≃ 0.4 and n ≃ -1 (β = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Ω_m,0 = 0.3 then the favoured model is close to concordance ΛCDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the ΛCDM model, while intermediate distant SNIa should be fainter than in the ΛCDM model. We also investigate whether the model with scaling fluid is actually preferred by data over ΛCDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.     

On the Boltzmann Equation for Fermi–Dirac Particles with Very Soft Potentials: Averaging Compactness of Weak Solutions

The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L ¹-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ _*|^γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫₀ ^π b(cos θ)sin ³θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L ^∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy.     

A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = C _γ ρ ^γ for γ > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied.     

SCQGP in quark stars

From an analogy with non-relativistic degenerate QED plasma we make an estimate of the coupling strength of QGP hypothesized to be present in compact star interiors. At densities ranging from 3ρ ₀–10ρ ₀ (normal nuclear density ρ ₀=0.16 fm⁻³), quark matter is found to be strongly to intermediately coupled. The equation of state for QED plasma obtained via Pade approximation, modified to QGP, yields stable stellar sequences with maximum mass ≳2M _⊙ for B ^1/4≲215 MeV.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Spin-Dependent Bohmian Electronic Trajectories for Helium

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates. First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical. We then examine higher-dimensional approximations, i.e., eigenstates Ψ _α of the Hamiltonian in this truncated basis, and show that ∇ _i S _α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation. The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Flow equations for the spin-boson problem

Using continuous unitary transformations recently introduced by Wegner [1], we obtain flow equations for the parameters of the spin-boson Hamiltonian. Interactions not contained in the original Hamiltonian are generated by this unitary transformation. Within an approximation that neglects additional interactions quadratic in the bath operators, we can close the flow equations. Applying this formalism to the case of Ohmic dissipation at zero temperature, we calculate the renormalized tunneling frequency. We find a transition from an untrapped to trapped state at the critical coupling constant α _c =1. We also obtain the static susceptibility via the equilibrium spin correlation function. Our results are both consistent with results known from the Kondo problem and those obtained from mode-coupling theories. Using this formalism at finite temperature, we find a transition from coherent to incoherent tunneling atT ₂ ^* ≈2T ₁ ^* , whereT ₁ ^* is the crossover temperature of the dynamics known from the NIBA.