Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Influence of the kinematical constraints on the transverse momentum correlation features

The influence of the kinematical constraints on the transverse momentum correlation features in multiparticle processes is studied by means of thedN/(d r ₁ d r ₂) distribution,r ₁ andr ₂ being the transverse momenta of the particles entering in each pair. Using a limited transverse momentum phase space we obtain for high energy reactions a simple analytical expression fordN/(d r ₁ d r ₂). This expression, similar to a phenomenological parametrization proposed for analyzing¯pp annihilation data, served to define a correlation parameter, the non vanishing value of which is due to the energy-momentum conservation constraints.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Bloch electron dynamics

New equations of motion for a Bloch electron [momentum p=h k,energy ε _n(p),zone number n, charge -e]: $$m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j $$ are proposed, where v≡?ε_n(p)/?p is the velocity, and {m_j}are the principal masses m _j ^? 1=?²ε_n/?p _j ² along the normal and the two principal axes of curvatures at each point of the constant-energy surface represented by ε=ε_n(p).Their advantages over the prevalent equations of motion where the left-hand-side is replaced by hk _j are demonstrated by examining de Haas-van Alphen oscillations and orientation-dependent cyclotron resonance peaks.     

A model of the holographic principle: Randomness and additional dimension

In recent years an idea has emerged that a system in a 3-dimensional space can be described from an information point of view by a system on its 2-dimensional boundary. This mysterious correspondence is called the Holographic Principle and has had profound effects in string theory and our perception of space-time. In this note we describe a purely mathematical model of the Holographic Principle using ideas from nonlinear dynamical systems theory. We show that a random map on the surface S² of a 3-dimensional open ball B has a natural counterpart in B, and the two maps acting in different dimensional spaces have the same entropy. We can reverse this construction if we start with a special 3-dimensional map in B called a skew product. The key idea is to use the randomness, as imbedded in the parameter of the 2-dimensional random map, to define a third dimension. The main result shows that if we start with an arbitrary dynamical system in B with entropy E we can construct a random map on S² whose entropy is arbitrarily close to E.     

Fast calculation of HELAS amplitudes using graphics processing unit (GPU)

We use the graphics processing unit (GPU) for fast calculations of helicity amplitudes of physics processes. As our first attempt, we compute $u\overline{u}\rightarrow n\gamma$ (n=2 to 8) processes in pp collisions at $\sqrt{s}=14$  TeV by transferring the MadGraph generated HELAS amplitudes (FORTRAN) into newly developed HEGET (HELAS Evaluation with GPU Enhanced Technology) codes written in CUDA, a C-platform developed by NVIDIA for general purpose computing on the GPU. Compared with the usual CPU programs, we obtain a 40–150 times better performance on the GPU.     

Entangling capabilities of symmetric two-qubit gates

Our work addresses the problem ofgenerating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, μ〉; μ = + 1, 0, ?1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators J _x , J _y , J _z . We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Self energy of heavy quarks in confined QCD

We calculate the self energy of a heavy quark in order α _s of QCD confined to a spherical cavity. Only the radius-(and position-) dependent terms which cannot be renormalized away are taken into account. Besides the leadingO(M ⁰) contribution which acts as a confining potential we determine theO (1/M ²) corrections which contain orbital terms and contributions to theLS potential. This calculation completes the determination of the Breit-Fermi Hamiltonian for a confinedQ \(\bar Q\) system whose interaction parts have been discussed previously. We give some preliminary estimates of the resultant spin dependent level splittings in charmonium.     

Another supersymmetric extension of local Lorentz symmetry in the vierbein formalism of Einstein gravity

A supersymmetric extension of the vierbein formalism of Einstein gravity is investigated by takingSL(N, 2;C) superalgebra, which is shown to be the sole possibility other than the previously investigatedOSp(N 2;C). After general discussion on the ξ-field realization, a non-linear realization of linear representation introduced in a previous paper, it is applied to the fundamental representation ofSL(N, 2;C) t0 which the vierbein supermultiplet belongs. The chiral symmetry derived in the theory is shown to beSO(N) in the same way as in theOSp(N,2;C)-symmetric extension.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.     

Analyzing Power of 3He(n, n)3He Between 1.60 and 5.54 MeV

We report the measurements of the analyzing power A _y (θ) of n-³He elastic scattering with unprecedented accuracy and angular coverage at five incident neutron energies between 1.60 and 5.54 MeV. To this end, we employed the polarization-transfer reactions ³H(p, n)³He and ²H(d, n)³He at 0° for neutron generation and a recently developed high-pressure ³He gas scintillator as an active target, enabling neutron-time-of-flight and ³He recoil-energy determinations. We obtained simultaneously the neutron polarization with a ⁴He-based polarimeter, capitalizing on the well-known n-⁴He A _y (θ). Our n-³He A _y (θ) data are compared to rigorous four-nucleon calculations using high-precision nucleon–nucleon potential models. The agreement between data and calculations is fair at the lower energies and becomes less satisfactory with increasing neutron energy. However, in comparison to the pure isotriplet p-³He system in the same energy region, the agreement between measured and calculated A _y is much better for the mixed (isotriplet and isosinglet) n-³He system, indicating large and somewhat counterintuitive isospin effects. We note that the incorporation of a Δ-mediated three-nucleon force in calculations of n-³He scattering was found to affect A _y (θ) negligibly, suggesting the need for the reconsideration of fundamental interactions in resolving the four-nucleon analyzing power puzzle first established about a decade ago in p-³He scattering.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Three-wave mixing and light diffraction by transient light induced gratings for the study of fast relaxation processes

The action of two successive intense ultrashort coherent light pulses with different wave vectorsk ₁ andk ₂ on a nonlinear inhomogeneously broadened medium is considered. The resulting spatial and temporal polarization and saturation structure is calculated within a two level density matrix approach. Without use of perturbation theory, both the dynamic behaviour of the nonlinear medium under hole burning conditions and the temporal behaviour of the output pulse in the2k ₁ -k ₂ direction generated by the polarization of the medium during and after the action of the second pulse are discussed. The diffraction of a third probe pulse by the saturation grating as well as by the polarization of the medium is calculated. Possibilities for measuring the longitudinal, transverse and inhomogeneous relaxation times are discussed.     

Trovacenyl-based organometallic triradicals: Spin frustration, competing interactions and redox splitting

Two new triradicals based on trovacene [η⁷-tropylium)vanadium(η⁵-cyclopentadienyl)], 1,3,5-tri([5]trovacenyl) benzene4 and 1,3,5-tri([5]trovacenyl)-6-methoxybenzene5 were prepared and their magnetic properties were studied by continuous-wave X-band electron paramagnetic resonance (EPR) spectroscopy and by temperature-dependent magnetic susceptometry. The EPR spectra of4 and5 in liquid toluene solution demonstrate that the three unpaired electrons localized on the vanadium atoms interact with each other in both complexes. The data from magnetic susceptometry revealed that the electron spins in both triradicals are antiferromagnetically coupled despite themeta-phenylene bridge. The exchange coupling constants are equal in the C₃-symmetrical triradical4 (J=J′=?0.68 cm^?1), which leads to a twofold degenerate spin ground state (spin frustration). The symmetry lowering by methoxy substitution of the benzene spacer in5 results in the effect of c ompeting interactions (J=?1.83 cm^?1 andJ′=?2.38 cm^?1). In addition to magnetocommunication, the effect of ring substitution on electrocommunication is also discernable. It manifests itself indisparate redox splittings δE _1/2 (0/?, ?/2?) and δE _1/2 (?/2?, 2?/3?) for5, while these parameters are equal for the C₃-symmetrical trinuclear complex4.     

EPR study of Gd3+ in a ferroelastic BiVO4 single crystal

Electron paramagnetic resonance of the Gd³⁺ ion in a ferroelastic BiVO₄ single crystal with a single domain, grown by the Czochralski method, has been investigated at room temperature using a Q-band spectrometer. The rotation patterns of the resonance fields measured in the crystallographic planes are analyzed using a monoclinic spin Hamiltonian. The principal Z-axis of the second-order zero-field splitting tensorD is found to be along the crystallographicb-axis. Spin Hamiltonian parameters together with the principal axes ofg andD tensors in the monoclinic plane show that the local site symmetry of Gd³⁺ ion in BiVO₄ crystal is monoclinic and that the Gd³⁺ ion substitutes for Bi³⁺ ion.     

QCD on the Light-Front

Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x ⁺ = x ⁰ + x ³, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H _LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H _LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable \({\zeta^2=b^2_\perp x(1-x)}\) , which is conjugate to the invariant mass squared \({{M^2_{q\bar q}}}\) . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories \({M^2(n, L, S) = 4\kappa^2( n+L +S/2)}\) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter \({\kappa}\) appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS₅ space with a unique dilaton profile to QCD (3 + 1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

The influence of disorder on magnetocaloric effect and the order of transition in ferromagnetic manganite (La1−x Nd x )2/3(Ca1−y Sr y )1/3MnO3

Magnetocaloric effect and order of transition in (La_1?x Nd _x )_2/3(Ca_1?y Sr _y )_1/3MnO₃, prepared by conventional solid-state reaction, have been investigated. Using Banerjee criterion, we demonstrate first-order transition for (J1) and (J2 ) as well as second-order transition for (J3 ), (J4 ), and (J5 ) samples. The ΔS _M ^max is ranging between 9.18 Jkg^?1 K^?1 and 4.87 when Nd and Sr content changes leading to relative cooling power (RCP) varying between 330 and 229.35 J/kg. Both ΔS _M ^max and the RCP are found sensitive to the disorder σ ². The universal behavior obtained from ΔS variation curves confirmed the first-order transition for (J1) and (J2 ) samples and second-order transition for (J3), (J4), and (J5 ) samples obtained by Banerjee criterion. All samples with second-order phase transition exhibit inhomogeneous character estimated from local exponent n.