Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

Magnetic excitations and phase transition of CsFeBr3 in an external magnetic field

In CSFeBr₃ the Fe²⁺ ion with effective spin one has locally a singlet ground state (m=0). The antiferromagnetic interactions between neighbouring Fe-ions are too weak as compared with the anisotropy constant to introduce long range order in the absence of an external field. By inelastic neutron scattering we studied the magnetic excitations in an external magnetic field up to 5 Tesla applied along thec-axis. A linear Zeeman splitting was observed with a Landé factorg=2.4. The field renormalizes the dispersion curves in such a way that the exchange interaction has decreasing influence with increasing field. Theoretical calculations according to the excitonic model of Lindgård describe the experimental results very well. At 4.1 Tesla a phase transition appears to a commensurate long range order with a 120° arrangement of the spins in the hexagonal plane. Within the limits of experimental observation this phase transition has no influence on the dynamical behaviour. No critical phenomena could be observed. The dynamical structure factor |G _j()|² of the lower Zeeman split modes decreases with increasing field.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong coupling negativeU Hubbard model

We calculate fluctuation effects on Bose condensation type superconductivity in the strong coupling negative U Hubbard model by means of a new loop expansion. Our method is based on a spin-dependent modification of the Popov-Fedotov trick. We replace the Popov-Fedotov chemical potential by a fictitious imaginary magnetic field. This field is absorbed in spindependent semionic Matsubara frequencies, which allows for a mixed statistics representation of the anisotropic quantum spin 1/2 Heisenberg model. We report results at one loop order for the superconducting order parameter , for the critical temperature, for the chemical potential, and for the excitation spectra both above and belowT _c. We identify mean field results in zeroth loop order and we find both dimensional and filling (v-)depending singularities in interaction fluctuations at one loop order. Renormalization of dimensional singularities is carried out in 4 dimensions. Divergencies withv (1–v)0 in the dilute limits indicate the breakdown of mean field solutions, but superconductivity persists for arbitrarily smallv(1–v) if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma model.     

Contribution of octahedrally co-ordinated Mn3+ ion to magnetic torque

In order to understand experimentally measured magnetic torque in Mn _x Fe_3–x O₄(x1) systems an extensive study of the behaviour of octahedrally co-ordinated Mn³⁺ ion is made. Special attention is paid to orbit-lattice coupling and to interaction of Mn³⁺ ion with the lattice defects. Also the use of molecular field approximation in calculation of torque is critically reviewed.     

Ab initio pair potential and phase equilibria predictions for the refrigerant methyl fluoride

Ab initio pair interaction energies for methyl fluoride (CH₃F) were calculated using symmetry adapted perturbation theory with the aug-cc-pVDZ basis set plus bond functions for a large number of configurations of a pair of methyl fluoride molecules in order to obtain a good representation of the two-body potential energy surface. These interaction energies were used to develop a site-site intermolecular potential that accurately reproduced the calculated energies and had the correct asymptotic behaviour at long range. This pair potential was used in Gibbs ensemble Monte Carlo simulations to predict the phase behaviour of methyl fluoride. The predicted equilibrium properties with the ab initio pair potential are in good agreement with the experimentally measured phase boundary, and give an estimated critical point in excellent agreement with measured values. Multi-body effects were then added to the pair potential using a polarizable model. The small changes to the phase behaviour that resulted established that pairwise interactions account for most of the molecular interactions in CH₃F.     

Influence of cubic anisotropy in dipole-dipole interactions on structural phase transitions using the renormalization group transformation

The critical behaviour of ferroelectrics is studied forT>T _c and for zero electric field, by the renormalization group techniques ind=3 dimensions. The model hamiltonian we used contains an isotropic exchange coupling and a dipolar interaction with strong cubic anisotropy. A quadratic anisotropic fixed point is found to be stable for the cubic anisotropic scale field. Experiments on BaTiO₃ and KTaO₃ are compared with our results.Work supported by N.F.W.O.     

Magnetic and optical properties of Zn1– x Fe x O ( x = 0.05 and 0.10) diluted magnetic semiconducting nanoparticles

We have investigated the magnetic and optical properties of chemically low temperature-synthesized Zn_{1– x} Fe _x O (x = 0.05 and 0.10) diluted magnetic semiconducting nanoparticles (～7 nm). Observed magnetic behaviour of x = 0.05 samples showed that the net magnetic interaction was antiferromagnetic-like, a feature established by Curie–Weiss fit, concave Arrott–Belov–Kouvel (ABK) plots with the absence of spontaneous magnetization even at 5 K and stretched exponential-type time-dependent magnetization behaviour. Optimization of the Fe(x) dopant concentration in Zn_{1– x} Fe _x O gave the most favourable room-temperature ferromagnetism for x = 0.10, as supported by finite coercive field (～94.4 Oe) and remanent magnetization (0.011 µ_B/Fe ion) from strong hysteretic magnetization vs. magnetic-field curves at room temperature. The Curie temperature of the x = 0.10 sample was estimated at ～388 K. The existence of a room-temperature ferromagnetic phase was further established by the convex nature of the ABK plots with finite spontaneous magnetization. The observed magnetic behaviour for different x values is best explained by a magnetic polaron model.     

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R ^-5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading pressure, excess surface energy and entropy are also obtained for a dilute gas of rod-like molecules near a surface. We find that the extent of surface binding increases nearly exponentially with molecular length at constant temperature and surface density, and that the excess surface energy and entropy are essentially proportional to the molecular length.     

Local three-nucleon interaction from chiral effective field theory

The three-nucleon (NNN) interaction derived within the chiral effective field theory at the next-to-next-to-leading order (N²LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction is then local in the coordinate space, which is advantageous for some many-body techniques. Matrix elements of the local chiral NNN interaction are evaluated in a three-nucleon basis. Using the ab initio no-core shell model (NCSM) the NNN matrix elements are employed in ³H and ⁴He bound-state calculations. Correspondence: P. Navrátil, Lawrence Livermore National Laboratory, L-414, P.O. Box 808, Livermore, CA 94551, USA     

Electrical resistivity behaviour of sodium substituted manganites: electron-phonon,electron-electron and electron-magnon interactions

The present paper focuses on a quantitative analysis of the metallic and semiconducting behaviour of electrical resistivity in perovskite manganites La_{1- x} Na _x MnO₃ (x = 0.1, 0.17). An effective interionic interaction potential (EIoIP) with the long-range Coulomb, van der Waals (vdW) interaction and short-range repulsive interaction up to second neighbour ions within the Hafemeister and Flygare approach was formulated to estimate the Debye and Einstein temperature and was found to be consistent with the available experimental data. For both doping concentration x = 0.1 and 0.17 the electron-phonon, electron-electron and electron-magnon interactions are effective to describe the resistivity behaviour for temperatures less than the metal-insulator transition (T _P ). For temperatures, T > T _P , the semiconducting nature is discussed with Mott's variable range hopping (VRH) model and small polaron conduction (SPC) model. The fitted density of states as revealed from VRH differs drastically from the experimental value and therefore means the VRH model is not a viable option for describing the resistivity behaviour in high temperature region, T > T _P . The SPC model consistently retraces the higher temperature resistivity behaviour (T > θ _D /2). The metallic and semiconducting resistivity behaviour of sodium substituted manganites are analysed, to our knowledge, for the first time highlighting the importance of electron-phonon, electron-electron, electron-magnon interactions and small polaron conduction.     

Equation of motion and nonlinear response near the critical point

For a one-component (Ising-like) Ginzburg-Landau field we have derived an equation of motion which governs the behaviour of the order parameter nearT _c . We present this equation in a general scaling form dictated by the renormalization group, and calculate the form explicitly to first order in=4–d. There is a memory term in the result which in order contains the full nonlinear response of the order parameter. As a special case we obtain the linear response function for a nonvanishing external field.     

Biquadratic exchange and critical behaviour in the diluted antiferromagnet EuxSr1−xTe

Magnetization, specific heat, magnetocaloric effect, and neutron diffraction measurements have been performed in order to better understand the magnetic interactions and phase transitions in the diluted antiferromagnetic system Eu_xSr_1–xTe. Due to the low Néel temperature ofT _N =9.8 K and the associated small critical field ofB _C (T=0)=7.5 T, EuTe provides the opportunity to change the angle between the antiferromagnetic moments continuously between 180° and 0° by applying a magnetic field and allows thus to probe the type of the magnetic interaction. It is found that in addition to the common bilinear Heisenberg exchange mechanism there is evidence for a small biquadratic exchange term, which has important consequences on the critical behaviour of Eu_xSr_1–xTe. In the case of EuTe the biquadratic exchange supports the antiferromagnetic order, such that virtually no anisotropy exists and this restricts the anti-Herromagnetic (AF) to spin-flop (SF) transition toB ₀=0. On dilution with strontium, the biquadratic interaction decreases strongly and changes its sign at x0.83 thus favouring the perpendicular moment orientation. This acts like an anisotropy on the dominating antiferromagnetic bilinear interaction and shifts the AF-SF phase line to finite fields which reach values of 0.3 T forT0. No bicritical behaviour is observed, but instead, the SF phase is the state of lowest energy in a small temperature interval belowT _N . The critical exponent (x) of the specific heat decreases in a non-linear way with dilution starting from a large positive value for EuTe. (x) is close to the Heisenberg value –0.12 nearx0.83 where the biquadratic interaction is zero. The same applies for the exponent of the sublattice magnetization.     

DPAC study of radiation damage in178W recoil implanted silicon

The annealing behaviour of radiation damage in¹⁷⁸W recoil implanted n-type Si is studied from 295 to 641 K by the differential perturbed angular correlation method (DPAC), using¹⁷⁸Hf as probe nuclei for the first time. Preliminary results suggest that oxygen-vacancy (O-V) pairs are observed, which give rise to a quadrupole interaction characterized by |V _zz|=5.41×10¹⁸ V/cm² (v _Q=2550 MHz). The probe nuclei also experience an electric field gradient (EFG) due to distant defects.     

QED Derived from the Two-Body Interaction

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.⁽¹⁾ In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.     

Thermal Fields as Causal Fluids

In a previous paper we investigated a divergence-type theory (DDT) describing the dissipative interaction between a field and a fluid. In this paper we compare the macroscopic view of DDT with a microscopic special case, an O(N) scalar field to leading order in the large N approximation and its thermal fluctuations. Our aim is to compare within a simple model the two approaches.     

Scaling of entanglement entropy for spin chain with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement in an XX-type spin chain with Dzyaloshinskii-Moriya interaction under an external magnetic field.The von Neumann entropy of entanglement between two blocks for the ground state of the system is evaluated.It analyses and discusses the scaling behaviour of the entanglement entropy.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

Anomalous anisotropies and field dependencies of the muon Knight shift and the relaxation rate in monocrystalline Bi

The angular dependence of the muon Knight shift,K _μ, and the muon relaxation rate in Bi at 11 K were measured in external magnetic fields up to 1 T. BothK _μ and the second moment,M ₂, are field dependent and involveP ₄ ⁰(cos θ) andP ₄ ³(cos θ) terms in the angular dependence. The Knight shift behaviour is discussed in terms of the dipole-dipole interaction and the de Haas-van Alphen effect, a consistent interpretation was not achieved in either case. The field dependence ofM ₂ is in complete contrast to the second moment calculations and points to a field dependent redistribution of the charge distribution around the interstitial site.