Phase Diagram of the BCS–Hubbard Model in a Magnetic Field

We propose an extended BCS–Hubbard model and investigate its ground state phase diagram in an external magnetic field. By mapping the model onto a model of spinless fermions coupled with conserving Z₂ variables which are mimicked by pseudospins, the model is shown to be exactly solvable along the symmetric lines for an arbitrary on-site Hubbard interaction on the bipartite lattice. In the zero field limit, the ground states exhibit an antiferromagnetic order of pseudospins. In the lar...     

The Linearized Vlasov and Vlasov–Fokker–Planck Equations in a Uniform Magnetic Field

Journal of Statistical Physics - We study the linearized Vlasov equations and the linearized Vlasov–Fokker–Planck equations in the weakly collisional limit in a uniform magnetic field....     

The Effect of Finiteness in the Saffman–Taylor Viscous Fingering Problem

We derive a family of exact time-evolving solutions for the the evolution of a finite blob of fluid confined to a channel in a Hele–Shaw cell. We show rigorously that, for large fluid volume, there are solutions for which one of the interfaces approaches the steady Saffman–Taylor finger solution of arbitrary width λ∈(0, 1). On the basis of this, we argue that the far-field effects of a displaced second interface do not provide a selection mechanism for the formation of a width- $ \frac{1}{2} $ finger when surface tension, or any other regularization, is ignored.     

Effect of Magnetic Field Annealing on Magnetic Properties of Iron–Gallium Alloys

Physics of the Solid State - The concentration dependence of magnetic properties of iron alloys with 3–25% of gallium is studied. It was shown that the saturation induction monotonically...     

Spin Filter Effect in Organic Polymers in the Presence of Local Magnetic Field

Using a nonadiabatic evolution method, we investigate the spin filter effect in organic polymers in the presence of a local magnetic field. Through a spin-dependent magnetic field, polarons （charge carrier） with different spins will feel repulsive or attractive force determined by their spins. Our simulations show that in a single-site magnetic field （affecting electrons at a single site）, for example V150 = 0.35 eV, or V150 = 0.45 eV, a spin-up polaron accelerated to saturated velocity by an electric field can pass through the field while the spin-down polaron is trapped. When the local field extends over several sites （Vn～ exp[-（n - nc）2/nw^2]）, similar behaviour is also found. Simultaneously we find that it is more likely to realize the spin filter effect in a comparatively large field since the polaron which feels attractive force is easily trapped by a local magnetic field.     

Generalized Rashba Coupling Approximation to a Resonant Spin Hall Effect of the Spin–Orbit Coupling System in a Magnetic Field

We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases,the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.     

Effect of the Initial Laser Phase on the Interaction Between Relativistic Electron and Ultra－Intense Laser Field in a Strong Uniform Magnetic Field

We investigate the influence of the initial laser phase on the interaction between relativistic electron and ultraintense linear polarized laser field in a strong uniform magnetic field. It is found that the dynamic behaviour of the relativistic electron and the emission spectrum varies dramatically with different initial laser field phases.The effect of changing initial phase is contrary in the two parameter regions divided by the resonance condition.The phase dependence of the electron energy and velocity components are also studied. Some beat structure is found when the initial laser phase is zero and this structure is absent when the initial laser phase is a quarter of a period.     

Development of the Fast Ionization Gauge in a Strong Magnetic Field

The neutral gas pressure near plasma or divertor plates are very important for the plasma-wall interaction, which determines the operating mode of divertor and confining performances of plasma in tokamaks. A fast ionization gauge (fast gauge) is designed for this purpose in the HL-2A tokamak.     

Neutrino–Electron Processes in a Magnetic Field and Their Crossing Symmetry

We have studied the neutrino–electron processes in a matter with an external magnetic field of an arbitrary strength. Invariant squares of S-matrix elements, which have been obtained for such reactions using the technique based on the density matrix of a particle propagating in an external magnetic field, are valid in an arbitrary frame of reference moving along the magnetic field lines. The transition probabilities obtained can easily be generalized to the processes of interaction of a neutrino with other charged leptons and protons. The probabilities of the processes have been integrated over the transverse momenta of charged particles for the rates of neutrino–electron reactions as well as the energy and momentum transferred in them from the medium to neutrinos. The expressions obtained are written in the unified form for all neutrino–electron processes.     

Microcanonical Analysis of the Curie–Weiss Anisotropic Quantum Heisenberg Model in a Magnetic Field

The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying the concavity properties of entropies. The microcanonical entropy \(s(e,\varvec{m})\) is obtained as a function of the energy \(e\) and the magnetization vector \({\varvec{m}}\) in the thermodynamic limit. Since, for this model, \(e\) is uniquely determined by \({\varvec{m}}\) , the same information can be encoded either in \(s(\varvec{m})\) or \(s(e,m_1,m_2)\) . Although these two entropies correspond to the same physical setting of fixed \(e\) and \({\varvec{m}}\) , their concavity properties differ. The entropy \(s_{{\varvec{h}}}(u)\) , describing the model at fixed total energy \(u\) and in a homogeneous external magnetic field \({\varvec{h}}\) of arbitrary direction, is obtained by reduction from the nonconcave entropy \(s(e,m_1,m_2)\) . In doing so, concavity, and therefore equivalence of ensembles, is restored. \(s_{{\varvec{h}}}(u)\) has nonanalyticities on surfaces of co-dimension 1 in the \((u,\varvec{h})\) -space. Projecting these surfaces into lower-dimensional phase diagrams, we observe that the resulting phase transition lines are situated in the positive-temperature region for some parameter values, and in the negative-temperature region for others. In the canonical setting of a system coupled to a heat bath of positive temperatures, the nonanalyticities in the microcanonical negative-temperature region cannot be observed, and this leads to a situation of effective nonequivalence even when formal equivalence holds.     

Effect of Magnetic Field and Equilibrium Flow on Rayleigh-Taylor Instability

We investigate the effect of a finite equilibrium flow and magnetic field on the Rayleigh-Taylor instability. It is found that the equilibrium flow only makes a frequency shift of perturbation and the growth rate of the Rayleigh-Taylor instability remains unchanged. However, the magnetic field can change the growth rate and, in particular,a very strong magnetic field suppresses the growth rate.     

The Toda Equations and the Gromov–Witten Theory of the Riemann Sphere

Consequences of the Toda equations arising from the conjectural matrix model for the Riemann sphere are investigated. The Toda equations determine the Gromov–Witten descendent potential (including all genera) of the Riemann sphere from the degree 0 part. Degree 0 series computations via Hodge integrals then lead to higher-degree predictions by the Toda equations. First, closed series forms for all 1-point invariants of all genera and degrees are given. Second, degree 1 invariants are investigated with new applications to Hodge integrals. Third, a differential equation for the generating function of the classical simple Hurwitz numbers (in all genera and degrees) is found – the first such equation. All these results depend upon the conjectural Toda equations. Finally, proofs of the Toda equations in genus 0 and 1 are given.     

Effect of Magnetic Field on a p-Type δ-Doped GaAs Layer

The energy levels of holes in a p-type δ-doped GaAs structure under a magnetic field are theoretically calculated within the framework of the effective mass approximation for a uniform aceeptor distribution. The electronic structure is calculated by solving the Schrodinger and Poisson equations self-consistently. The effect of the magnetic field on the potential profile changes the degree of the confinement and localization, and thus this behavior can be used to study these systems in regions of interest, without the need to grow many different samples. It is found that the heavy-hole subbands contain many more energy states than the light-hole ones; the population of the heavy-hole levels represents approximately 91 % of all the carriers without magnetic field. With increasing magnetic field the total population of the heavy-holes increases and the number of filled states changes.     

The Magnetocaloric Effect in the Vicinity of the Magnetic Compensation Temperature of Amorphous Gd–Co Ferrimagnetic Films

Physics of the Solid State - The results of the study of the magnetic and magnetocaloric properties of amorphous Gd–Co ferrimagnetic films possessing perpendicular magnetic anisotropy in a...     

Effect of Ionosphere and Inhomogeneity of the Earth Structure on the Polarization Characteristics of Magnetic Field at Frequencies of 0.2–200 Hz in the Near-Field Zone of a Horizontal Grounded Antenna

Technical Physics - Polarization characteristics of the field of an on-Earth emitter located at the Kola Peninsula are experimentally measured at a distance that is no greater than the height of an...     

Binding Energies of Excitons in Square Quantum-Well Wires in the Presence of a Magnetic Field

The binding energies of the ground state of excitons in the GaAs/Ga1-xAlxAs square quantum-well wire in the presence of a magnetic field are investigated by using the variational method. It is assumed that the magnetic field is applied parallel to the axis of the wire. The calculations of the binding energy as a fimction of the wire size have been performed for infinite and finite confinement potentials. The contribution of the magnetic field makes the binding energy larger obviously, particularly for the wide wire, and the magnetic field is much more pronounced for the binding energy in a square quantum wire than that in a cylindrical quantum wire. The mismatch of effective masses between the well and the barrier is also considered in the calculation.     

Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

We showed in Part I that the Hopf algebra ℋ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at ɛ= 0 the holomorphic part γ₊(ɛ) of the Riemann–Hilbert decomposition γ₋(ɛ)^{− 1}γ₊(ɛ) of the loop γ(ɛ)∈G provided by dimensional regularization. We show in this paper that the group G acts naturally on the complex space X of dimensionless coupling constants of the theory. More precisely, the formula g ₀=gZ ₁ Z ₃ ^−3/2 for the effective coupling constant, when viewed as a formal power series, does define a Hopf algebra homomorphism between the Hopf algebra of coordinates on the group of formal diffeomorphisms to the Hopf algebra ℋ. This allows first of all to read off directly, without using the group G, the bare coupling constant and the renormalized one from the Riemann–Hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms. This shows that renormalization is intimately related with the theory of non-linear complex bundles on the Riemann sphere of the dimensional regularization parameter ɛ. It also allows to lift both the renormalization group and the β-function as the asymptotic scaling in the group G. This exploits the full power of the Riemann–Hilbert decomposition together with the invariance of γ₋(ɛ) under a change of unit of mass. This not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group G for the full higher pole structure of minimal subtracted counterterms in terms of the residue. Received: 21 March 2000 / Accepted: 3 October 2000