Theory of the anisotropic magnetoresistance in copper

The motion of the guiding center of magnetic circulation generates a charge transport. The application of kinetic theory to the motion gives a modified Drude formula for the magnetoconductivity: σ=e²n_cτ/M^*, where M^? is the magnetotransport mass distinct from the cyclotron mass, n_c the density of the conduction electrons, and τ the relaxation time. The density n_c depends on the applied magnetic field direction relative to copper's face-centered-cubic lattice, when the Fermi surface of copper is nonspherical with necks. The anisotropic magnetoresistance of copper is calculated with the assumption of the necks representing by spheres of radius a centered at the eight singular points on the ideal Fermi surface. A good fit with experiments is obtained.     

THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

The properties of fermion causal Green's function is discussed according to the theory of spectral representation. The definition of effective mass is established from the view point of field theory, and the approximate expression of S_F' (p) as |p²|«M² and the asymptotic formula of S_F' (p) as p²→+∞ is given. In terms of these result the problem of quark confinement is discussed. We find that: (ⅰ) Based on the theory of spectral re presentation the concept of relative confinement is allowed, and if renormalization effect is strong, the quarks can demonstrate definitely lighter effective mass when they are far away from the mass shell; (ⅱ) Based on the theory of spectral representation the concept of absolute confinement is unallowable, even the absolute confinement is taken as the limit of relative confinement. That is if the concept of absolute confinement is introduced, we must discard a part of elementary hypothesis of spectral representation theory.     

Physical consequences of quantized fiber-bundled space

Considering the motion of charged particles and the charge density in the quantized space, we obtain the effect of charge screening at small distances, which leads to the representation of the vacuum as a medium. A vector potential satisfying the confinement condition of a magnetic monopole is constructed.     

Four-body Efimov effect for three fermions and a lighter particle

We study three same-spin-state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384相似文献   

Efimov effect in an analytically solvable model

The Efimov effect is demonstrated in a model consisting of two heavy particles and a light one when the light-heavy interaction leads to a zero-energy two-body bound state. The model is solved in the Born-Oppenheimer approximation with the light-heavy interaction taken to be a separable S-wave potential of Yamaguchi form. It is demonstrated that in the case of a- two-body zero-energy bound state the binding energy of the light particle in the two-center potential exactly yields an effective $\text{1}\text{r}{}^2$ potential for the relative motion of the heavies. If the light-heavy mass ratio is made small enough, infinitely many bound states (the Efimov effect) are obtained. The approach to this limit is studied and the nature of the potential for large scattering length is obtained. An upper bound for the number of bound states is calculated using a result of Bargmann and Calogero and Efimov's $\text{ln}\text{(}\text{a}\text{r}{}_0\text{)}$ result is found. We note that the long-range effect arises from the large extent of the bound state, the pair wave function being essentially $\text{exp}\text{(?}\text{r}\text{a}\text{)}$ when the scattering length a is large.     

Electronic structure of modulation-doped heterostructures: electric field effects

Self-consistent energy levels of electrons in modulation-doped GaAs/Ga_1−xAl_xAs heterostructures are presented and their dependence on various device parameters are examined. The results of the calculation of the electric field effects on the shape of the confinement potential, the electron concentration and the shape of the wavefunction are presented.     

Field evaporation: Model and experiment

The ability of the image potential and charge exchange models to describe the evaporation of metals in a high electric field is examined. At present only the field dependence of the evaporation rate can be compared with the predictions of the two models. An analysis of experiments on the evaporation of tungsten atoms from kink sites, as well as from sites on top of the (110), suggests that the image potential model gives the most satisfactory representation of the data. The quantity α, which indicates the difference between the polarizability of a neutral surface atom and an ion, is found to differ little from one kind of site to another when obtained from a least-squares analysis. For tungsten at a kink site α =4.80 ± ± 0.03A?³; for an adatom on the (110), α = 5.24 ±0.04ų.     

Numerical transmission probabilities and the oscillatory photo-induced field emission current: Static and dynamic image charge effects

Numerical calculations are reported for the transmission probability of electrons incident upon a model potential barrier typically used in discussing electron emission from metal surfaces. These calculations are utilized in an attempt to explain the unexpected oscillatory photocurrent which was observed in a previous study of the electric field dependence of the photoinduced field emission current. Transmission resonances are observed in these calculations and a simple theory is described which adequately accounts for the electric field strengths at which these resonances occur. An important result of these calculations is that the model potential barrier given by $\text{V(x) = ?eFx ? (}\text{1}\text{4π?}{}_0\text{)(}\text{e}{}^2\text{4x}\text{)}$ cannot explain the oscillatory behavior of the photo-field current. Arguments are presented which question the static nature of the image charge potential employed in this simple model and a modification is introduced which incorporates in a very approximate fashion the time dependence involved in the formation of the image charge potential. Calculations based on this model correctly predict the periodicity of the observed oscillations and give a frequency which is in reasonable agreement with the measured value.     

Scattering of relativistic electrons by a focused laser pulse

The problem of the motion of a classical relativistic electron in a focused high-intensity laser pulse is solved. A new three-dimensional model of the electromagnetic field, which is an exact solution of Maxwell’s equations, is proposed to describe a stationary laser beam. An extension of the model is proposed. This extension describes a laser pulse of finite duration and is an approximate solution of Maxwell’s equations. The equations for the average motion of an electron in the field of a laser pulse, described by our model, are derived assuming weak spatial and temporal nonuniformities of the field. It is shown that, to a first approximation in the parameters of the nonuniformities, the average (ponderomotive) force acting on a particle is described by the gradient of the ponderomotive potential, but it loses its potential character even in second order. It is found that the three-dimensional ponderomotive potential is asymmetric. The trajectories of relativistic electrons moving in a laser field are obtained and the cross sections for scattering of electrons by a stationary laser beam are calculated. It is shown that reflection of electrons from the laser pulse and the surfing effect are present in the model studied. It is found that for certain impact parameters of the incident electrons the asymmetic ponderomotive potential can manifest itself effectively as an attractive potential. It is also shown that even in the case of a symmetric potential the scattering cross section contains singularities, known as rainbow scattering. The results are applicable for fields characterized by large (compared to 1) values of the dimensionless parameter η² = e ²〈E ²〉/m ²ω² and arbitrary electron energies.     

Effective charge in the II–VI and III–V compounds with zincblende or wurtzite type structure

The effective charge in the II–VI and III–V compounds was analyzed by using a linear chain model. On the assumption that the ionic lattice is immersed in a cloud of valence electrons with the dielectric constant of ?(∞) = n²?₀ (n: refractive index, ?₀ = 8·85 × 10^?12f/m), the effective charge on an ion is equal to 2e in the II–VI compounds and to e in the III–V compounds (e: electronic charge), respectively. These values of the effective charge are just n times the Szigeti charge.Although direct connection between neighboring atoms is the main part of the binding force, the fact can not be neglected that the second nearest neighbor atoms are connected by sharing some of valence electrons between them. The electrons in valence bonds contribute to the refractive index and are estimated to be e and 2e per atom in the II–VI and III–V compounds, respectively.     

Drag effect of one-dimensional electrons upon photoionization of D<Superscript>(−)</Superscript> centers in a longitudinal magnetic field

A theory is elaborated for the impurity photon drag effect in a semiconductor quantum wire exposed to a longitudinal magnetic field B directed along the axis of the quantum wire. The phonon drag effect is associated with the transfer of the longitudinal photon momentum to localized electrons in optical transitions from D^(?) states to hybrid-quantized states of the quantum wire, which is described by a confinement parabolic potential. An analytical expression for the drag current density is derived within the model of a zero-range potential in the effective mass approximation, and the spectral dependence of the drag current density is examined at different magnitudes of B and parameters of the quantum wire upon electron scattering by a system of impurities with short-range potentials. It is established that the spectral dependence of the drag current density exhibits a Zeeman doublet with a clear beak-shaped peak due to optical transitions of electrons from D^(?) states to states with the magnetic quantum number m=1. The possibility of using the photon drag effect in a longitudinal magnetic field for the development of laser radiation detectors is analyzed.     

Homotopy analysis method to study a quadrupole mass filter

The homotopy analysis method (HAM) is applied to study the behavior of a hyperbolic rods of quadrupole mass filter and a sinusoidal potential form V(ac) cos(Ωt). Numerical computation method of a 20th-order HAM is employed to compare the physical properties of the confined ions with fifth-order Runge-Kutta method. Also, comparison is made for the first stability region, the ion trajectories in real time, the polar plots, and the ion trajectory in x?-?y plan. The results show that the two methods are fairly similar; therefore, the HAM method has potential application to solve linear and nonlinear equations of the charge particle confinement in quadrupole field.     

Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.     

Particle-two-particle interaction in configuration space

The problem of three identical particles with zero-range two-particle interaction is considered. An explicit expression for the effective potential between one particle and the remaining two-particle system is obtained in the coordinate representation. It is shown that for arbitrary energies, at small and, for zero energy, at large distances ρ between the one particle and centre of mass of the other two particles the diagonal matrix element of the effective potential is attractive and proportional to 1/ρ². This property of the effective potential explains both the Thomas singularity and the Efimov effect. In the case of zero total energy of the system the general form of the solution of the three-particle integral equation is found in configuration space.     

Quasi-normal Modes of AdS5 Black Hole at $\mathcal{N}=2$ Supergravity

In this paper we consider the AdS ₅ black hole at the \(\mathcal{N}=2\) supergravity background. By using the AdS/CFT correspondence we discuss about the quasi-normal modes of the scalar field in the black hole, which is dual of the scalar glueballs spectrum on the boundary. We obtain phase transition conditions from stable to unstable theory, which interpreted as confinement and deconfinement states in the QCD. We obtain the specific heat in terms of the temperature and charge of black hole, we find the temperature where the black hole is stable. Also we rewrite the equation of motion in the Schrödinger form and discuss the effective potential.     

Die dreidimensionale Stabilisierung von Ladungsträgern in einem Vierpolfeld

It is shown that particles of a specific chargee/m are confined in three dimensions by a high frequency electric quadrupole field with the potential?=c · U(t)· (x ²+y ²?2z ²). The confinement is mass selective. The theoretical predictions are verified by experiments with ions of different masses and with electrons. The mass selection, maximum number of stored charges and their mean life time in the field are measured. Furthermore the influence of a magnetic field on the motion of the charges is investigated.     

Rescattering of electrons at laser-cluster interactions

The goal of this work is to derive the angular distributions of electrons irradiated at the outer ionization of large atomic clusters from Xe atoms by relativistic laser pulses taking into account rescattering processes. Both the magnetic field of the laser pulse and the Coulomb field of the ionized cluster significantly influence the rescattering of ejected electrons. The multiply inner ionization of atoms occurs at the leading edge of the laser pulse. The atomic ions with charge multiplicities up to Z = 26 are subsequently produced (each atomic ion with the next charge multiplicity appears in 3–5 fs) when the laser intensity increases. The measurements of the angular distributions of electrons allow us to reproduce the imaging dynamics of outer ionization of the cluster at the leading edge of the relativistic femtosecond laser pulse.     

The C*-algebra of the electromagnetic field

We show that there is a unique C*-algebra for the transverse quantum electromagnetic field obeying the Maxwell equations with any classical charge-current. For nonzero charge, the representation of the C*-algebra differs from the representation with zero charge.