Spin-Dependent Forces and Current Quark Masses

The J = (3/2) , J = 1/2 Nucleon mass difference shows the quark energies can be spin dependent. It is natural to expect that the quark wave functions also depend on spin. A spin-dependent quark force is fitted to the proton and neutron magnetic moments, axial charge, and spin content using a (1/2⁺)³ configuration for the quarks and assuming only zero mass u and d quarks are in the nucleon. In the octet, such spin-dependent forces lead to different wave functions for quarks with spin parallel or antiparallel to the nucleon spin. The eigen-energy of this potential is 0.15 GeV higher for quark spin parallel than for the quark spin antiparallel to the proton spin. This potential predicts a single quark energy of 0.37 GeV for mass-less quarks in the Delta. Assuming the quark forces are flavor independent, this potential predicts magnetic moments of a bound strange quark to be very close to those determined empirically from the octet magnetic moments.     

A simple model of the classicalZitterbewegung: Photon wave function

We propose a simple classical model of the zitterbewegung. In this model spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with2p frequency. The quantization of the system gives wave equations for spin,0, 1/2, 1, 3/2,…, etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-1, massless free particle is equivalent to the Maxwell equations and the state functions have a probability interpretation and exhibit conserved current densities. The ground state has zero energy.     

Approximate solution of the Schrödinger equation for an atom in the field of a standing wave

We present an approximate method of calculation of energy spectrum and wave functions of translational motion of a two-level atom in the field of a standing wave at zero value of the quasimomentum. Wave functions in the momentum representation are expressed in terms of confluent hypergeometric functions in case of continuous spectrum and in terms of Hermitian polynomials in case of discrete spectrum. The energy spectrum exhibits infinite compaction at transition from discrete part to continuous, as it is the case for, e.g., Coulombian potential.     

Bound-state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry<Superscript>⋆</Superscript>

The energy spectra and the corresponding two-component spinor wave functions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The s -wave ( k \kappa = 0 state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wave functions for this potential and other special types of this potential are obtained. The extension of this result to the k \kappa 1 \neq 0 state is suggested.     

Dimensional crossover in alternating spin chains

The effect of antiferromagnetic interchain coupling in alternating spin chains is studied by means of spin wave (SW) theory and density matrix renormalization group (DMRG). Two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. For the 2D case, SW approximation predicts a smooth-dimensional crossover keeping the ground state ordered, whereas in the ladder case the DMRG results show a gapped ground state for any J>0. Furthermore, the behavior of the correlation functions closely resemble the uniform spin- ladder. However, for small J, the gap behaves quadratically as Δ0.6J². Similarly to uniform spin chains, it is conjectured an analogous spin gap behavior for an arbitrary number of mixed spin chains.     

Exactly solvable two-dimensional quantum spin models

A method is proposed for constructing an exact ground-state wave function of a two-dimensional model with spin 1/2. The basis of the method is to represent the wave function by a product of fourth-rank spinors associated with the nodes of a lattice and the metric spinors corresponding to bonds between nearest neighbor nodes. The function so constructed is an exact wave function of a 14-parameter model. The special case of this model depending on one parameter is analyzed in detail. The ground state is always a nondegenerate singlet, and the spin correlation functions decay exponentially with distance. The method can be generalized for models with spin 1/2 to other types of lattices. Zh. éksp. Teor. Fiz. 115, 249–267 (January 1999)     

Dynamical instability of the XY spiral state of ferromagnetic condensates

We calculate the spectrum of collective excitations of the XY spiral state prepared adiabatically or suddenly from a uniform ferromagnetic F=1 condensate. For spiral wave vectors past a critical value, spin wave excitation energies become imaginary indicating a dynamical instability. We construct phase diagrams as functions of spiral wave vector and quadratic Zeeman energy.     

Electronic quasiparticles and evolution of Fermi level spin states in thin magnetic layers

Here we report on high-resolution photoemission of iron layers grown on a W(1 1 0) substrate. The evolution of the substrate states upon sub-monolayer adsorption of Fe atoms leads to a shift in surface state binding energy. For thicker (1 1 0) films, sharp metallic surface states are obtained. Their dispersion displays the signature of quasiparticle renormalization due to dressing with excitations. The energy scale is characteristic for the spin wave spectrum in iron, thereby giving evidence of electron-magnon coupling. Furthermore, it is found that quantum well states occur as a function of layer thickness. These modify the spin density of states at the Fermi level in the ferromagnetic film.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein-Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

Two-phonon processes in Heisenberg ferromagnet

Using the method of double-time retarded Green function, an expression for the spin energy spectrum including the contributions of one-phonon and two-phonon processes has been derived. Calculations have been performed using the spin wave approximation. The broadening of the energy level is roughly estimated in a peculiar case.I would like to thank Dr. Dagmat Fraitová for her advice and help.     

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

Zitterbewegung of wave packets and conductance of a quasi-one-dimensional channel in the presence of spin-orbit coupling

The electron energy spectrum and wave functions for a quasi-one-dimensional channel with Rashba spin-orbit coupling are calculated. The dynamics of wave packets in thin wires based on GaAs/In_0.23Ga_0.77As and AlGaAs/GaAs heterostructures with Rashba spin-orbit coupling are studied. Spin polarizations are found. The effect of splitting of wave packets with respect to their centers of mass and Zitterbewegung of their centers are discovered. The characteristics of wave-packet oscillations and spin density for free electrons and under confinement conditions are compared. A method for controlling the conductance of the quasi-one-dimensional channel using a controlling electrode is proposed.     

Spinor Structure and Matter Spectrum

Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations). All these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type (l, 0) ⊕ (0, l), where l is a spin value, whereas for arbitrary spin chains we have degenerate spectrum. Energy spectra of the stability levels (electron and proton states) of the matter spectrum are studied in detail. It is shown that these stability levels have a nature of threshold scales of the fractal structure associated with the system of interlocking representations of the Lorentz group.     

Path integral for one-dimensional Dirac oscillator

In this paper we derive the propagator for the one-dimensional Dirac oscillator using the supersymmetric path integral formalism. The spin calculations are carried out with the help of the technique of Grassmann functional integration. The Green function is exactly evaluated. The Polyakov spin factor is explicitly derived and the energy spectrum and the corresponding wave functions are deduced. PACS 03.65.Ca; 03.65.Db; 03.65.Ge; 03.65.Pm     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

On the relativistic equation for particles with spinj in the 2[2j+1] — component formalism

The equation describing a relativistic particle with spinj and massm by a 2[2j+1] component wave function is derived using the method of boost transformations. The formalism developed in this paper allows us to find the wave functions satisfying the equation obtained and to construct the relativistically invariant quantities from these functions in an easy way. For the case of spin 3/2 the unitary equivalence with earlier results is demonstrated.     

Dipole-dipole spin anisotropy energy for spin density waves in highly anisotropic crystals: (TMTSF) 2X

The dipole-dipole spin anisotropy energy for a spin density wave (SDW) is compatible with experimental easy, intermediate, and hard spin polarization axes in the (TMTSF) ₂X class of organic conductors only when electron-hole correlations of the SDW are atomic in size. Magnitudes of the spin anisotropy energy and the spin-flip magnetic field in this case agree with experiment for a SDW amplitude comparable to 10^-2 Bohr magnetons/TMTSF molecule.     

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.     

The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.