How many electrons are needed to flip a local spin?

Considering the spin of a local magnetic atom as a quantum mechanical operator, we illustrate the dynamics of a local spin interacting with a ballistic electron represented by a wave packet. This approach improves the semi-classical approximation and provides a complete quantum mechanical understanding for spin transfer phenomena. Sending spin-polarized electrons towards a local magnetic atom one after another, we estimate the minimum number of electrons needed to flip a local spin.Comment: 3 figure

Equivalence Theorems for Pseudoscalar Coupling

By a unitary transformation a rigorous equivalence theorem is established for the pseudoscalar coupling of pseudoscalar mesons (neutral and charged) to a second-quantized nucleon field. By the transformation the linear pseudoscalar coupling is eliminated in favor of a nonlinear pseudovector coupling term together with other terms. Among these is a term corresponding to a variation of the effective rest mass of the nucleons with position through its dependence on the meson potentials. The question of the connection of the nonlinear pseudovector coupling with heuristic proposals that such a coupling may account for the saturation of nuclear forces and the independence of single nucleon motions in nuclei is briefly discussed. The new representation of the Hamiltonian may have particular value in constructing a strong coupling theory of pseudoscalar coupled meson fields. Some theorems on a class of unitary transformations of which the present transformation is an example are stated and proved in an appendix.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86126/1/PhysRev.87.1061-RKO.pd

WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review

Berry phase in generalized chiral QED2QED_2

We consider the generalized chiral $QED_2$ on $S^1$ with a $U(1)$ gauge field coupled with different charges to both chiral components of a fermionic field. Using the adiabatic approximation we calculate the Berry phase and the corresponding ${\rm U}(1)$ connection and curvature for the vacuum and many particle Fock states. We show that the nonvanishing vacuum Berry phase is associated with a projective representation of the local gauge symmetry group and contributes to the effective action of the model.Comment: LATEX file, 17 pages; extended version of a talk given at Int. Colloquium on Group-Theoretical Methods in Physics, 15-20 July, 1996, Goslar, German

On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions

The Dirac equation has been studied in which the Dirac matrices \hat{\boldmath\alpha}, \hat\beta have space factors, respectively $f$ and $f_1$, dependent on the particle's space coordinates. The $f$ function deforms Heisenberg algebra for the coordinates and momenta operators, the function $f_1$ being treated as a dependence of the particle mass on its position. The properties of these functions in the transition to the Schr\"odinger equation are discussed. The exact solution of the Dirac equation for the particle motion in the Coulomnb field with a linear dependence of the $f$ function on the distance $r$ to the force centre and the inverse dependence on $r$ for the $f_1$ function has been found.Comment: 13 page

Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata (CA) by putting a fraction of sites of the slave equal to those of the master and finding the distance between both as a function of this fraction. We present three control strategies that exploit local information about the CA, mainly, the number of nonzero Boolean derivatives. When no local information is used, we speak of synchronization. We find the critical properties of control and discuss the best control strategy compared with synchronization

Interrelations Between the Neutron's Magnetic Interactions and the Magnetic Aharonov-Bohm Effect

It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the field-free region is not a profound property of the system and that it cannot be regarded as a sufficient condition for a nonzero phase shift.Comment: 18 pages, 1 postscript figure, Late

Charge Order in the Falicov-Kimball Model

We examine the spinless one-dimensional Falicov-Kimball model (FKM) below half-filling, addressing both the binary alloy and valence transition interpretations of the model. Using a non-perturbative technique, we derive an effective Hamiltonian for the occupation of the localized orbitals, providing a comprehensive description of charge order in the FKM. In particular, we uncover the contradictory ordering roles of the forward-scattering and backscattering itinerant electrons: the latter are responsible for the crystalline phases, while the former produces the phase separation. We find an Ising model describes the transition between the phase separated state and the crystalline phases; for weak-coupling we present the critical line equation, finding excellent agreement with numerical results. We consider several extensions of the FKM that preserve the classical nature of the localized states. We also investigate a parallel between the FKM and the Kondo lattice model, suggesting a close relationship based upon the similar orthogonality catastrophe physics of the associated single-impurity models.Comment: 39 pages, 6 figure