Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Electric-Wiggler-Enhanced Three-Quantum Scattering and the Output Power Affected by this Scattering in a Free-Electron Laser

We derive the cross section of scattering through the three-quantum interaction of an electron with the incident laser field, the emitted photon, and an axial electrostatic field produced by the magnetic wiggler in the magnetic wiggler acting as the sole zeroth-order perturbing classical field in the first free-electron laser （FEL）. In the derivation, we apply quantum-wiggler electrodynamics （QWD）. We find that this scattering predominates the usual two-quantum scattering. The output power of spontaneous free-electron two-quantum Stark emission driven by the above electrostatic field attenuated by the three-quantum scattering agrees within a factor of 10 with the measured power in the case of the first FEL.     

Steady-state and transient Raman gain in magnetoactive narrow band-gap semiconductors

Using the hydrodynamic model of semiconductor-plasmas and following the coupled-mode approach, a detailed analytical investigation is undertaken to study both steady-state and the transient Raman gain in transversely magnetized narrow band-gap semiconductors arising from electron density perturbations and molecular vibrations of the medium. Using the fact that the origin of stimulated Raman scattering (SRS) lies in the third-order susceptibility of the medium, we obtain an expression for the gain coefficient of the backward Stokes mode in steady-state and transient regimes and study the dependence of the magnetic field and pump pulse duration on its growth rate. The threshold pump intensity and optimum pulse duration for the onset of transient SRS are estimated. An externally applied magnetic field substantially enhances the transient SRS gain coefficient in narrow band-gap semiconductors, which can be of great use in the compression of scattered pulses.     

Semiclassical calculation of ionisation rate for Rydberg helium atoms in an electric field

The ionisation of Rydberg helium atoms in an electric field above the classical ionisation threshold has been examined using the semiclassical method, with particular emphasis on discussing the influence of the core scattering on the escape dynamics of electrons. The results show that the Rydberg helium atoms ionise by emitting a train of electron pulses. Unlike the case of the ionisation of Rydberg hydrogen atom in parallel electric and magnetic fields, where the pulses of the electron are caused by the external magnetic field, the pulse trains for Rydberg helium atoms are created through core scattering. Each peak in the ionisation rate corresponds to the contribution of one core-scattered combination trajectory. This fact further illustrates that the ionic core scattering leads to the chaotic property of the Rydberg helium atom in external fields. Our studies provide a simple explanation for the escape dynamics in the ionisation of nonhydrogenic atoms in external fields.     

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.     

Exact Solutions of the Dirac Equation for an Electron in a Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions oI the Dirac equation for an electron moving in the presence of a certain varying magnetic field, then we also show its non-relativistic limit.     

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.     

Direct Evaluation of Transition Amplitude Using Determinant of Wave Operator in One-Dimensional Potential Scattering System

A determinantal formula is developed for direct evaluation of transition amplitude without solving the wave equation in a one-dimensional potential scattering system. Our formulation is 5ased on the principle that a desired quantity can be extracted from the wave operator, which is the master operator maintaining all the information of the system. This principle is tested in a simplified system, i.e,, in a one-dimensional potential scattering system. We are now developing a formula for direct evaluation of near-field amplitude to design a system, in which local field enhancement is desired.     

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.     

Finite correction to Aharonov-Bohm scattering by a contact potential

We study the influence of a contact (or delta) potential on the Aharonov-Bohm scattering of nonrelativistic particles. In general the contact potential has no effect on the scattering as expected. However, when the magnetic flux and the strength of the contact potential take some special values, the Aharonov-Bohm scattering cross-section is manifestly changed. It is shown that these special values correspond to the simultaneous existence of two half-bound states in two adjacent angular momentum channels. Two limiting processes are presented to deal with the singularity of the contact potential and results of the same nature are obtained.     

Canonical quantization of Galilean covariant field theories

The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ⁴. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called ‘non-relativistic’ approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.     

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for some specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.     

Geometric phase in a composite system subjected to decoherence

In this paper, we investigate the geometric phase of a composite system which is composed of two spin- particles driven by a time-varying magnetic field. Firstly, we consider the special case that only one subsystem driven by time-varying magnetic field. Using the quantum jump approach, we calculate the geometric phase associated with the adiabatic evolution of the system subjected to decoherence. The results show that the lowest order corrections to the phase in the no-jump trajectory is only quadratic in decoherence coefficient. Then, both subsystem driven by time-varying magnetic field is considered, we show that the geometric phase is related to the exchange-interaction coefficient and polar angle of the magnetic field.     

Geometric phases and entanglement of two qubits with XY type interaction

It is shown that geometric phases and entanglement may fail to detect level crossings for two qubits with XY interaction. The rotating magnetic field produces a magnetic monopole sphere like conducting spheres in that only a ground state evolving adiabatically outside the sphere acquires a geometric phase.     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

The chaotic property in the autoionization of Rydberg lithium atom

This paper presents theoretical computations of the ionization rate of Rydberg lithium atom above the classical ionization threshold using semiclassical approximation. The yielded random pulse trains of the escape electrons are recorded as a function of emission time such that they can be related to the terms of the recurrence periods of the photoabsorption. This fact illustrates that it is ionic core scattering processes which give rise to chaos in autoionization dynamics and this is verified by comparison of our results with the hydrogen atom situation. In order to reveal the chaotic properties in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed for different scaled energies. This approach provides a simple explanation for the chaotic character in autoionization decay of Rydberg alkali-metal atoms.     

Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously, and can also cause sudden change of the Berry phase for some weak magnetic field cases.     

Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin -1/2 particles with one of particles driven by rotating magnetic field. The influences of coupling and precession frequency of the magnetic field on geometric phase are also discussed in detail.     

Scattering of Attosecond Electromagnetic Field Pulses by Atomic and Molecular Anions Including the Magnetic Field Component

Scattering of an attosecond electromagnetic field pulse by atomic and molecular anions is considered in the sudden perturbation approximation. In the interaction with anions, the effect of the magnetic field of the incident pulse is considered. The inclusion of the magnetic component of the ultrashort pulse leads to new results in the scattering spectra for atomic and molecular anions. Analytic dependences of the partial spectrum on frequency are obtained. It is shown that during scattering, the second harmonic is generated, which makes it possible to determine the type of anions and the spatial orientation of molecular anions.     

Coherent states of a particle in a magnetic field and the Stieltjes moment problem

A solution to a version of the Stieltjes moment problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and resolves the unity. By the help of these coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion.