Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution

Letter from F. J. Littlejohn to Governor E. Ransom

A letter of F. J. Littlejohn to Governor E. Ransom, who seeks the post of special commissioner, under the provisions of a Bill for constructing a wharf etc. for the benefit of the Holland Colony.https://digitalcommons.hope.edu/vrp_1840s/1187/thumbnail.jp

Diagonalization of multicomponent wave equations with a Born-Oppenheimer example

A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed

Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)

A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding center operators of a particle coupled to a homogenous magnetic filed is constructed. The Pauli Hamiltonian rewrites in this way as a power series in the magnetic length $l_B= \sqrt{\hbar c/eB}$ making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns to be in coupling with a gauge filed and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include

Raman spectrometry as a screening tool for solvent-extracted azo dyes from polyester-based textile fibres

Some types of textile fibres are considered to be the cause of allergic reactions and other adverse health effects on humans. The main compounds behind these health problems usually contain azo groups in their chemical structure, which are widely employed as azo dyes in the manufacture of textile and clothing products. In this respect, availability of simple analytical procedures for identifying azo groups in textiles is of concern, not only for toxicological studies, but also for clinical and forensic investigations. In this work, conventional Raman spectrometry was assessed as an analytical tool for identification of the azo function in the extracts of fibres obtained after applying a liquid-solvent extraction procedure to the polyester-based textile products. A medium-polarity solvent of ethanol-diethyl ether (1:1 mixture) was shown to be the most effective extraction medium. Two laser lines at 514.5 nm and 785 nm were compared, with the longer wavelength preferred as additional peaks were identified in the Raman spectrum, which had better signal-to-background and signal-to-noise ratios owing to decreased fluorescence in contrast to excitation at 514.5 nm. The method reported is a convenient procedure that can be applied in many instances when rapid screening of fibre dyes is required

Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

Quantum dynamics and breakdown of classical realism in nonlinear oscillators

The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the deformation of the classical flow by the quantum nonlinearity in the semiclassical limit. The breakdown of the classical trajectories under the quantum nonlinear dynamics is quantified by the mismatch of the quasi-flow carried by different observables. It is shown that the failure of classical realism can give rise to a dynamical violation of Bell's inequalities.Comment: RevTeX 4 pages, no figure

Takotsubo cardiomyopathy associated with anesthesia: three case reports

Takotsubo cardiomyopathy is a form of transient, reversible left ventricular dysfunction that can mimic an acute coronary event. However, cardiac catheterization often reveals normal coronary arteries. Patients are often postmenopausal women who experience acute physical or emotional distress. The prognosis for this entity is quite favorable. In this report, we present three cases of Takotsubo cardiomyopathy in patients having procedures involving anesthesia. Each case illustrates a different etiology for the syndrome: Patient, procedure, and anesthetic management