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

Low temperature coefficient of resistance and high gage factor in beryllium-doped silicon

The gage factor and resistivity of p-type silicon doped with beryllium was studied as a function of temperature, crystal orientation, and beryllium doping concentration. It was shown that the temperature coefficient of resistance can be varied and reduced to zero near room temperature by varying the beryllium doping level. Similarly, the magnitude of the piezoresistance gage factor for beryllium-doped silicon is slightly larger than for silicon doped with a shallow acceptor impurity such as boron, whereas the temperature coefficient of piezoresistance is about the same for material containing these two dopants. These results are discussed in terms of a model for the piezoresistance of compensated p-type silicon

Adiabatic Motion of a Quantum Particle in a Two-Dimensional Magnetic Field

The adiabatic motion of a charged, spinning, quantum particle in a two - dimensional magnetic field is studied. A suitable set of operators generalizing the cinematical momenta and the guiding center operators of a particle moving in a homogeneous magnetic field is constructed. This allows us to separate the two degrees of freedom of the system into a {\sl fast} and a {\sl slow} one, in the classical limit, the rapid rotation of the particle around the guiding center and the slow guiding center drift. In terms of these operators the Hamiltonian of the system rewrites as a power series in the magnetic length \lb=\sqrt{\hbar c\over eB} and the fast and slow dynamics separates. The effective guiding center Hamiltonian is obtained to the second order in the adiabatic parameter \lb and reproduces correctly the classical limit.Comment: 17 pages, LaTe

Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

Weyl-Wigner-Moyal formulation of a Dirac quantized constrained system

An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl product of these equivalent classes is defined. The new Moyal bracket is shown to be compatible with the Dirac bracket for constrained systems

A simple method for imaging Arabidopsis leaves using perfluorodecalin as an infiltrative imaging medium

This is the final version. Available from JoVE via the DOI in this record. The problem of acquiring high-resolution images deep into biological samples is widely acknowledged. In air-filled tissue such as the spongy mesophyll of plant leaves or vertebrate lungs further difficulties arise from multiple transitions in refractive index between cellular components, between cells and airspaces and between the biological tissue and the rest of the optical system. Moreover, refractive index mismatches lead to attenuation of fluorophore excitation and signal emission in fluorescence microscopy. We describe here the application of the perfluorocarbon, perfluorodecalin (PFD), as an infiltrative imaging medium which optically improves laser scanning confocal microscopy (LSCM) sample imaging at depth, without resorting to damaging increases in laser power and has minimal physiological impact. We describe the protocol for use of PFD with Arabidopsis thaliana leaf tissue, which is optically complex as a result of its structure (Figure 1). PFD has a number of attributes that make it suitable for this use. The refractive index of PFD (1.313) is comparable with that of water (1.333) and is closer to that of cytosol (approx. 1.4) than air (1.000). In addition, PFD is readily available, non-fluorescent and is non-toxic. The low surface tension of PFD (19 dynes cm -1 ) is lower than that of water (72 dynes cm -1 ) and also below the limit (25-30 dyne cm -1 ) for stomatal penetration, which allows it to flood the spongy mesophyll airspaces without the application of a potentially destructive vacuum or surfactant. Finally and crucially, PFD has a great capacity for dissolving CO 2 and O 2 , which allows gas exchange to be maintained in the flooded tissue, thus minimizing the physiological impact on the sample. These properties have been used in various applications which include partial liquid breathing and lung inflation, surgery, artificial blood, oxygenation of growth media, and studies of ice crystal formation in plants. Currently, it is common to mount tissue in water or aqueous buffer for live confocal imaging. We consider that the use of PFD as a mounting medium represents an improvement on existing practice and allows the simple preparation of live whole leaf samples for imaging.Biotechnology and Biological Sciences Research Counci

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

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

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