A rigorous path integral for quantum spin using flat-space Wiener regularization

Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schr\"odinger semigroup on the Hilbert space $L^2(R^2)$ of Lebesgue square-integrable functions on the Euclidean plane $R^2$. The path-integral formula emerges from the standard Feynman-Kac-It\^o formula for the Schr\"odinger semigroup in the ultra-diffusive limit of the underlying Brownian bridge on $R^2$. In a similar vein, a path-integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin Hamiltonian.Comment: revised versio

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev.

Polarisation dependence of magnetic Bragg scattering in YMn2_2O5_5

The polarisation dependence of the intensity of elastic magnetic scattering from \ymno\ single crystals has been measured at 25 K in magnetic fields between 1 and 9 T. A significant polarisation dependence was observed in the intensities of magnetic satellite reflections, propagation vector \pv=0.5,0,0.25 measured with both the [100] and [010] axes parallel to the common polarisation and applied field direction. The intensity asymmetries $A$ observed in sets of orthorhombicly equivalent reflections show systematic relationships which allow the phase relationship between different components of their magnetic interaction vectors to be determined. They fix the orientation relationships between the small $y$ and $z$ moments on the \mnfp\ and \mntp\ sub-lattices and lend support to the structure reported by Kim et al. It was found that that $A(hkl)\ne A(\bar h\bar k\bar l)$ which suggests that there is a small modulation of the nuclear structure which has the same wave-vector as the magnetic modulation leading to a small nuclear structure factor for the satellite reflections. The differences $A(hkl)- A(\bar h\bar k\bar l)$ observed indicate shifts in the atomic positions of order 0.005 \AA

On the Path Integral in Imaginary Lobachevsky Space

The path integral on the single-sheeted hyperboloid, i.e.\ in $D$-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call ``Kepler-problem'', and the case of a constant magnetic field are also discussed.Comment: 16 pages, LATEX, DESY 93-14

Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors

We show that the massive (or massless) neutrinos can be described as special states of Heisenberg nonlinear spinors. As a by-product of this decomposition a particularly attractive consequence appears: the possibility of relating the existence of only three species of mass-less neutrinos to such internal non-linear structure. At the same time it allows the possibility that neutrino oscillation can occurs even for massless neutrinos

Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest m+1 states, if the superpotential is defined in terms of the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown that in case of the infinite 1-dim potential well nothing new emerges (the partner potential is still of P\"oschl-Teller type I, for all m), whilst in case of the 1-dim harmonic oscillator we get a new class of infinitely many partner potentials: for each m the partner potential is expressed as the sum of the quadratic harmonic potential plus rational function, defined as the derivative of the ratio of two consecutive Hermite polynomials. These partner potentials of course have m singularities exactly at the locations of the nodes of the generating (m+1)-st wavefunction. The susy formalism applies everywhere between the singularities. A systematic application of the formalism to other potentials with known spectra would yield an infinitely rich class of "solvable" potentials, in terms of their partner potentials. If the potentials are shape invariant they can be solved at least partially and new types of analytically obtainable spectra are expected. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted for publication

Magnetic Properties of Epitaxial and Polycrystalline Fe/Si Multilayers

Fe/Si multilayers with antiferromagnetic interlayer coupling have been grown via ion-beam sputtering on both glass and single-crystal substrates. High-angle x-ray diffraction measurements show that both sets of films have narrow Fe peaks, implying a large crystallite size and crystalline iron silicide spacer layers. Low-angle x-ray diffraction measurements show that films grown on glass have rougher interfaces than those grown on single-crystal substrates. The multilayers grown on glass have a larger remanent magnetization than the multilayers grown on single-crystal substrates. The observation of magnetocrystalline anisotropy in hysteresis loops and $(hkl)$ peaks in x-ray diffraction demonstrates that the films grown on MgO and Ge are epitaxial. The smaller remanent magnetization in Fe/Si multilayers with better layering suggests that the remanence is not an intrinsic property.Comment: 9 pages, RevTex, 4 figures available by fax. Send email to [email protected] for more info. Submitted to '95 MMM proceeding

Epitaxial Co2Cr0.6Fe0.4Al thin films and magnetic tunneling junctions

Epitaxial thin films of the theoretically predicted half metal Co2Cr0.6Fe0.4Al were deposited by dc magnetron sputtering on different substrates and buffer layers. The samples were characterized by x-ray and electron beam diffraction (RHEED) demonstrating the B2 order of the Heusler compound with only a small partition of disorder on the Co sites. Magnetic tunneling junctions with Co2Cr0.6Fe0.4Al electrode, AlOx barrier and Co counter electrode were prepared. From the Julliere model a spin polarisation of Co2Cr0.6Fe0.4Al of 54% at T=4K is deduced. The relation between the annealing temperature of the Heusler electrodes and the magnitude of the tunneling magnetoresistance effect was investigated and the results are discussed in the framework of morphology and surface order based of in situ STM and RHEED investigations.Comment: accepted by J. Phys. D: Appl. Phy

SU(N) Coherent States and Irreducible Schwinger Bosons

We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging to irreducible representations of SU(N) are labeled by the eigenvalues of the $(N-1)$ SU(N) Casimir operators and are characterized by $(N-1)$ complex orthonormal vectors describing the SU(N) group manifold.Comment: 12 pages, 3 figure