Pairs of Bloch electrons and magnetic translation groups

A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these representations. In particular, they are important in descriptions of pairs of electrons in a magnetic field and a periodic potential. The periodicity of some properties with respect to the charge of a particle is briefly discussed.Comment: 4 pages, RevTex. Latex2.09, amsfont

An explicit Schr\"odinger picture for Aharonov's Modular Variable concept

We propose to address in a natural manner, the modular variable concept explicitly in a Schr\"odinger picture. The idea of Modular Variables was introduced in 1969 by Aharonov, Pendleton and Petersen to explain certain non-local properties of quantum mechanics. Our approach to this subject is based on Schwinger's finite quantum kinematics and it's continuous limit.Comment: 16 pages, 9 figure

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Vacuum Compatibility of 3D-Printed Materials

The fabrication fidelity and vacuum properties are tested for currently available 3D-printed materials including polyamide, glass, acrylic, and sterling silver. The silver was the only material found to be suitable to ultrahigh vacuum environments due to outgassing and sublimation observed in other materials.Comment: 3 pages, 2 figures, preprin

Ectomycorrhizal fungi and the enzymatic liberation of nitrogen from soil organic matter: why evolutionary history matters

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139921/1/nph14598.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139921/2/nph14598_am.pd

A phased array-based method for damage detection and localization in thin plates

A method for damage localization based on the phased array idea has been developed. Four arrays oftransducers are used to perform a beam-forming procedure. Each array consists of nine transducersplaced along a line, which are able to excite and register elastic waves. The A0 Lamb wave mode hasbeen chosen for the localization method. The arrays are placed in such a way that the angulardifference between them is 458 and the rotation point is the middle transducer, which is common for allthe arrays. The idea has been tested on a square aluminium plate modeled by the Spectral Element Method. Two types of damage were considered, namely distributed damage, which was modeled asstiffness reduction, and cracks, modeled as separation of nodes between selected spectral elements.The plate is excited by a wave packet. The whole array system is placed in the middle of the plate.Each linear phased array in the system acts independently and produces maps of a scanned fieldbased on the beam-forming procedure. These maps are made of time signals (transferred to spacedomain) that represent the difference between the damaged plate signals and those from the intactplate. An algorithm was developed to join all four maps. The final map is modified by proposed signal processing algorithm to indicate the damaged area of the plate more precisely. The problem fordamage localization was investigated and exemplary maps confirming the effectiveness of theproposed system were obtained. It was also shown that the response of the introduced configurationremoves the ambiguity of damage localization normally present when a linear phased array is utilized.The investigation is based exclusively on numerical data

Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the $1/r$ and $r^2$ potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the $\theta$-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters $\theta_x$ and $\theta_y$ explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.Comment: 25 pages, 2 figure

Theory of a magnetic microscope with nanometer resolution

We propose a theory for a type of apertureless scanning near field microscopy that is intended to allow the measurement of magnetism on a nanometer length scale. A scanning probe, for example a scanning tunneling microscope (STM) tip, is used to scan a magnetic substrate while a laser is focused on it. The electric field between the tip and substrate is enhanced in such a way that the circular polarization due to the Kerr effect, which is normally of order 0.1% is increased by up to two orders of magnitude for the case of a Ag or W tip and an Fe sample. Apart from this there is a large background of circular polarization which is non-magnetic in origin. This circular polarization is produced by light scattered from the STM tip and substrate. A detailed retarded calculation for this light-in-light-out experiment is presented.Comment: 17 pages, 8 figure