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

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres

Experimental determination of grain density function of AZ91/SiC composite with different mass fractions of SiC and undercoolings using heterogeneous nucleation model

The grain density, Nv, in the solid state after solidification of AZ91/SiC composite is a function of maximum undercooling, ΔT, of a liquid alloy. This type of function depends on the characteristics of heterogeneous nucleation sites and number of SiC present in the alloy. The aim of this paper was selection of parameters for the model describing the relationship between the grain density of primary phase and undercooling. This model in connection with model of crystallisation, which is based on chemical elements diffusion and grain interface kinetics, can be used to predict casting quality and its microstructure. Nucleation models have parameters, which exact values are usually not known and sometimes even their physical meaning is under discussion. Those parameters can be obtained after mathematical analysis of the experimental data. The composites with 0, 1, 2, 3 and 4wt.% of SiC particles were prepared. The AZ91 alloy was a matrix of the composite reinforcement SiC particles. This composite was cast to prepare four different thickness plates.They were taken from the region near to the thermocouple, to analyze the undercooling for different composites and thickness plates and its influence on the grain size. The microstructure and thermal analysis gave set of values that connect mass fraction of SiC particles, and undercooling with grain size. These values were used to approximate nucleation model adjustment parameters. Obtained model can be very useful in modelling composites microstructure

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

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.

An invariant analytic orthonormalization procedure with applications

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis

Anthropogenic nitrogen deposition ameliorates the decline in tree growth caused by a drier climate

Most forest ecosystems are simultaneously affected by concurrent global change drivers. However, when assessing these effects, studies have mainly focused on the responses to single factors and have rarely evaluated the joined effects of the multiple aspects of environmental change. Here, we analyzed the combined effects of anthropogenic nitrogen (N) deposition and climatic conditions on the radial growth of Acer saccharum, a dominant tree species in eastern North American forests. We capitalized on a long‐term N deposition study, replicated along a latitudinal gradient, that has been taking place for more than 20 yr. We analyzed tree radial growth as a function of anthropogenic N deposition (ambient and experimental addition) and of summer temperature and soil water conditions. Our results reveal that experimental N deposition enhances radial growth of this species, an effect that was accentuated as temperature increased and soil water became more limiting. The spatial and temporal extent of our data also allowed us to assert that the positive effects of growing under the experimental N deposition are likely due to changes in the physiological performance of this species, and not due to the positive correlation between soil N and soil water holding capacity, as has been previously speculated in other studies. Our simulations of tree growth under forecasted climate scenarios specific for this region also revealed that although anthropogenic N deposition may enhance tree growth under a large array of environmental conditions, it will not mitigate the expected effects of growing under the considerably drier conditions characteristic of our most extreme climatic scenario.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/1/ecy2095-sup-0004-AppendixS4.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/2/ecy2095-sup-0001-AppendixS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/3/ecy2095-sup-0006-AppendixS6.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/4/ecy2095-sup-0007-AppendixS7.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/5/ecy2095_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/6/ecy2095-sup-0008-AppendixS8.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/7/ecy2095-sup-0003-AppendixS3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/8/ecy2095-sup-0002-AppendixS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/9/ecy2095-sup-0005-AppendixS5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142341/10/ecy2095.pd

Growth and C allocation of Populus tremuloides genotypes in response to atmospheric CO 2 and soil N availability

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65485/1/j.1469-8137.1998.00264.x.pd

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Drought Reduces Root Respiration In Sugar Maple Forests

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117195/1/eap199883771.pd