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

Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.Comment: 8 pages, latex, revised version for Phys. Lett.

Dispersal limitation structures fungal community assembly in a long‐term glacial chronosequence

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107360/1/emi12281.pd

Soil microbial communities are shaped by plant‐driven changes in resource availability during secondary succession

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116975/1/ecy201596123374.pd

Initial colonization, community assembly and ecosystem function: fungal colonist traits and litter biochemistry mediate decay rate

Priority effects are an important ecological force shaping biotic communities and ecosystem processes, in which the establishment of early colonists alters the colonization success of later‐arriving organisms via competitive exclusion and habitat modification. However, we do not understand which biotic and abiotic conditions lead to strong priority effects and lasting historical contingencies. Using saprotrophic fungi in a model leaf decomposition system, we investigated whether compositional and functional consequences of initial colonization were dependent on initial colonizer traits, resource availability or a combination thereof. To test these ideas, we factorially manipulated leaf litter biochemistry and initial fungal colonist identity, quantifying subsequent community composition, using neutral genetic markers, and community functional characteristics, including enzyme potential and leaf decay rates. During the first 3 months, initial colonist respiration rate and physiological capacity to degrade plant detritus were significant determinants of fungal community composition and leaf decay, indicating that rapid growth and lignolytic potential of early colonists contributed to altered trajectories of community assembly. Further, initial colonization on oak leaves generated increasingly divergent trajectories of fungal community composition and enzyme potential, indicating stronger initial colonizer effects on energy‐poor substrates. Together, these observations provide evidence that initial colonization effects, and subsequent consequences on litter decay, are dependent upon substrate biochemistry and physiological traits within a regional species pool. Because microbial decay of plant detritus is important to global C storage, our results demonstrate that understanding the mechanisms by which initial conditions alter priority effects during community assembly may be key to understanding the drivers of ecosystem‐level processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113681/1/mec13361.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/113681/2/mec13361_am.pd

A three-dimensional electrostatic actuator with a locking mechanism for a new generation of atom chips

A micromachined three-dimensional electrostatic actuator that is optimized for aligning and tuning optical microcavities on atom chips is presented. The design of the 3D actuator is outlined in detail, and its characteristics are verified by analytical calculations and finite element modelling. Furthermore, the fabrication process of the actuation device is described and preliminary fabrication results are shown. The actuation in the chip plane which is used for mirror positioning has a working envelope of 17.5 ?m. The design incorporates a unique locking mechanism which allows the out-of-plane actuation that is used for cavity tuning to be carried out once the in-plane actuation is completed. A maximum translation of 7 ?m can be achieved in the out-of-plane direction

A cloud model simulation of space shuttle exhaust clouds in different atmospheric conditions

A three-dimensional cloud model was used to characterize the dominant influence of the environment on the Space Shuttle exhaust cloud. The model was modified to accept the actual heat and moisture from rocket exhausts and deluge water as initial conditions. An upper-air sounding determined the ambient atmosphere in which the cloud could grow. The model was validated by comparing simulated clouds with observed clouds from four actual Shuttle launches. The model successfully produced clouds with dimensions, rise, decay, liquid water contents and vertical motion fields very similar to observed clouds whose dimensions were calculated from 16 mm film frames. Once validated, the model was used in a number of different atmospheric conditions ranging from very unstable to very stable. In moist, unstable atmospheres simulated clouds rose to about 3.5 km in the first 4 to 8 minutes then decayed. Liquid water contents ranged from 0.3 to 1.0 g kg-1 mixing ratios and vertical motions were from 2 to 10 ms-1. An inversion served both to reduce entrainment (and erosion) at the top and to prevent continued cloud rise. Even in the most unstable atmospheres, the ground cloud did not rise beyond 4 km and in stable atmospheres with strong low level inversions the cloud could be trapped below 500 m. Wind shear strongly affected the appearance of both the ground cloud and vertical column cloud. The ambient low-level atmospheric moisture governed the amount of cloud water in model clouds. Some dry atmospheres produced little or no cloud water. One case of a simulated TITAN rocket explosion is also discussed

von Neumann Lattices in Finite Dimensions Hilbert Spaces

The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger's quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space that characterizes the Hilbert space and specifies the simultaneous definitions of both (modular) positions and (modular) momenta. The area in phase space for each quantum state in each of these quantum degrees of freedom, is shown to be exactly $h$, Planck's constant.Comment: 16 page

Elk, sagebrush, and saprotrophs: indirect top‐down control on microbial community composition and function

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116352/1/ecy20159692383.pd