Variational wave functions of a vortex in cyclotron motion

In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational states of a vortex in a cylinder and the cyclotron states of an electron in the central gauge is found. Like the Landau levels of an electron, the energy levels of a vortex are highly degenerate. However, the gap between two adjacent energy levels does not only depend on the quantized circulation, but also increases with the energy, and scales with the size of the vortex.Comment: LaTeX, 4 pages, 2 EPS figures, To appear in ``Series on Advances in Quantum Many-Body Theory'' ed. by R.F. Bishop, C.E. Campbell, J.W. Clark and S. Fantoni (World Scientific, 2000

Gauge fields, quantized fluxes and monopole confinement of the honeycomb lattice

Electron hopping models on the honeycomb lattice are studied. The lattice consists of two triangular sublattices, and it is non-Bravais. The dual space has non-trivial topology. The gauge fields of Bloch electrons have the U(1) symmetry and thus represent superconducting states in the dual space. Two quantized Abrikosov fluxes exist at the Dirac points and have fluxes $2pi$ and $-2pi$, respectively. We define the non-Abelian SO(3) gauge theory in the extended 3$d$ dual space and it is shown that a monopole and anti-monoplole solution is stable. The SO(3) gauge group is broken down to U(1) at the 2$d$ boundary.The Abrikosov fluxes are related to quantized Hall conductance by the topological expression. Based on this, monopole confinement and deconfinement are discussed in relation to time reversal symmetry and QHE. The Jahn-Teller effect is briefly discussed.Comment: 10 pages, 11 figure

Holstein model and Peierls instability in 1D boson-fermion lattice gases

We study an ultracold bose-fermi mixture in a one dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A Bosonic density wave with a wavenumber of twice the Fermi wavenumber will appear in the quasi one-dimensional system.Comment: 5 pages, 4 figure

Dark-field transmission electron microscopy and the Debye-Waller factor of graphene

Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multi-layer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.Comment: 10 pages, 4 figure

Resonant atom-field interaction in large-size coupled-cavity arrays

We consider an array of coupled cavities with staggered inter-cavity couplings, where each cavity mode interacts with an atom. In contrast to large-size arrays with uniform-hopping rates where the atomic dynamics is known to be frozen in the strong-hopping regime, we show that resonant atom-field dynamics with significant energy exchange can occur in the case of staggered hopping rates even in the thermodynamic limit. This effect arises from the joint emergence of an energy gap in the free photonic dispersion relation and a discrete frequency at the gap's center. The latter corresponds to a bound normal mode stemming solely from the finiteness of the array length. Depending on which cavity is excited, either the atomic dynamics is frozen or a Jaynes-Cummings-like energy exchange is triggered between the bound photonic mode and its atomic analogue. As these phenomena are effective with any number of cavities, they are prone to be experimentally observed even in small-size arrays.Comment: 12 pages, 4 figures. Added 5 mathematical appendice

Symmetry breaking in the self-consistent Kohn-Sham equations

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.Comment: a few typos eliminate

Unified Picture for Magnetic Correlations in Iron-Based Superconductors

The varying metallic antiferromagnetic correlations observed in iron-based superconductors are unified in a model consisting of both itinerant electrons and localized spins. The decisive factor is found to be the sensitive competition between the superexchange antiferromagnetism and the orbital-degenerate double-exchange ferromagnetism. Our results reveal the crucial role of Hund's rule coupling for the strongly correlated nature of the system and suggest that the iron-based superconductors are closer kin to manganites than cuprates in terms of their diverse magnetism and incoherent normal-state electron transport. This unified picture would be instrumental for exploring other exotic properties and the mechanism of superconductivity in this new class of superconductors.Comment: Revised for publication. 3 figure

Noncommuting spherical coordinates

Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a magnetic monopole. Restricting the dynamics to the lowest energy level results in noncommutativity for angular variables and to a definition of a noncommuting spherical product. The values of the commutators of various angular variables are not arbitrary but are restricted by the discrete magnitude of the magnetic monopole charge. An algebra, isomorphic to angular momentum, appears. This algebra is used to define a spherical star product. Solutions are obtained for dynamics in the presence of additional angular dependent potentials.Comment: 5 pages, RevTex4 fil

Phonon-phonon interactions in transition metals

In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be reasonable for bcc and fcc metals. For hcp metals we show that the Raman active mode decays into a pair of acoustic phonons, their wave vector being located on a surface defined by conservation laws.Comment: 14 pages, 3 figure

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page