23,700 research outputs found
Eigenvalue estimates for the Aharonov-Bohm operator in a domain
We prove semi-classical estimates on moments of eigenvalues of the
Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present
a counterexample to the generalized diamagnetic inequality which was proposed
by Erdos, Loss and Vougalter. Numerical studies complement these results.Comment: 22 pages, 10 figure
Ground states of a frustrated quantum spin chain with long-range interactions
The ground state of a spin-1/2 Heisenberg chain with both frustration and
long-range interactions is studied using Lanczos exact diagonalization. The
evolution of the well known dimerization transition of the system with
short-range frustrated interactions (the J1-J2 chain) is investigated in the
presence of additional unfrustrated interactions decaying with distance as
1/r^a. It is shown that the continuous (infinite-order) dimerization transition
develops into a first-order transition between a long-range ordered
antiferromagnetic state and a state with coexisting dimerization and critical
spin correlations at wave-number k=\pi/2. The relevance of the model to real
systems is discussed.Comment: 4 pages, 5 figures, final published versio
Geometrically constructed bases for homology of partition lattices of types A, B and D
We use the theory of hyperplane arrangements to construct natural bases for
the homology of partition lattices of types A, B and D. This extends and
explains the "splitting basis" for the homology of the partition lattice given
in [Wa96], thus answering a question asked by R. Stanley. More explicitly, the
following general technique is presented and utilized. Let A be a central and
essential hyperplane arrangement in R^d. Let R_1,...,R_k be the bounded regions
of a generic hyperplane section of A. We show that there are induced polytopal
cycles \rho_{R_i} in the homology of the proper part \bar{L_A} of the
intersection lattice such that {\rho_{R_i}}_{i=1,...,k} is a basis for \tilde
H_{d-2}(\bar{L_A}). This geometric method for constructing combinatorial
homology bases is applied to the Coxeter arrangements of types A, B and D, and
to some interpolating arrangements.Comment: 29 pages, 4 figure
N-body simulations of star clusters
Two aspects of our recent N-body studies of star clusters are presented: (1)
What impact does mass segregation and selective mass loss have on integrated
photometry? (2) How well compare results from N-body simulations using NBODY4
and STARLAB/KIRA?Comment: 2 pages, 1 figure with 4 panels (in colour, not well visible in
black-and-white; figures screwed in PDF version, ok in postscript; to see
further details get the paper source). Conference proceedings for IAUS246
'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief
Editor), M. Giersz, A. Sills, Capri, Sept. 2007; v2: references correcte
On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
We propose a numerical renormalization group (NRG) approach to steady-state
currents through nano-devices. A discretization of the scattering-states
continuum ensures the correct boundary condition for an open quantum system. We
introduce two degenerate Wilson chains for current carrying left and
right-moving electrons reflecting time-reversal symmetry in the absence of a
finite bias . We employ the time-dependent NRG to evolve the known
steady-state density operator for a non-interacting junction into the density
operator of the fully interacting nano-device at finite bias. We calculate the
temperature dependent current as function of and applied external magnetic
field using a recently developed algorithm for non-equilibrium spectral
functions.Comment: 4 pages, 6 figure
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