7,120 research outputs found
D-branes and the Non-commutative Structure of Quantum Spacetime
A worldsheet approach to the study of non-abelian D-particle dynamics is
presented based on viewing matrix-valued D-brane coordinate fields as coupling
constants of a deformed sigma-model which defines a logarithmic conformal field
theory. The short-distance structure of spacetime is shown to be naturally
captured by the Zamolodchikov metric on the corresponding moduli space which
encodes the geometry of the string interactions between D-particles. Spacetime
quantization is induced directly by the string genus expansion and leads to new
forms of uncertainty relations which imply that general relativity at very
short-distance scales is intrinsically described by a non-commutative geometry.
The indeterminancies exhibit decoherence effects suggesting the natural
incorporation of quantum gravity by short-distance D-particle probes. Some
potential experimental tests are briefly described.Comment: 20 pages LaTeX, 3 eps figures, uses epsf.sty; Based on talks given by
R.J.S. at SUSY'98, Oxford, England, July 11-17, 1998, and by N.E.M. at the
6th Hellenic School and Workshop on Elementary Particle Physics, TMR project
"Physics Beyond the Standard Model", Corfu, Greece, September 15-18, 199
Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
We obtain the exact non-perturbative solution of a scalar field theory
defined on a space with noncommuting position and momentum coordinates. The
model describes non-locally interacting charged particles in a background
magnetic field. It is an exactly solvable quantum field theory which has
non-trivial interactions only when it is defined with a finite ultraviolet
cutoff. We propose that small perturbations of this theory can produce solvable
models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte
Working with Nonassociative Geometry and Field Theory
We review aspects of our formalism for differential geometry on
noncommutative and nonassociative spaces which arise from cochain twist
deformation quantization of manifolds. We work in the simplest setting of
trivial vector bundles and flush out the details of our approach providing
explicit expressions for all bimodule operations, and for connections and
curvature. As applications, we describe the constructions of physically viable
action functionals for Yang-Mills theory and Einstein-Cartan gravity on
noncommutative and nonassociative spaces, as first steps towards more elaborate
models relevant to non-geometric flux deformations of geometry in closed string
theory.Comment: 20 pages; v2: Reference added; Contribution to the proceedings of the
Corfu Summer Institute on Elementary Particle Physics and Gravity, September
1-26, 2015, Corfu, Greece; Final version published in Proceedings of Scienc
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
Matrix Sigma-models for Multi D-brane Dynamics
We describe a dynamical worldsheet origin for the Lagrangian describing the
low-energy dynamics of a system of parallel D-branes. We show how matrix-valued
collective coordinate fields for the D-branes naturally arise as couplings of a
worldsheet sigma-model, and that the quantum dynamics require that these
couplings be mutually noncommutative. We show that the low-energy effective
action for the sigma-model couplings describes the propagation of an open
string in the background of the multiple D-brane configuration, in which all
string interactions between the constituent branes are integrated out and the
genus expansion is taken into account, with a matrix-valued coupling. The
effective field theory is governed by the non-abelian Born-Infeld target space
action which leads to the standard one for D-brane field theory.Comment: 14 pages LaTeX, 1 encapsulated postscript figure; uses epsf.te
Gradient Flow in Logarithmic Conformal Field Theory
We establish conditions under which the worldsheet beta-functions of
logarithmic conformal field theories can be derived as the gradient of some
scalar function on the moduli space of running coupling constants. We derive a
renormalization group invariant version of this function and relate it to the
usual Zamolodchikov C-function expressed in terms of correlation functions of
the worldsheet energy-momentum tensor. The results are applied to the example
of D-brane recoil in string theory.Comment: 12 pages LaTeX; references updated, one added; to be published in
Physics Letters
Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
We analyse the symmetries underlying nonassociative deformations of geometry
in non-geometric R-flux compactifications which arise via T-duality from closed
strings with constant geometric fluxes. Starting from the non-abelian Lie
algebra of translations and Bopp shifts in phase space, together with a
suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that
deforms the algebra of functions and the exterior differential calculus in the
phase space description of nonassociative R-space. In this setting
nonassociativity is characterised by the associator 3-cocycle which controls
non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists
to construct maps between the dynamical nonassociative star product and a
family of associative star products parametrized by constant momentum surfaces
in phase space. We define a suitable integration on these nonassociative spaces
and find that the usual cyclicity of associative noncommutative deformations is
replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star
product quantization on phase space together with 3-cyclicity, we formulate a
consistent version of nonassociative quantum mechanics, in which we calculate
the expectation values of area and volume operators, and find coarse-graining
of the string background due to the R-flux.Comment: 38 pages; v2: typos corrected, reference added; v3: typos corrected,
comments about cyclicity added in section 4.2, references updated; Final
version to be published in Journal of Mathematical Physic
Cold atoms in real-space optical lattices
Cold atoms in optical lattices are described in {\it real space} by
multi-orbital mean-field Ans\"atze. In this work we consider four typical
systems: (i) spinless identical bosons, (ii) spinor identical bosons (iii),
Bose-Bose mixtures, and (iv) Bose-Fermi mixtures and derive in each case the
corresponding multi-orbital mean-field energy-functional and working equations.
The notions of {\it dressed} Wannier functions and Wannier spinors are
introduced and the equations defining them are presented and discussed. The
dressed Wannier functions are the set of orthogonal, translationally-equivalent
orbitals which minimizes the energy of the Hamiltonian including boson-boson
(particle-particle) interactions. Illustrative examples of dressed Wannier
functions are provided for spinless bosonic atoms and mixtures in
one-dimensional optical lattices.Comment: 27 pages, 4 figures; [version minus figures published
Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field
We investigate the way that the degenerate manifold of midgap edge states in
quasicircular graphene quantum dots with zig-zag boundaries supports, under
free-magnetic-field conditions, strongly correlated many-body behavior
analogous to the fractional quantum Hall effect (FQHE), familiar from the case
of semiconductor heterostructures in high magnetic fields. Systematic
exact-diagonalization (EXD) numerical studies are presented for the first time
for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in
the range of N(N-1)/2 <= L <= 150. We present a derivation of a
rotating-electron-molecule (REM) type wave function based on the methodology
introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315
(2002)] in the context of the FQHE in two-dimensional semiconductor quantum
dots. The EXD wave functions are compared with FQHE trial functions of the
Laughlin and the derived REM types. It is found that a variational extension of
the REM offers a better description for all fractional fillings compared with
that of the Laughlin functions (including total energies and overlaps), a fact
that reflects the strong azimuthal localization of the edge electrons. In
contrast with the multiring arrangements of electrons in circular semiconductor
quantum dots, the graphene REMs exhibit in all instances a single (0,N)
polygonal-ring molecular (crystalline) structure, with all the electrons
localized on the edge. Disruptions in the zig-zag boundary condition along the
circular edge act effectively as impurities that pin the electron molecule,
yielding single-particle densities with broken rotational symmetry that portray
directly the azimuthal localization of the edge electrons.Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in
press. For related papers, see http://www.prism.gatech.edu/~ph274cy
Many-body theory for systems with particle conversion: Extending the multiconfigurational time-dependent Hartree method
We derive a multiconfigurational time-dependent Hartree theory for systems
with particle conversion. In such systems particles of one kind can convert to
another kind and the total number of particles varies in time. The theory thus
extends the scope of the available and successful multiconfigurational
time-dependent Hartree methods -- which were solely formulated for and applied
to systems with a fixed number of particles -- to new physical systems and
problems. As a guiding example we treat explicitly a system where bosonic atoms
can combine to form bosonic molecules and vise versa. In the theory for
particle conversion, the time-dependent many-particle wavefunction is written
as a sum of configurations made of a different number of particles, and
assembled from sets of atomic and molecular orbitals. Both the expansion
coefficients and the orbitals forming the configurations are time-dependent
quantities that are fully determined according to the Dirac-Frenkel
time-dependent variational principle. Particular attention is paid to the
reduced density matrices of the many-particle wavefunction that appear in the
theory and enter the equations of motion. There are two kinds of reduced
density matrices: particle-conserving reduced density matrices which directly
only couple configurations with the same number of atoms and molecules, and
particle non-conserving reduced density matrices which couple configurations
with a different number of atoms and molecules. Closed-form and compact
equations of motion are derived for contact as well as general two-body
interactions, and their properties are analyzed and discussed.Comment: 46 page
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