19,799 research outputs found
Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories
The equation of motion of affine Toda field theory is a coupled equation for
fields, is the rank of the underlying Lie algebra. Most of the theories
admit reduction, in which the equation is satisfied by fewer than fields.
The reductions in the existing literature are achieved by identifying (folding)
the points in the Dynkin diagrams which are connected by symmetry
(automorphism). In this paper we present many new reductions. In other words
the symmetry of affine Dynkin diagrams could be extended and it leads to
non-canonical foldings. We investigate these reductions in detail and formulate
general rules for possible reductions. We will show that eventually most of the
theories end up in that is the theory cannot have a further
dimension reduction where .Comment: 26 pages, Latex2e, usepackage `graphics.sty', 15 figure
Instability of Solitons in imaginary coupling affine Toda Field Theory
Affine Toda field theory with a pure imaginary coupling constant is a
non-hermitian theory. Therefore the solutions of the equation of motion are
complex. However, in dimensions it has many soliton solutions with
remarkable properties, such as real total energy/momentum and mass. Several
authors calculated quantum mass corrections of the solitons by claiming these
solitons are stable. We show that there exists a large class of classical
solutions which develops singularity after a finite lapse of time. Stability
claims, in earlier literature, were made ignoring these solutions. Therefore we
believe that a formulation of quantum theory on a firmer basis is necessary in
general and for the quantum mass corrections of solitons, in particular.Comment: 17 pages, latex, no figure
Holographic classification of Topological Insulators and its 8-fold periodicity
Using generic properties of Clifford algebras in any spatial dimension, we
explicitly classify Dirac hamiltonians with zero modes protected by the
discrete symmetries of time-reversal, particle-hole symmetry, and chirality.
Assuming the boundary states of topological insulators are Dirac fermions, we
thereby holographically reproduce the Periodic Table of topological insulators
found by Kitaev and Ryu. et. al, without using topological invariants nor
K-theory. In addition we find candidate Z_2 topological insulators in classes
AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table
Medium effects of magnetic moments of baryons on neutron stars under strong magnetic fields
We investigate medium effects due to density-dependent magnetic moments of
baryons on neutron stars under strong magnetic fields. If we allow the
variation of anomalous magnetic moments (AMMs) of baryons in dense matter under
strong magnetic fields, AMMs of nucleons are enhanced to be larger than those
of hyperons. The enhancement naturally affects the chemical potentials of
baryons to be large and leads to the increase of a proton fraction.
Consequently, it causes the suppression of hyperons, resulting in the stiffness
of the equation of state. Under the presumed strong magnetic fields, we
evaluate relevant particles' population, the equation of state and the maximum
masses of neutron stars by including density-dependent AMMs and compare them
with those obtained from AMMs in free space
Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
A time-reversal invariant Kitaev-type model is introduced in which spins
(Dirac matrices) on the square lattice interact via anisotropic
nearest-neighbor and next-nearest-neighbor exchange interactions. The model is
exactly solved by mapping it onto a tight-binding model of free Majorana
fermions coupled with static Z_2 gauge fields. The Majorana fermion model can
be viewed as a model of time-reversal invariant superconductor and is
classified as a member of symmetry class DIII in the Altland-Zirnbauer
classification. The ground-state phase diagram has two topologically distinct
gapped phases which are distinguished by a Z_2 topological invariant. The
topologically nontrivial phase supports both a Kramers' pair of gapless
Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana
states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying
correlation functions of spins along the edge are obtained by taking the
gapless Majorana edge modes into account. The model is also defined on the
one-dimension ladder, in which case again the ground-state phase diagram has
Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure
On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
A new type of correlated disorder is shown to be responsible for the
appearance of extended electronic states in one-dimensional aperiodic systems
like the Thue-Morse lattice. Our analysis leads to an understanding of the
underlying reason for the extended states in this system, for which only
numerical evidence is available in the literature so far. The present work also
sheds light on the restrictive conditions under which the extended states are
supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in
Physical Review Letter
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