21,362 research outputs found
The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields
The non-commutative theory of charge transport in mesoscopic aperiodic
systems under magnetic fields, developed by Bellissard, Shulz-Baldes and
collaborators in the 90's, is complemented with a practical numerical
implementation. The scheme, which is developed within a -algebraic
framework, enable efficient evaluations of the non-commutative Kubo formula,
with errors that vanish exponentially fast in the thermodynamic limit.
Applications to a model of a 2-dimensional Quantum spin-Hall insulator are
given. The conductivity tensor is mapped as function of Fermi level, disorder
strength and temperature and the phase diagram in the plane of Fermi level and
disorder strength is quantitatively derived from the transport simulations.
Simulations at finite magnetic field strength are also presented.Comment: 10 figure
Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice
We study the phase diagram for spin-2 bosons loaded in a one-dimensional
optical lattice. By using non-Abelian density matrix renormalization group
(DMRG) method we identify three possible phases: ferromagnetic, dimerized, and
trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate
two methods for identifying the phases. The first method is based on the
spin-spin correlation function while in the second method one observes the
excitation gap as a dimerization or a trimerization superlattice is imposed.
The advantage of the second method is that it can also be easily implemented in
experiments. By using the scattering lengths in the literature we estimate that
Rb, Na, and Rb be ferromagnetic, dimerized, and trimerized
respectively.Comment: 4 pages, 3 figures. Add acknowledgemen
A further study of the possible scaling region of lattice chiral fermions
In the possible scaling region for an SU(2) lattice chiral fermion advocated
in {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breaking
occurs and doublers are gauge-invariantly decoupled via mixing with composite
three-fermion-states that are formed by local multifermion interactions.
However the strong coupling expansion breaks down due to no ``static limit''
for the low-energy limit (). In both neutral and charged channels, we
further analyze relevant truncated Green functions of three-fermion-operators
by the strong coupling expansion and analytical continuation of these Green
functions in the momentum space. It is shown that in the low-energy limit,
these relevant truncated Green functions of three-fermion-states with the
``wrong'' chiralities positively vanish due to the generalized form factors
(the wave-function renormalizations) of these composite three-fermion-states
vanishing as O((pa)^4) for . This strongly implies that the composite
three-fermion-states with ``wrong'' chirality are ``decoupled'' in this limit
and the low-energy spectrum is chiral, as a consequence, chiral gauge
symmetries can be exactly preserved.Comment: A few typing-errors, in particular in Eq.50, have been correcte
Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry
We study the quantum critical phase of a SU(2) symmetric spin-2 chain
obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling
of the entanglement entropy and finite-size energies by exact diagonalization
and density-matrix renormalization group methods. From the numerical results of
the energy spectrum, central charge, and scaling dimension we identify the
conformal field theory describing the whole critical phase to be the SU(3)
Wess-Zumino-Witten model. We find that while in the whole critical phase the
Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the
thermodynamic limit
Equity in mathematics education in Hong Kong : Evidence from TIMSS 2011 to 2019
This study investigated the status of equity in mathematics education in Hong Kong based on data from TIMSS 2011 to 2019 and the changes in education equity across the three cycles. The effects of various student-, family-, and school-level variables on students’ mathematics achievement were examined and compared using multilevel modeling. Results showed that there were significant variances between schools in mathematics achievement in Hong Kong, especially for eighth grade students. Overall, boys performed better in mathematics than girls in these three TIMSS cycles in Hong Kong, except for eighth grade boys in the cycles of 2011 and 2019. The family and school socio-economic status (SES) related to the possession of traditional materials (e.g., desks and books) and parents’ highest education level had positive and significant effects on students’ mathematics achievement, and the effects of the predictors increased from the 2011 cycle to the 2019 cycle. SES related to the possession of home digital devices (e.g., computers and internet connection) also had positive but much less substantial effects. School location and resource availability did not have significant effects. In general, the mean levels of SES and school resource availability in Hong Kong is improving. However, the effects of some important student- and school-level factors on mathematics achievement increased. Suggestions for improving education equity in Hong Kong are discussed
Strong electric fields induced on a sharp stellar boundary
Due to a first order phase transition, a compact star may have a
discontinuous distribution of baryon as well as electric charge densities, as
e.g. at the surface of a strange quark star. The induced separation of positive
and negative charges may lead to generation of supercritical electric fields in
the vicinity of such a discontinuity. We study this effect within a
relativistic Thomas-Fermi approximation and demonstrate that the strength of
the electric field depends strongly on the degree of sharpness of the surface.
The influence of strong electric fields on the stability of compact stars is
discussed. It is demonstrated that stable configurations appear only when the
counter-pressure of degenerate fermions is taken into consideration.Comment: 13 pages, 2 figure
Response of Alluvial Valleys to Incident SH, SV and P Waves
Results of an extensive numerical study on two dimensional wave scattering by valleys of semi-elliptical cross section due to incident SH, SV and P waves are presented. The investigation has been conducted using a rigorous Boundary element algorithm. The influence of key parameters, such as, valley depth, impedance ratio, frequency, and angle of incidence on surface ground motion are studied in detail. Furthermore, the case of a valley within a layered half space is analyzed and results compared with those obtained for a valley within a homogeneous half space
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