6,653 research outputs found
Disordered Topological Insulators via -Algebras
The theory of almost commuting matrices can be used to quantify topological
obstructions to the existence of localized Wannier functions with time-reversal
symmetry in systems with time-reversal symmetry and strong spin-orbit coupling.
We present a numerical procedure that calculates a Z_2 invariant using these
techniques, and apply it to a model of HgTe. This numerical procedure allows us
to access sizes significantly larger than procedures based on studying twisted
boundary conditions. Our numerical results indicate the existence of a metallic
phase in the presence of scattering between up and down spin components, while
there is a sharp transition when the system decouples into two copies of the
quantum Hall effect. In addition to the Z_2 invariant calculation in the case
when up and down components are coupled, we also present a simple method of
evaluating the integer invariant in the quantum Hall case where they are
decoupled.Comment: Added detail regarding the mapping of almost commuting unitary
matrices to almost commuting Hermitian matrices that form an approximate
representation of the sphere. 6 pages, 6 figure
Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model
We show that the fractal growth described by the dielectric breakdown model
exhibits a phase transition in the multifractal spectrum of the growth measure.
The transition takes place because the tip-splitting of branches forms a fixed
angle. This angle is eta dependent but it can be rescaled onto an
``effectively'' universal angle of the DLA branching process. We derive an
analytic rescaling relation which is in agreement with numerical simulations.
The dimension of the clusters decreases linearly with the angle and the growth
becomes non-fractal at an angle close to 74 degrees (which corresponds to eta=
4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure
Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma
The equations governing a collisionless obliquely-flowing plasma around an
ion-absorbing object in a strong magnetic field are shown to have an exact
analytic solution even for arbitrary (two-dimensional) object-shape, when
temperature is uniform, and diffusive transport can be ignored. The solution
has an extremely simple geometric embodiment. It shows that the ion collection
flux density to a convex body's surface depends only upon the orientation of
the surface, and provides the theoretical justification and calibration of
oblique `Mach-probes'. The exponential form of this exact solution helps
explain the approximate fit of this function to previous numerical solutions.Comment: Four pages, 2 figures. Submitted to Phys. Rev. Letter
Solving Gapped Hamiltonians Locally
We show that any short-range Hamiltonian with a gap between the ground and
excited states can be written as a sum of local operators, such that the ground
state is an approximate eigenvector of each operator separately. We then show
that the ground state of any such Hamiltonian is close to a generalized matrix
product state. The range of the given operators needed to obtain a good
approximation to the ground state is proportional to the square of the
logarithm of the system size times a characteristic "factorization length".
Applications to many-body quantum simulation are discussed. We also consider
density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional
discussion of numerics; additional explanation of nonzero temperature matrix
product for
m6A mRNA Methylation: A New Circadian Pacesetter
The purpose of m6A methylation of RNA, first observed in the 1970s, has been a longstanding mystery. Fustin et al. now show that it regulates RNA processing and determines the period and oscillatory stability of the mammalian circadian clockwork
The Energy Challenge–Gone Today, Back Tomorrow: Maine’s Key Role
World energy trends suggest that increased demand for fossil fuels is likely to continue, even as producers are not replacing what is being used. William Hastings argues that in spite of this, Maine is poised to potentially become an energy leader in the near future. He points out that a surprising number of new projects are increasing the diversity of the state’s energy supply
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