134 research outputs found
Graph Partitioning with Fujitsu Digital Annealer
Graph partitioning, or community detection, is the cornerstone of many
fields, such as logistics, transportation and smart power grids. Efficient
computation and efficacious evaluation of communities are both essential,
especially in commercial and industrial settings. However, the solution space
of graph partitioning increases drastically with the number of vertices and
subgroups. With an eye to solving large scale graph partitioning and other
optimization problems within a short period of time, the Digital Annealer (DA),
a specialized CMOS hardware also featuring improved algorithms, has been
devised by Fujitsu Ltd. This study gauges Fujitsu DA's performance and running
times. The modularity was implemented as both the objective function and metric
for the solutions. The graph partitioning problems were formatted into
Quadratic Unconstrained Binary Optimization (QUBO) structures so that they
could be adequately imported into the DA. The DA yielded the highest modularity
among other studies when partitioning Karate Club, Les Miserables, American
Football, and Dolphin. Moreover, the DA was able to partition the Case
1354pegase power grid network into 45 subgroups, calling for 60,930 binary
variables, whilst delivering optimal modularity results within a solving time
of roughly 80 seconds. Our results suggest that the Fujitsu DA can be applied
for rapid and efficient optimization for graph partitioning
Conductance fluctuations in disordered 2D topological insulator wires: From quantum spin-Hall to ordinary quantum phases
Impurities and defects are ubiquitous in topological insulators (TIs) and
thus understanding the effects of disorder on electronic transport is
important. We calculate the distribution of the random conductance fluctuations
of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ)
Hamiltonian with realistic parameters. As we show, the disorder drives the TIs
into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and
ordinary insulator (OI). By varying the disorder strength and Fermi energy, we
calculate analytically and numerically across the entire phase diagram.
The conductance fluctuations follow the statistics of the unitary universality
class . At strong disorder and high energy, however, the size of the
fluctutations reaches the universal value of the orthogonal symmetry
class (). At the QSHI-M and QSHI-OI crossovers, the interplay between
edge and bulk states plays a key role in the statistical properties of the
conductance.Comment: 17 pages, 5 figure
Nonlinear photoconductivities and quantum geometry of chiral multifold fermions
Chiral multifold fermions are quasi-particles that appear only in chiral
crystals such as transition metal silicides in the cubic B20 structure (i.e.,
the CoSi family), and they may show exotic physical properties. Here we study
the injection and shift photoconductivities and also the related geometrical
quantities for several types of chiral multifold fermions, including spin-1/2
as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple point
and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal
symmorphic model to describe the triple point fermions (TPF). We also consider
the more realistic model Hamiltonian for the CoSi family including both linear
and quadratic terms. We find that circular injection currents are quantized as
a result of the Chern numbers carried by the multifold fermions within the
linear models. Surprisingly, we discover that in the TPF model, linear shift
conductivities are proportional to the pseudo spin-orbit coupling and
independent of photon frequency. In contrast, for the RSW and Kramer Weyl
fermions, the linear shift conductivity is linearly proportional to photon
frequency. The numerical results agree with the power-counting analysis for
quadratic Hamiltonians. The frequency independence of the linear shift
conductivity could be attributed to the strong resonant symplectic Christoffel
symbols of the flat bands. Moreover, the calculated symplectic Christoffel
symbols show significant peaks at the nodes, suggesting that the shift currents
are due to the strong geometrical response near the topological nodes
Transverse force generated by an electric field and transverse charge imbalance in spin-orbit coupled systems
We use linear response theory to study the transverse force generated by an
external electric field and hence possible charge Hall effect in spin-orbit
coupled systems. In addition to the Lorentz force that is parallel to the
electric field, we find that the transverse force perpendicular to the applied
electric field may not vanish in a system with an anisotropic energy
dispersion. Surprisingly, in contrast to the previous results, the transverse
force generated by the electric field does not depend on the spin current, but
in general, it is related to the second derivative of energy dispersion only.
Furthermore, we find that the transverse force does not vanish in the
Rashba-Dresselhaus system. Therefore, the non-vanishing transverse force acts
as a driving force and results in charge imbalance at the edges of the sample.
The estimated ratio of the Hall voltage to the longitudinal voltage is . The disorder effect is also considered in the study of the
Rashba-Dresselhaus system. We find that the transverse force vanishes in the
presence of impurities in this system because the vertex correction and the
anomalous velocity of the electron accidently cancel each other
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