2,902 research outputs found
Matrix-valued Quantum Lattice Boltzmann Method
We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum
Boltzmann equation, with the classical Maxwell distribution replaced by
Fermi-Dirac functions. To accommodate the spin density matrix, the distribution
functions become 2 x 2 matrix-valued. From an analytic perspective, the
efficient, commonly used BGK approximation of the collision operator is valid
in the present setting. The numerical scheme could leverage the principles of
LBM for simulating complex spin systems, with applications to spintronics.Comment: 18 page
FISH: A 3D parallel MHD code for astrophysical applications
FISH is a fast and simple ideal magneto-hydrodynamics code that scales to ~10
000 processes for a Cartesian computational domain of ~1000^3 cells. The
simplicity of FISH has been achieved by the rigorous application of the
operator splitting technique, while second order accuracy is maintained by the
symmetric ordering of the operators. Between directional sweeps, the
three-dimensional data is rotated in memory so that the sweep is always
performed in a cache-efficient way along the direction of contiguous memory.
Hence, the code only requires a one-dimensional description of the conservation
equations to be solved. This approach also enable an elegant novel
parallelisation of the code that is based on persistent communications with MPI
for cubic domain decomposition on machines with distributed memory. This scheme
is then combined with an additional OpenMP parallelisation of different sweeps
that can take advantage of clusters of shared memory. We document the detailed
implementation of a second order TVD advection scheme based on flux
reconstruction. The magnetic fields are evolved by a constrained transport
scheme. We show that the subtraction of a simple estimate of the hydrostatic
gradient from the total gradients can significantly reduce the dissipation of
the advection scheme in simulations of gravitationally bound hydrostatic
objects. Through its simplicity and efficiency, FISH is as well-suited for
hydrodynamics classes as for large-scale astrophysical simulations on
high-performance computer clusters. In preparation for the release of a public
version, we demonstrate the performance of FISH in a suite of astrophysically
orientated test cases.Comment: 27 pages, 11 figure
Relativistic quantum effects of Dirac particles simulated by ultracold atoms
Quantum simulation is a powerful tool to study a variety of problems in
physics, ranging from high-energy physics to condensed-matter physics. In this
article, we review the recent theoretical and experimental progress in quantum
simulation of Dirac equation with tunable parameters by using ultracold neutral
atoms trapped in optical lattices or subject to light-induced synthetic gauge
fields. The effective theories for the quasiparticles become relativistic under
certain conditions in these systems, making them ideal platforms for studying
the exotic relativistic effects. We focus on the realization of one, two, and
three dimensional Dirac equations as well as the detection of some relativistic
effects, including particularly the well-known Zitterbewegung effect and Klein
tunneling. The realization of quantum anomalous Hall effects is also briefly
discussed.Comment: 22 pages, review article in Frontiers of Physics: Proceedings on
Quantum Dynamics of Ultracold Atom
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