41,823 research outputs found
A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel
The Trotter-Suzuki approximation leads to an efficient algorithm for solving
the time-dependent Schr\"odinger equation. Using existing highly optimized CPU
and GPU kernels, we developed a distributed version of the algorithm that runs
efficiently on a cluster. Our implementation also improves single node
performance, and is able to use multiple GPUs within a node. The scaling is
close to linear using the CPU kernels, whereas the efficiency of GPU kernels
improve with larger matrices. We also introduce a hybrid kernel that
simultaneously uses multicore CPUs and GPUs in a distributed system. This
kernel is shown to be efficient when the matrix size would not fit in the GPU
memory. Larger quantum systems scale especially well with a high number nodes.
The code is available under an open source license.Comment: 11 pages, 10 figure
Finding Exponential Product Formulas of Higher Orders
In the present article, we review a continual effort on generalization of the
Trotter formula to higher-order exponential product formulas. The exponential
product formula is a good and useful approximant, particularly because it
conserves important symmetries of the system dynamics. We focuse on two
algorithms of constructing higher-order exponential product formulas. The first
is the fractal decomposition, where we construct higher-order formulas
recursively. The second is to make use of the quantum analysis, where we
compute higher-order correction terms directly. As interludes, we also have
described the decomposition of symplectic integrators, the approximation of
time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings
''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and
A.Das (Springer, Heidelberg
Intriguing sets of vertices of regular graphs
Intriguing and tight sets of vertices of point-line geometries have recently been studied in the literature. In this paper, we indicate a more general framework for dealing with these notions. Indeed, we show that some of the results obtained earlier can be generalized to larger classes of graphs. We also give some connections and relations with other notions and results from algebraic graph theory. One of the main tools in our study will be the Bose-Mesner algebra associated with the graph
Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder
We study the non-equilibrium slow dynamics for the Kitaev model both in the
presence and the absence of disorder. For the case without disorder, we
demonstrate, via an exact solution, that the model provides an example of a
system with an anisotropic critical point and exhibits unusual scaling of
defect density and residual energy for a slow linear quench. We provide
a general expression for the scaling of () generated during a slow
power-law dynamics, characterized by a rate and exponent ,
from a gapped phase to an anisotropic quantum critical point in dimensions,
for which the energy gap for momentum
components () and for the rest components
() with : ().
These general expressions reproduce both the corresponding results for the
Kitaev model as a special case for and and the well-known
scaling laws of and for isotropic critical points for . We also
present an exact computation of all non-zero, independent, multispin
correlation functions of the Kitaev model for such a quench and discuss their
spatial dependence. For the disordered Kitaev model, where the disorder is
introduced via random choice of the link variables in the model's
Fermionic representation, we find that and () for a slow linear quench ending in the gapless
(gapped) phase. We provide a qualitative explanation of such scaling.Comment: 10 pages, 11 Figs. v
Fast and stable method for simulating quantum electron dynamics
A fast and stable method is formulated to compute the time evolution of a
wavefunction by numerically solving the time-dependent Schr{\"o}dinger
equation. This method is a real space/real time evolution method implemented by
several computational techniques such as Suzuki's exponential product, Cayley's
form, the finite differential method and an operator named adhesive operator.
This method conserves the norm of the wavefunction, manages periodic conditions
and adaptive mesh refinement technique, and is suitable for vector- and
parallel-type supercomputers. Applying this method to some simple electron
dynamics, we confirmed the efficiency and accuracy of the method for simulating
fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure
Quantum walks with an anisotropic coin I: spectral theory
We perform the spectral analysis of the evolution operator U of quantum walks
with an anisotropic coin, which include one-defect models, two-phase quantum
walks, and topological phase quantum walks as special cases. In particular, we
determine the essential spectrum of U, we show the existence of locally
U-smooth operators, we prove the discreteness of the eigenvalues of U outside
the thresholds, and we prove the absence of singular continuous spectrum for U.
Our analysis is based on new commutator methods for unitary operators in a
two-Hilbert spaces setting, which are of independent interest.Comment: 26 page
Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach
Negative dimensional integration method (NDIM) is a technique which can be
applied, with success, in usual covariant gauge calculations. We consider three
two-loop diagrams: the scalar massless non-planar double-box with six
propagators and the scalar pentabox in two cases, where six virtual particles
have the same mass and in the case where all of them are massless. Our results
are given in terms hypergeometric functions of Mandelstam variables and for
arbitrary exponents of propagators and dimension as well.Comment: Latex, 12 pages, 2 figures, uses axodraw (included
Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions
In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear
Grassmann sigma models in any dimension and, moreover, an infinite number of
conserved currents and a wide class of exact solutions.
In this paper, we first construct almost all conserved currents for the
submodels and all ones for the one of -model. We next review the
Smirnov and Sobolev construction for the equations of -submodel and
extend the equations, the S-S construction and conserved currents to the higher
order ones.Comment: 13 pages, AMSLaTex; an new section and an appendix adde
H-T phase diagram and the nature of Vortex-glass phase in a quasi two-dimensional superconductor: Sn metal layer sandwiched between graphene sheets
The magnetic properties of a quasi two-dimensional superconductor, Sn-metal
graphite (MG), are studied using DC and AC magnetic susceptibility. Sn-MG has a
unique layered structure where Sn metal layer is sandwiched between adjacent
graphene sheets. This compound undergoes a superconducting transition at
= 3.75 K at = 0. The - diagram of Sn-MG is similar to that of
a quasi two-dimensional superconductors. The phase boundaries of vortex liquid,
vortex glass, and vortex lattice phase merge into a multicritical point located
at = 3.4 K and = 40 Oe. There are two irreversibility lines
denoted by (de Almeida-Thouless type) and
(Gabay-Toulouse type), intersecting at = 2.5 K and
= 160 Oe. The nature of slow dynamic and nonlinearity of the
vortex glass phase is studied.Comment: 24 pages, 13 figures; Physica C (2003), in pres
Vortex Structure in Abelian-Projected Lattice Gauge Theory
We report on a breakdown of both monopole dominance and positivity in
abelian-projected lattice Yang-Mills theory. The breakdown is associated with
observables involving two units of the abelian charge. We find that the
projected lattice has at most a global symmetry in the confined phase,
rather than the global U(1) symmetry that might be expected in a dual
superconductor or monopole Coulomb gas picture. Implications for monopole and
center vortex theories of confinement are discussed.Comment: LATTICE99(confine), 3 pages, 2 figure
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