89,509 research outputs found
Classical, semiclassical, and quantum investigations of the 4-sphere scattering system
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering
system, is investigated with classical, semiclassical, and quantum mechanical
methods at various center-to-center separations of the spheres. The efficiency
and scaling properties of the computations are discussed by comparisons to the
two-dimensional 3-disk system. While in systems with few degrees of freedom
modern quantum calculations are, in general, numerically more efficient than
semiclassical methods, this situation can be reversed with increasing dimension
of the problem. For the 4-sphere system with large separations between the
spheres, we demonstrate the superiority of semiclassical versus quantum
calculations, i.e., semiclassical resonances can easily be obtained even in
energy regions which are unattainable with the currently available quantum
techniques. The 4-sphere system with touching spheres is a challenging problem
for both quantum and semiclassical techniques. Here, semiclassical resonances
are obtained via harmonic inversion of a cross-correlated periodic orbit
signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.
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An automatically curated first-principles database of ferroelectrics.
Ferroelectric materials have technological applications in information storage and electronic devices. The ferroelectric polar phase can be controlled with external fields, chemical substitution and size-effects in bulk and ultrathin film form, providing a platform for future technologies and for exploratory research. In this work, we integrate spin-polarized density functional theory (DFT) calculations, crystal structure databases, symmetry tools, workflow software, and a custom analysis toolkit to build a library of known, previously-proposed, and newly-proposed ferroelectric materials. With our automated workflow, we screen over 67,000 candidate materials from the Materials Project database to generate a dataset of 255 ferroelectric candidates, and propose 126 new ferroelectric materials. We benchmark our results against experimental data and previous first-principles results. The data provided includes atomic structures, output files, and DFT values of band gaps, energies, and the spontaneous polarization for each ferroelectric candidate. We contribute our workflow and analysis code to the open-source python packages atomate and pymatgen so others can conduct analogous symmetry driven searches for ferroelectrics and related phenomena
Deep Learning Topological Invariants of Band Insulators
In this work we design and train deep neural networks to predict topological
invariants for one-dimensional four-band insulators in AIII class whose
topological invariant is the winding number, and two-dimensional two-band
insulators in A class whose topological invariant is the Chern number. Given
Hamiltonians in the momentum space as the input, neural networks can predict
topological invariants for both classes with accuracy close to or higher than
90%, even for Hamiltonians whose invariants are beyond the training data set.
Despite the complexity of the neural network, we find that the output of
certain intermediate hidden layers resembles either the winding angle for
models in AIII class or the solid angle (Berry curvature) for models in A
class, indicating that neural networks essentially capture the mathematical
formula of topological invariants. Our work demonstrates the ability of neural
networks to predict topological invariants for complicated models with local
Hamiltonians as the only input, and offers an example that even a deep neural
network is understandable.Comment: 8 pages, 5 figure
Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
The determination of the energy spectra of small spin systems as for instance
given by magnetic molecules is a demanding numerical problem. In this work we
review numerical approaches to diagonalize the Heisenberg Hamiltonian that
employ symmetries; in particular we focus on the spin-rotational symmetry SU(2)
in combination with point-group symmetries. With these methods one is able to
block-diagonalize the Hamiltonian and thus to treat spin systems of
unprecedented size. In addition it provides a spectroscopic labeling by
irreducible representations that is helpful when interpreting transitions
induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance
(NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the
reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure
Double Occupancy Errors in Quantum Computing Operations: Corrections to Adiabaticity
We study the corrections to adiabatic dynamics of two coupled quantum dot
spin-qubits, each dot singly occupied with an electron, in the context of a
quantum computing operation. Tunneling causes double occupancy at the
conclusion of an operation and constitutes a processing error. We model the
gate operation with an effective two-level system, where non-adiabatic
transitions correspond to double occupancy. The model is integrable and
possesses three independent parameters. We confirm the accuracy of Dykhne's
formula, a nonperturbative estimate of transitions, and discuss physically
intuitive conditions for its validity. Our semiclassical results are in
excellent agreement with numerical simulations of the exact time evolution. A
similar approach applies to two-level systems in different contexts
Topological and Dynamical Complexity of Random Neural Networks
Random neural networks are dynamical descriptions of randomly interconnected
neural units. These show a phase transition to chaos as a disorder parameter is
increased. The microscopic mechanisms underlying this phase transition are
unknown, and similarly to spin-glasses, shall be fundamentally related to the
behavior of the system. In this Letter we investigate the explosion of
complexity arising near that phase transition. We show that the mean number of
equilibria undergoes a sharp transition from one equilibrium to a very large
number scaling exponentially with the dimension on the system. Near
criticality, we compute the exponential rate of divergence, called topological
complexity. Strikingly, we show that it behaves exactly as the maximal Lyapunov
exponent, a classical measure of dynamical complexity. This relationship
unravels a microscopic mechanism leading to chaos which we further demonstrate
on a simpler class of disordered systems, suggesting a deep and underexplored
link between topological and dynamical complexity
Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration
The search for symmetry as an unusual yet profoundly appealing phenomenon,
and the origin of regular, repeating configuration patterns have long been a
central focus of complexity science and physics. To better grasp and understand
symmetry of configurations in decentralized toroidal architectures, we employ
group-theoretic methods, which allow us to identify and enumerate these inputs,
and argue about irreversible system behaviors with undesired effects on many
computational problems. The concept of so-called configuration shift-symmetry
is applied to two-dimensional cellular automata as an ideal model of
computation. Regardless of the transition function, the results show the
universal insolvability of crucial distributed tasks, such as leader election,
pattern recognition, hashing, and encryption. By using compact enumeration
formulas and bounding the number of shift-symmetric configurations for a given
lattice size, we efficiently calculate the probability of a configuration being
shift-symmetric for a uniform or density-uniform distribution. Further, we
devise an algorithm detecting the presence of shift-symmetry in a
configuration.
Given the resource constraints, the enumeration and probability formulas can
directly help to lower the minimal expected error and provide recommendations
for system's size and initialization. Besides cellular automata, the
shift-symmetry analysis can be used to study the non-linear behavior in various
synchronous rule-based systems that include inference engines, Boolean
networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice
Reduction of continuous symmetries of chaotic flows by the method of slices
We study continuous symmetry reduction of dynamical systems by the method of
slices (method of moving frames) and show that a `slice' defined by minimizing
the distance to a single generic `template' intersects the group orbit of every
point in the full state space. Global symmetry reduction by a single slice is,
however, not natural for a chaotic / turbulent flow; it is better to cover the
reduced state space by a set of slices, one for each dynamically prominent
unstable pattern. Judiciously chosen, such tessellation eliminates the singular
traversals of the inflection hyperplane that comes along with each slice, an
artifact of using the template's local group linearization globally. We compute
the jump in the reduced state space induced by crossing the inflection
hyperplane. As an illustration of the method, we reduce the SO(2) symmetry of
the complex Lorenz equations.Comment: to appear in "Comm. Nonlinear Sci. and Numer. Simulat. (2011)" 12
pages, 8 figure
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