4,888 research outputs found
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 electrons), applicable to
metals and insulators alike. In lieu of explicit diagonalization of the
Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ
a two-level Chebyshev polynomial filter based complementary subspace strategy
to: 1) compute a set of vectors that span the occupied subspace of the
Hamiltonian; 2) reduce subspace diagonalization to just partially occupied
states; and 3) obtain those states in an efficient, scalable manner via an
inner Chebyshev-filter iteration. By reducing the necessary computation to just
partially occupied states, and obtaining these through an inner Chebyshev
iteration, our approach reduces the cost of large metallic calculations
significantly, while eliminating subspace diagonalization for insulating
systems altogether. We describe the implementation of the method within the
framework of the Discontinuous Galerkin (DG) electronic structure method and
show that this results in a computational scheme that can effectively tackle
bulk and nano systems containing tens of thousands of electrons, with chemical
accuracy, within a few minutes or less of wall clock time per SCF iteration on
large-scale computing platforms. We anticipate that our method will be
instrumental in pushing the envelope of large-scale ab initio molecular
dynamics. As a demonstration of this, we simulate a bulk silicon system
containing 8,000 atoms at finite temperature, and obtain an average SCF step
wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2
From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
We consider one-dimensional topological insulators hosting fractionally
charged midgap states in the presence and absence of induced superconductivity
pairing. Under the protection of a discrete symmetry, relating positive and
negative energy states, the solitonic midgap states remain pinned at zero
energy when superconducting correlations are induced by proximity effect. When
the superconducting pairing dominates the initial insulating gap, Majorana
fermion phases develop for a class of insulators. As a concrete example, we
study the Creutz model with induced s-wave superconductivity and repulsive
Hubbard-type interactions. For a finite wire, without interactions, the
solitonic modes originating from the nonsuperconducting model survive at zero
energy, revealing a fourfold-degenerate ground state. However, interactions
break the aforementioned discrete symmetry and completely remove this
degeneracy, thereby producing a unique ground state which ischaracterized by a
topological bulk invariant with respect to the product of fermion parity and
bond inversion. In contrast, the Majorana edge modes are globally robust to
interactions. Moreover, the parameter range for which a topological Majorana
phase is stabilized expands when increasing the repulsive Hubbard interaction.
The topological phase diagram of the interacting model is obtained using a
combination of mean-field theory and density matrix renormalization group
techniques.Comment: 20 pages, 20 figure
The sources and nature of long-term memory in the business cycle
This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, focusing on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-range dependence, a consequence of aggregation in the presence of real business cycles. We then derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data and discuss how fiscal policy may alter the stochastic behavior of the former. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test, which is robust to short-term dependence, is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle..Business cycles ; Time-series analysis
Scaling transition for nonlinear random fields with long-range dependence
We obtain a complete description of anisotropic scaling limits and the
existence of scaling transition for nonlinear functions (Appell polynomials) of
stationary linear random fields on with moving average
coefficients decaying at possibly different rate in the horizontal and vertical
direction. The paper extends recent results on scaling transition for linear
random fields in Puplinskait\.e and Surgailis (2016), Puplinskait\.e and
Surgailis (2015)
Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics
We study transport through an electronic Mach-Zehnder interferometer recently
devised at the Weizmann Institute. We show that this device can be used to
probe statistics of quasiparticles in the fractional quantum Hall regime. We
calculate the tunneling current through the interferometer as the function of
the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its
flux-dependent component is strongly sensitive to the statistics of tunneling
quasiparticles. More specifically, the flux-dependent and flux-independent
contributions to the current are related by a power law, the exponent being a
function of the quasiparticle statistics.Comment: 22 pages; 8 figure
Biorthogonal partners and applications
Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications
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