1,165 research outputs found
Accuracy of Electronic Wave Functions in Quantum Monte Carlo: the Effect of High-Order Correlations
Compact and accurate wave functions can be constructed by quantum Monte Carlo
methods. Typically, these wave functions consist of a sum of a small number of
Slater determinants multiplied by a Jastrow factor. In this paper we study the
importance of including high-order, nucleus-three-electron correlations in the
Jastrow factor. An efficient algorithm based on the theory of invariants is
used to compute the high-body correlations. We observe significant improvements
in the variational Monte Carlo energy and in the fluctuations of the local
energies but not in the fixed-node diffusion Monte Carlo energies. Improvements
for the ground states of physical, fermionic atoms are found to be smaller than
those for the ground states of fictitious, bosonic atoms, indicating that
errors in the nodal surfaces of the fermionic wave functions are a limiting
factor.Comment: 9 pages, no figures, Late
Angular Momentum and Energy-Momentum Densities as Gauge Currents
If we replace the general spacetime group of diffeomorphisms by
transformations taking place in the tangent space, general relativity can be
interpreted as a gauge theory, and in particular as a gauge theory for the
Lorentz group. In this context, it is shown that the angular momentum and the
energy-momentum tensors of a general matter field can be obtained from the
invariance of the corresponding action integral under transformations taking
place, not in spacetime, but in the tangent space, in which case they can be
considered as gauge currents.Comment: RevTeX4, 7 pages, no figures. Presentation changes; version to appear
in Phys. Rev.
Jastrow correlation factor for atoms, molecules, and solids
A form of Jastrow factor is introduced for use in quantum Monte Carlo
simulations of finite and periodic systems. Test data are presented for atoms,
molecules, and solids, including both all-electron and pseudopotential atoms.
We demonstrate that our Jastrow factor is able to retrieve a large fraction of
the correlation energy
The quantum dilogarithm and representations quantum cluster varieties
We construct, using the quantum dilogarithm, a series of *-representations of
quantized cluster varieties. This includes a construction of infinite
dimensional unitary projective representations of their discrete symmetry
groups - the cluster modular groups. The examples of the latter include the
classical mapping class groups of punctured surfaces.
One of applications is quantization of higher Teichmuller spaces.
The constructed unitary representations can be viewed as analogs of the Weil
representation. In both cases representations are given by integral operators.
Their kernels in our case are the quantum dilogarithms.
We introduce the symplectic/quantum double of cluster varieties and related
them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version.
To appear in Inventiones Math. The last Section of the previous versions was
removed, and will become a separate pape
On Nonlinear Diffusion with Multiplicative Noise
Nonlinear diffusion is studied in the presence of multiplicative noise. The
nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing
field. A dynamic phase transition occurs when the system ``unbinds'' from the
wall. Two different universality classes, corresponding to the cases of an
``upper'' and a ``lower'' wall, are identified and their critical properties
are characterized. While the lower wall problem can be understood by applying
the knowledge of linear diffusion with multiplicative noise, the upper wall
problem exhibits an anomaly due to nontrivial dynamics in the vicinity of the
wall. Broad power-law distribution is obtained throughout the bound phase.Comment: 4 pages, LaTeX, text and figures also available at
http://matisse.ucsd.edu/~hw
Black hole puncture initial data with realistic gravitational wave content
We present improved post-Newtonian-inspired initial data for non-spinning
black-hole binaries, suitable for numerical evolution with punctures. We
revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P.
Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining
integral terms. These terms improve accuracy in the far zone and, for the first
time, include realistic gravitational waves in the initial data. We investigate
the behavior of these data both at the center of mass and in the far zone,
demonstrating agreement of the transverse-traceless parts of the new metric
with quadrupole-approximation waveforms. These data can be used for numerical
evolutions, enabling a direct connection between the merger waveforms and the
post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio
Circular Orbits in Einstein-Gauss-Bonnet Gravity
The stability under radial and vertical perturbations of circular orbits
associated to particles orbiting a spherically symmetric center of attraction
is study in the context of the n-dimensional: Newtonian theory of gravitation,
Einstein's general relativity, and Einstein-Gauss-Bonnet theory of gravitation.
The presence of a cosmological constant is also considered. We find that this
constant as well as the Gauss-Bonnet coupling constant are crucial to have
stability for .Comment: 11 pages, 4 figs, RevTex, Phys. Rev. D, in pres
Noncommutative spaces, the quantum of time and the Lorentz symmetry
We introduce three space-times that are discrete in time and compatible with
the Lorentz symmetry. We show that these spaces are no commutative, with
commutation relations similar to the relations of the Snyder and Yang spaces.
Furthermore, using a reparametrized relativistic particle we obtain a
realization of the Snyder type spaces and we construct an action for them.Comment: 8 pages, to appear in PR
On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
We consider two families of commuting Hamiltonians on the cotangent bundle of
the group GL(n,C), and show that upon an appropriate single symplectic
reduction they descend to the spectral invariants of the hyperbolic Sutherland
and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The
duality symplectomorphism between these two integrable models, that was
constructed by Ruijsenaars using direct methods, can be then interpreted
geometrically simply as a gauge transformation connecting two cross sections of
the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex
Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion
We study the numerical solution of the non-relativistic Schr\"{o}dinger
equation for two-electron atoms in ground and excited S-states using
pseudospectral (PS) methods of calculation. The calculation achieves
convergence rates for the energy, Cauchy error in the wavefunction, and
variance in local energy that are exponentially fast for all practical
purposes. The method requires three separate subdomains to handle the
wavefunction's cusp-like behavior near the two-particle coalescences. The use
of three subdomains is essential to maintaining exponential convergence. A
comparison of several different treatments of the cusps and the semi-infinite
domain suggest that the simplest prescription is sufficient. For many purposes
it proves unnecessary to handle the logarithmic behavior near the
three-particle coalescence in a special way. The PS method has many virtues: no
explicit assumptions need be made about the asymptotic behavior of the
wavefunction near cusps or at large distances, the local energy is exactly
equal to the calculated global energy at all collocation points, local errors
go down everywhere with increasing resolution, the effective basis using
Chebyshev polynomials is complete and simple, and the method is easily
extensible to other bound states. This study serves as a proof-of-principle of
the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some
references added, some stylistic changes, added paragraph to matrix methods
section, added last sentence to abstract
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