1,460 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
Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series
Anions and radicals are important for many applications including
environmental chemistry, semiconductors, and charge transfer, but are poorly
described by the available approximate energy density functionals. Here we test
an approximate exchange-correlation functional based on the exact
strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case
of the He isoelectronic series with varying nuclear charge , which
includes weakly bound negative ions and a quantum phase transition at a
critical value of , representing a big challenge for density functional
theory. We use accurate wavefunction calculations to validate our results,
comparing energies and Kohn-Sham potentials, thus also providing useful
reference data close to and at the quantum phase transition. We show that our
functional is able to bind H and to capture in general the physics of
loosely bound anions, with a tendency to strongly overbind that can be proven
mathematically. We also include corrections based on the uniform electron gas
which improve the results.Comment: Accepted for the JCP Special Topic Issue "Advances in DFT
Methodology
Low-energy general relativity with torsion: a systematic derivative expansion
We attempt to build systematically the low-energy effective Lagrangian for
the Einstein--Cartan formulation of gravity theory that generally includes the
torsion field. We list all invariant action terms in certain given order; some
of the invariants are new. We show that in the leading order the fermion action
with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4
components of the torsion (out of the general 24) playing the role of Abelian
gauge bosons. The bosonic action quadratic in torsion gives masses to those
gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action
of a general form containing vector-vector, axial-vector and axial-axial
interactions. We present a quantum field-theoretic method to average the
4-fermion interaction over the fermion medium, and perform the explicit
averaging for free fermions with given chemical potential and temperature. The
result is different from that following from the "spin fluid" approach used
previously. On the whole, we arrive to rather pessimistic conclusions on the
possibility to observe effects of the torsion-induced 4-fermion interaction,
although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added.
Final (published) versio
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
On the structure of the post-Newtonian expansion in general relativity
In the continuation of a preceding work, we derive a new expression for the
metric in the near zone of an isolated matter system in post-Newtonian
approximations of general relativity. The post-Newtonian metric, a solution of
the field equations in harmonic coordinates, is formally valid up to any order,
and is cast in the form of a particular solution of the wave equation, plus a
specific homogeneous solution which ensures the asymptotic matching to the
multipolar expansion of the gravitational field in the exterior of the system.
The new form provides some insights on the structure of the post-Newtonian
expansion in general relativity and the gravitational radiation reaction terms
therein.Comment: 22 pages, to appear in Phys. Rev.
Operational indistinguishably of varying speed of light theories
The varying speed of light theories have been recently proposed to solve the
standard model problems and anomalies in the ultra high energy cosmic rays.
These theories try to formulate a new relativity with no assumptions about the
constancy of the light speed. In this regard, we study two theories and want to
show that these theories are not the new theories of relativity, but only
re-descriptions of Einstein's special relativity.Comment: 5 pages, 2 figures, title changed, minor changes in notations and
formulae, a paragraph added, Int. J. Mod. Phys. D (in press) v
Unimodular cosmology and the weight of energy
Some models are presented in which the strength of the gravitational coupling
of the potential energy relative to the same coupling for the kinetic energy
is, in a precise sense, adjustable. The gauge symmetry of these models consists
of those coordinate changes with unit jacobian.Comment: LaTeX, 23 pages, conclusions expanded. Two paragraphs and a new
reference adde
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 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
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