1,069 research outputs found
Rayleigh-Ritz variation method and connected-moments polynomial approach
We show that the connected-moments polynomial approach proposed recently is
equivalent to the well known Rayleigh-Ritz variation method in the Krylov
space. We compare the latter with one of the original connected-moments methods
by means of a numerical test on an anharmonic oscillato
Solution to the Equations of the Moment Expansions
We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach
Improved tensor-product expansions for the two-particle density matrix
We present a new density-matrix functional within the recently introduced
framework for tensor-product expansions of the two-particle density matrix. It
performs well both for the homogeneous electron gas as well as atoms. For the
homogeneous electron gas, it performs significantly better than all previous
density-matrix functionals, becoming very accurate for high densities and
outperforming Hartree-Fock at metallic valence electron densities. For isolated
atoms and ions, it is on a par with previous density-matrix functionals and
generalized gradient approximations to density-functional theory. We also
present analytic results for the correlation energy in the low density limit of
the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure
High--order connected moments expansion for the Rabi Hamiltonian
We analyze the convergence properties of the connected moments expansion
(CMX) for the Rabi Hamiltonian. To this end we calculate the moments and
connected moments of the Hamiltonian operator to a sufficiently large order.
Our large--order results suggest that the CMX is not reliable for most
practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl
The heat of atomization of sulfur trioxide, SO - a benchmark for computational thermochemistry
Calibration ab initio (direct coupled cluster) calculations including basis
set extrapolation, relativistic effects, inner-shell correlation, and an
anharmonic zero-point energy, predict the total atomization energy at 0 K of
SO to be 335.96 (observed 335.920.19) kcal/mol. Inner polarization
functions make very large (40 kcal/mol with , 10 kcal/mol with
basis sets) contributions to the SCF part of the binding energy. The molecule
presents an unusual hurdle for less computationally intensive theoretical
thermochemistry methods and is proposed as a benchmark for them. A slight
modification of Weizmann-1 (W1) theory is proposed that appears to
significantly improve performance for second-row compounds.Comment: Chem. Phys. Lett., in pres
An Approximate Spectral Density for the Estimation of so me Topological Indices of Alternant Systems
A symmetric two-delta-function model spectral density is used
to estimate several topological indices of alternant hydrocarbons,
namely: the total n-electron energy (E.), the modified topological
index (Z), the HOlVIO-LUMO separation (XHL) and the spectral
radius of adjacency matrix (R). It is found, that the invariants defined by integration (like E. and Z) are reproduced much better than the invariants defined as the Iimiting values of the spectral distribution (like XHL and R). The reason for the well known linear dependence between Er. and lnZ, is discussed
The on-shell self-energy of the uniform electron gas in its weak-correlation limit
The ring-diagram partial summation (or RPA) for the ground-state energy of
the uniform electron gas (with the density parameter ) in its
weak-correlation limit is revisited. It is studied, which treatment
of the self-energy is in agreement with the Hugenholtz-van
Hove (Luttinger-Ward) theorem and which is
not. The correlation part of the lhs h as the RPA asymptotics [in atomic units]. The use of renormalized RPA diagrams for the rhs
yields the similar expression with the sum rule
resulting from three sum rules for the components of and . This
includes in the second order of exchange the sum rule [P. Ziesche, Ann. Phys. (Leipzig), 2006].Comment: 19 pages, 10 figure
Kohn-Sham calculations combined with an average pair-density functional theory
A recently developed formalism in which Kohn-Sham calculations are combined
with an ``average pair density functional theory'' is reviewed, and some new
properties of the effective electron-electron interaction entering in this
formalism are derived. A preliminary construction of a fully self-consitent
scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th
International Workshop on Condensed Matter Theories
Shell Structure of Confined Charges at Strong Coupling
A theoretical description of shell structure for charged particles in a
harmonic trap is explored at strong coupling conditions of = 50 and
100. The theory is based on an extension of the hypernetted chain approximation
to confined systems plus a phenomenological representation of associated bridge
functions. Predictions are compared to corresponding Monte Carlo simulations
and quantitative agreement for the radial density profile is obtained.Comment: 9 pages, 5 figures. Presented at the 13th International Conference on
the Physics of Non-Ideal Plasmas (PNP 13) held in Chernogolovka, Russia
(September 13-18, 2009). Proceedings to be published in "Contributions to
Plasma Physics" (Dec. 2009-Jan. 2010
Correlations in excited states of local Hamiltonians
Physical properties of the ground and excited states of a -local
Hamiltonian are largely determined by the -particle reduced density matrices
(-RDMs), or simply the -matrix for fermionic systems---they are at least
enough for the calculation of the ground state and excited state energies.
Moreover, for a non-degenerate ground state of a -local Hamiltonian, even
the state itself is completely determined by its -RDMs, and therefore
contains no genuine -particle correlations, as they can be inferred from
-particle correlation functions. It is natural to ask whether a similar
result holds for non-degenerate excited states. In fact, for fermionic systems,
it has been conjectured that any non-degenerate excited state of a 2-local
Hamiltonian is simultaneously a unique ground state of another 2-local
Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version
of this conjecture states that any non-degenerate excited state of a 2-local
Hamiltonian is uniquely determined by its 2-matrix among all the pure
-particle states. We construct explicit counterexamples to show that both
conjectures are false. It means that correlations in excited states of local
Hamiltonians could be dramatically different from those in ground states. We
further show that any non-degenerate excited state of a -local Hamiltonian
is a unique ground state of another -local Hamiltonian, hence is uniquely
determined by its -RDMs (or -matrix)
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