580 research outputs found
Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the
single- and the multireference case to tackle both the many-body problem and
the decay problem encountered, for example, in the study of electronic
resonances in molecules. A complex absorbing potential (CAP) is employed to
facilitate a treatment of resonance states that is similar to the
well-established bound-state techniques. For the perturbative approach, the
full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned
according to the Epstein-Nesbet scheme. The equations we derive in the
framework of the single-reference perturbation theory turn out to be identical
to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The
multireference perturbation theory is studied for a model problem and is shown
to be an efficient and accurate method. Algorithmic aspects of the integration
of the perturbation theories into existing ab initio programs are discussed,
and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry
(1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and
particle physics (from 1953 to 2006). We show how the consideration of
symmetries, largely used in physics since the end of the 1920's, gave rise to a
new format of the periodic table in the 1970's. More specifically, this paper
is concerned with the application of the group SO(4,2)xSU(2) to the periodic
table of chemical elements. It is shown how the Madelung rule of the atomic
shell model can be used for setting up a periodic table that can be further
rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative
results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry
(special issue to commemorate the one hundredth anniversary of the death of
Mendeleev who died in 1907); version 2: 16 pages; some sentences added;
acknowledgment and references added; misprints correcte
Estimation of properties of low-lying excited states of Hubbard models : a multi-configurational symmetrized projector quantum Monte Carlo approach
We present in detail the recently developed multi-configurational symmetrized
projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard
model. We describe the implementation of the Monte Carlo method for a
multi-configurational trial wavefunction. We give a detailed discussion of
issues related to the symmetry of the projection procedure which validates our
Monte Carlo procedure for excited states and leads naturally to the idea of
symmetrized sampling for correlation functions, developed earlier in the
context of ground state simulations. It also leads to three possible averaging
schemes. We have analyzed the errors incurred in these various averaging
procedures and discuss and detail the preferred averaging procedure for
correlations that do not have the full symmetry of the Hamiltonian. We study
the energies and correlation functions of the low-lying excited states of the
half-filled Hubbard model in 1-D. We have used this technique to study the
pair-binding energies of two holes in and systems, which compare
well the Bethe ansatz data of Fye, Martins and Scalettar. We have also studied
small clusters amenable to exact diagonalization studies in 2-D and have
reproduced their energies and correlation functions by the MSPQMC method. We
identify two ways in which a multiconfigurational trial wavefunction can lead
to a negative sign problem. We observe that this effect is not severe in 1-D
and tends to vanish with increasing system size. We also note that this does
not enhance the severity of the sign problem in two dimensions.Comment: 29 pages, 2 figures available on request, submitted to Phys. Rev.
Spin-Orbit Interactions in Bilayer Exciton-Condensate Ferromagnets
Bilayer electron-hole systems with unequal electron and hole densities are
expected to have exciton condensate ground states with spontaneous
spin-polarization in both conduction and valence bands. In the absence of
spin-orbit and electron-hole exchange interactions there is no coupling between
the spin-orientations in the two quantum wells. In this article we show that
Rashba spin-orbit interactions lead to unconventional magnetic anisotropies,
whose strength we estimate, and to ordered states with unusual quasiparticle
spectra.Comment: 36 pages, 12 figure
Antiresonances in Molecular Wires
We present analytic and numerical studies based on Landauer theory of
conductance antiresonances of molecular wires. Our analytic treatment is a
solution of the Lippmann-Schwinger equation for the wire that includes the
effects of the non-orthogonality of the atomic orbitals on different atoms
exactly. The problem of non-orthogonality is treated by solving the transport
problem in a new Hilbert space which is spanned by an orthogonal basis. An
expression is derived for the energies at which antiresonances should occur for
a molecular wire connected to a pair of single-channel 1D leads. From this
expression we identify two distinct mechanisms that give rise to antiresonances
under different circumstances. The exact treatment of non-orthogonality in the
theory is found to be necessary to obtain reliable results. Our numerical
simulations extend this work to multichannel leads and to molecular wires
connected to 3D metallic nanocontacts. They demonstrate that our analytic
results also provide a good description of these more complicated systems
provided that certain well-defined conditions are met. These calculations
suggest that antiresonances should be experimentally observable in the
differential conductance of molecular wires of certain types.Comment: 22 pages, 5 figure
Particle-unstable nuclei in the Hartree-Fock theory
Ground state energies and decay widths of particle unstable nuclei are
calculated within the Hartree-Fock approximation by performing a complex
scaling of the many-body Hamiltonian. Through this transformation, the wave
functions of the resonant states become square integrable. The method is
implemented with Skyrme effective interactions. Several Skyrme parametrizations
are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let
Variational calculations for the hydrogen-antihydrogen system with a mass-scaled Born-Oppenheimer potential
The problem of proton-antiproton motion in the --
system is investigated by means of the variational method. We introduce a
modified nuclear interaction through mass-scaling of the Born-Oppenheimer
potential. This improved treatment of the interaction includes the nondivergent
part of the otherwise divergent adiabatic correction and shows the correct
threshold behavior.
Using this potential we calculate the vibrational energy levels with angular
momentum 0 and 1 and the corresponding nuclear wave functions, as well as the
S-wave scattering length. We obtain a full set of all bound states together
with a large number of discretized continuum states that might be utilized in
variational four-body calculations. The results of our calculations gives an
indication of resonance states in the hydrogen-antihydrogen system
The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion
The one-body and two-body density matrices in coordinate space and their
Fourier transforms in momentum space are studied for a nucleus (a
nonrelativistic, self-bound finite system). Unlike the usual procedure,
suitable for infinite or externally bound systems, they are determined as
expectation values of appropriate intrinsic operators, dependent on the
relative coordinates and momenta (Jacobi variables) and acting on intrinsic
wavefunctions of nuclear states. Thus, translational invariance (TI) is
respected. When handling such intrinsic quantities, we use an algebraic
technique based upon the Cartesian representation, in which the coordinate and
momentum operators are linear combinations of the creation and annihilation
operators a^+ and a for oscillator quanta. Each of the relevant multiplicative
operators can then be reduced to the form: one exponential of the set {a^+}
times other exponential of the set {a}. In the course of such a normal-ordering
procedure we offer a fresh look at the appearance of "Tassie-Barker" factors,
and point out other model-independent results. The intrinsic wavefunction of
the nucleus in its ground state is constructed from a
nontranslationally-invariant (nTI) one via existing projection techniques. As
an illustration, the one-body and two-body momentum distributions (MDs) for the
4He nucleus are calculated with the Slater determinant of the
harmonic-oscillator model as the trial, nTI wavefunction. We find that the TI
introduces important effects in the MDs.Comment: 13 pages, incl. 3 figures - to appear in Eur. Phys. J.
Molecular-orbital theory for the stopping power of atoms in the low velocity regime:the case of helium in alkali metals
A free-parameter linear-combination-of-atomic-orbitals approach is presented
for analyzing the stopping power of slow ions moving in a metal. The method is
applied to the case of He moving in alkali metals. Mean stopping powers for He
present a good agreement with local-density-approximation calculations. Our
results show important variations in the stopping power of channeled atoms with
respect to their mean values.Comment: LATEX, 3 PostScript Figures attached. Total size 0.54
Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model
A strong-coupling expansion is applied to the anharmonic Holstein model and
to the Holstein-Hubbard model through fourth order in the hopping matrix
element. Mean-field theory is then employed to determine transition
temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic
effects are not easily mimicked by an on-site Coulomb repulsion, and that
anharmonicity strongly favors superconductivity relative to charge-density-wave
order. Surprisingly, the phase diagram is strongly modified by relatively small
values of the anharmonicity.Comment: 34 pages, typeset in ReVTeX, 11 encapsulated postscript files
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