130 research outputs found
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
Quasiparticle Band Structure and Density Functional Theory: Single-Particle Excitations and Band Gaps in Lattice Models
We compare the quasiparticle band structure for a model insulator obtained
from the fluctuation exchange approximation (FEA) with the eigenvalues of the
corresponding density functional theory (DFT) and local density approximation
(LDA). The discontinuity in the exchange-correlation potential for this model
is small and the FEA and DFT band structures are in good agreement. In contrast
to conventional wisdom, the LDA for this model overestimates the size of the
band gap. We argue that this is a consequence of an FEA self-energy that is
strongly frequency dependent, but essentially local.Comment: 8 pages, and 5 figure
On the correct strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation
We consider the problem of the crossover from BCS superconductivity to
Bose-Einstein condensation in three dimensions for a system of fermions with an
attractive interaction, for which we adopt the simplifying assumption of a
suitably regularized point-contact interaction. We examine in a critical way
the fermionic (self-consistent) T-matrix approximation which has been widely
utilized in the literature to describe this crossover above the superconducting
critical temperature, and show that it fails to yield the correct behaviour of
the system in the strong-coupling limit, where composite bosons form as tightly
bound fermion pairs. We then set up the correct approximation for a ``dilute''
system of composite bosons and show that an entire new class of diagrams has to
be considered in the place of the fermionic T-matrix approximation for the
self-energy. This new class of diagrams correctly describes both the weak- and
strong-coupling limits, and consequently results into an improved interpolation
scheme for the intermediate (crossover) region. In this context, we provide
also a systematic mapping between the corresponding diagrammatic theories for
the composite bosons and the constituent fermions. As a preliminary result to
demonstrate the numerical effect of our new class of diagrams on physical
quantities, we calculate the value of the scattering length for composite
bosons in the strong-coupling limit and show that it is considerably modified
with respect to the result obtained within the self-consistent fermionic
T-matrix approximation.Comment: 25 pages, 14 figures included in pape
Image resonance in the many-body density of states at a metal surface
The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism that is able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the GW approximation of many-body perturbation theory. We demonstrate the presence of an unoccupied surface resonance peaked at the position of the first image state. The resonance encompasses the whole Rydberg series of image states and cannot be resolved into individual peaks. Its origin is the shift in spectral weight when many-body correlation effects are taken into account
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