345 research outputs found
Superconductivity in the attractive Hubbard model: functional renormalization group analysis
We present a functional renormalization group analysis of superconductivity
in the ground state of the attractive Hubbard model on a square lattice.
Spontaneous symmetry breaking is treated in a purely fermionic setting via
anomalous propagators and anomalous effective interactions. In addition to the
anomalous interactions arising already in the reduced BCS model, effective
interactions with three incoming legs and one outgoing leg (and vice versa)
occur. We accomplish their integration into the usual diagrammatic formalism by
introducing a Nambu matrix for the effective interactions. From a random-phase
approximation generalized through use of this matrix we conclude that the
impact of the 3+1 effective interactions is limited, especially considering the
effective interactions important for the determination of the order parameter.
The exact hierarchy of flow equations for one-particle irreducible vertex
functions is truncated on the two-particle level, with higher-order self-energy
corrections included in a scheme proposed by Katanin. Using a parametrization
of effective interactions by patches in momentum space, the flow equations can
be integrated numerically to the lowest scales without encountering
divergences. Momentum-shell as well as interaction-flow cutoff functions are
used, including a small external field or a large external field and a
counterterm, respectively. Both approaches produce momentum-resolved order
parameter values directly from the microscopic model. The size of the
superconducting gap is in reasonable agreement with expectations from other
studies.Comment: 22 pages, 16 figures, references added, some changes in the
introductio
Fermionic functional renormalization group for first-order phase transitions: a mean-field model
First-order phase transitions in many-fermion systems are not detected in the
susceptibility analysis of common renormalization-group (RG) approaches. Here
we introduce a counterterm technique within the functional
renormalization-group (fRG) formalism which allows access to all stable and
metastable configurations. It becomes possible to study symmetry-broken states
which occur through first-order transitions as well as hysteresis phenomena.
For continuous transitions, the standard results are reproduced. As an example,
we study discrete-symmetry breaking in a mean-field model for a commensurate
charge-density wave. An additional benefit of the approach is that away from
the critical temperature for the breaking of discrete symmetries large
interactions can be avoided at all RG scales.Comment: 17 pages, 8 figures. v2 corrects typos, adds references and a
discussion of the literatur
Neural Correlates of Temporal Credit Assignment in the Parietal Lobe
Empirical studies of decision making have typically assumed that value learning is governed by time, such that a reward prediction error arising at a specific time triggers temporally-discounted learning for all preceding actions. However, in natural behavior, goals must be acquired through multiple actions, and each action can have different significance for the final outcome. As is recognized in computational research, carrying out multi-step actions requires the use of credit assignment mechanisms that focus learning on specific steps, but little is known about the neural correlates of these mechanisms. To investigate this question we recorded neurons in the monkey lateral intraparietal area (LIP) during a serial decision task where two consecutive eye movement decisions led to a final reward. The underlying decision trees were structured such that the two decisions had different relationships with the final reward, and the optimal strategy was to learn based on the final reward at one of the steps (the “F” step) but ignore changes in this reward at the remaining step (the “I” step). In two distinct contexts, the F step was either the first or the second in the sequence, controlling for effects of temporal discounting. We show that LIP neurons had the strongest value learning and strongest post-decision responses during the transition after the F step regardless of the serial position of this step. Thus, the neurons encode correlates of temporal credit assignment mechanisms that allocate learning to specific steps independently of temporal discounting
Development of semiconductor detectors for fast neutron radiography
A high-energy neutron detector has been developed using a semiconductor diode fabricated from bulk gallium arsenide wafers with a polyethylene neutron converter layer. Typical thickness of the diode layer is 250 to 300 μm with bias voltages of 30 to 150 volts. Converter thicknesses up to 2030 μm have been tested. GaAs neutron detectors offer many advantages over existing detectors including positional information, directional dependence, gamma discrimination, radiation hardness, and spectral tailoring. Polyethylene-coated detectors have been shown to detect 14 MeV neutrons directly from a D-T neutron generator without interference from gamma rays or scattered neutrons. An array of small diode detectors can be assembled to perform fast neutron radiography with direct digital readout and real-time display of the image produced. In addition, because the detectors are insensitive to gamma rays and low energy neutrons, highly radioactive samples (such as spent nuclear fuel or transuranic waste drums) could be radiographed. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87673/2/1118_1.pd
A Droplet within the Spherical Model
Various substances in the liquid state tend to form droplets. In this paper
the shape of such droplets is investigated within the spherical model of a
lattice gas. We show that in this case the droplet boundary is always
diffusive, as opposed to sharp, and find the corresponding density profiles
(droplet shapes). Translation-invariant versions of the spherical model do not
fix the spatial location of the droplet, hence lead to mixed phases. To obtain
pure macroscopic states (which describe localized droplets) we use generalized
quasi-averaging. Conventional quasi-averaging deforms droplets and, hence, can
not be used for this purpose. On the contrary, application of the generalized
method of quasi-averages yields droplet shapes which do not depend on the
magnitude of the applied external field.Comment: 22 pages, 2 figure
Final state effects on superfluid He in the deep inelastic regime
A study of Final State Effects (FSE) on the dynamic structure function of
superfluid He in the Gersch--Rodriguez formalism is presented. The main
ingredients needed in the calculation are the momentum distribution and the
semidiagonal two--body density matrix. The influence of these ground state
quantities on the FSE is analyzed. A variational form of is used, even
though simpler forms turn out to give accurate results if properly chosen.
Comparison to the experimental response at high momentum transfer is performed.
The predicted response is quite sensitive to slight variations on the value of
the condensate fraction, the best agreement with experiment being obtained with
. Sum rules of the FSE broadening function are also derived and
commented. Finally, it is shown that Gersch--Rodriguez theory produces results
as accurate as those coming from other more recent FSE theories.Comment: 20 pages, RevTex 3.0, 11 figures available upon request, to be appear
in Phys. Rev.
Beyond the binary collision approximation for the large- response of liquid He
We discuss corrections to the linear response of a many-body system beyond
the binary collision approximation. We first derive for smooth pair
interactions an exact expression of the response , considerably
simplifying existing forms and present also the generalization for interactions
with a strong, short-range repulsion. We then apply the latter to the case of
liquid He. We display the numerical influence of the correction
around the quasi-elastic peak and in the low-intensity wings of the response,
far from that peak. Finally we resolve an apparent contradiction in previous
discussions around the fourth order cumulant expansion coefficient. Our results
prove that the large- response of liquid He can be accurately understood
on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques
Theoretical aspects of the CEBAF 89-009 experiment on inclusive scattering of 4.05 GeV electrons from nuclei
We compare recent CEBAF data on inclusive electron scattering on nuclei with
predictions, based on a relation between structure functions (SF) of a nucleus,
a nucleon and a nucleus of point-nucleons. The latter contains nuclear
dynamics, e.g. binary collision contributions in addition to the asymptotic
limit. The agreement with the data is good, except in low-intensity regions.
Computed ternary collsion contributions appear too small for an explanation. We
perform scaling analyses in Gurvitz's scaling variable and found that for
, ratios of scaling functions for pairs of nuclei differ by less
than 15-20% from 1. Scaling functions for are, for increasing ,
shown to approach a plateau from above. We observe only weak -dependence
in FSI, which in the relevant kinematic region is ascribed to the diffractive
nature of the NN amplitudes appearing in FSI. This renders it difficult to
separate asymptotic from FSI parts and seriously hampers the extraction of
from scaling analyses in a model-independnent fashion.Comment: 11 p. Latex file, 2 ps fig
Bose-Einstein condensation in the presence of a uniform field and a point-like impurity
The behavior of an ideal -dimensional boson gas in the presence of a
uniform gravitational field is analyzed. It is explicitly shown that,
contrarily to an old standing folklore, the three-dimensional gas does not
undergo Bose-Einstein condensation at finite temperature. On the other hand,
Bose-Einstein condensation occurs at for if there is a
point-like impurity at the bottom of the vessel containing the gas.Comment: 14 pages, REVTEX. Revised version, accepted for publication in Phys.
Rev.
Description of recent large- neutron inclusive scattering data from liquid He
We report dynamical calculations for large- structure functions of liquid
He at =1.6 and 2.3 K and compare those with recent MARI data. We extend
those calculations far beyond the experimental range q\le 29\Ain in order to
study the approach of the response to its asymptotic limit for a system with
interactions having a strong short-range repulsion. We find only small
deviations from theoretical behavior, valid for smooth . We repeat an
extraction by Glyde et al of cumulant coefficients from data. We argue that
fits determine the single atom momentum distribution, but express doubt as to
the extraction of meaningful Final State Interaction parameters.Comment: 37 pages, 13 postscript fig
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