1,743 research outputs found

### Encoding and processing of sensory information in neuronal spike trains

Recently, a statistical signal-processing technique has allowed the information carried by single spike trains of sensory neurons on time-varying stimuli to be characterized quantitatively in a variety of preparations. In weakly electric fish, its application to first-order sensory neurons encoding electric field amplitude (P-receptor afferents) showed that they convey accurate information on temporal modulations in a behaviorally relevant frequency range (<80 Hz). At the next stage of the electrosensory pathway (the electrosensory lateral line lobe, ELL), the information sampled by first-order neurons is used to extract upstrokes and downstrokes in the amplitude modulation waveform. By using signal-detection techniques, we determined that these temporal features are explicitly represented by short spike bursts of second-order neurons (ELL pyramidal cells). Our results suggest that the biophysical mechanism underlying this computation is of dendritic origin. We also investigated the accuracy with which upstrokes and downstrokes are encoded across two of the three somatotopic body maps of the ELL (centromedial and lateral). Pyramidal cells of the centromedial map, in particular I-cells, encode up- and downstrokes more reliably than those of the lateral map. This result correlates well with the significance of these temporal features for a particular behavior (the jamming avoidance response) as assessed by lesion experiments of the centromedial map

### Two particle correlations and orthogonality catastrophe in interacting Fermi systems

The wave function of two fermions, repulsively interacting in the presence of
a Fermi sea, is evaluated in detail. We consider large but finite systems in
order to obtain an unabiguous picture of the two-particle correlations. As
recently pointed out by Anderson, in two or lower dimensions the particles may
be correlated even when situated on the Fermi surface. The "partial exclusion
principle" for two particles with opposite spin on the same Fermi point is
discussed, and related to results from the T-matrix approximation. Particles on
different Fermi points are shown to be uncorrelated in dimensions d > 1. Using
the results for the two-particle correlations we find that the orthogonality
effect induced by adding an extra particle to a (tentative) two-dimensional
Fermi liquid is finite.Comment: 25 pages, LATEX, RWTH/ITP-C 10/9

### On the Analyticity of Solutions in the Dynamical Mean-Field Theory

The unphysical solutions of the periodic Anderson model obtained by H. Keiter
and T. Leuders [Europhys. Lett. 49, 801(2000)] in dynamical mean-field theory
(DMFT) are shown to result from the author's restricted choice of the
functional form of the solution, leading to a violation of the analytic
properties of the exact solution. By contrast, iterative solutions of the
self-consistency condition within the DMFT obtained by techniques which
preserve the correct analytic properties of the exact solution (e.g., quantum
Monte-Carlo simulations or the numerical renormalization group) always lead to
physical solutions.Comment: 4 pages, 1 figur

### 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

### Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model

We analyze the competition between antiferromagnetism and superconductivity
in the two-dimensional Hubbard model by combining a functional renormalization
group flow with a mean-field theory for spontaneous symmetry breaking.
Effective interactions are computed by integrating out states above a scale
Lambda_{MF} in one-loop approximation, which captures in particular the
generation of an attraction in the d-wave Cooper channel from fluctuations in
the particle-hole channel. These effective interactions are then used as an
input for a mean-field treatment of the remaining low-energy states, with
antiferromagnetism, singlet superconductivity and triplet pi-pairing as the
possible order parameters. Antiferromagnetism and superconductivity suppress
each other, leaving only a small region in parameter space where both orders
can coexist with a sizable order parameter for each. Triplet pi-pairing appears
generically in the coexistence region, but its feedback on the other order
parameters is very small.Comment: 28 pages, 14 figure

### Dynamical mean-field theory for the normal phase of the attractive Hubbard model

We analyze the normal phase of the attractive Hubbard model within dynamical
mean-field-theory. We present results for the pair-density, the
spin-susceptibility, the specific heat, the momentum distribution, and for the
quasiparticle weight. At weak coupling the low-temperature behavior of all
quantities is consistent with Fermi liquid theory. At strong coupling all
electrons are bound pairs, which leads to a spin gap and removes fermionic
quasi-particle excitations. The transition between the Fermi liquid phase and
the pair phase takes place at a critical coupling of the order of the
band-width and is generally discontinuous at sufficiently low temperatures

### Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals

We compute the transition temperature $T_c$ and the Ginzburg temperature
$T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an
ordered phase with a broken discrete symmetry in a two-dimensional metallic
electron system. Our calculation is based on a renormalization group analysis
of the Hertz action with a scalar order parameter. We provide analytic
expressions for $T_c$ and $T_{\rm G}$ as a function of the non-thermal control
parameter for the quantum phase transition, including logarithmic corrections.
The Ginzburg regime between $T_c$ and $T_{\rm G}$ occupies a sizable part of
the phase diagram.Comment: 5 pages, 1 figur

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