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arXiv1996

Self-organized branching processes: Avalanche models with dissipation

We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.

cond-mat↗

arXiv1996

Anomalous Scaling in the N-Point Functions of Passive Scalar

A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

chao-dyn↗

arXiv1996

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $ξ\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=ρ(r) t^{-1/2} ξ^{-2} f_d(ξ)$, where $ρ(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(ξ)$ in powers of $ξ$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(ξ)$. Namely, for $d=2$, $f_2(ξ)\simeq a_2ξ^2\lnξ+b_2ξ^2$; for $3\le d\le 5$, $f_d(ξ)\simeq a_dξ^2+b_dξ^d$; for $d=6$, $f_6(ξ)\simeq a_6ξ^2+b_6ξ^6\lnξ$; for $7\le d\le 9$, $f_d(ξ)\simeq a_dξ^2+b_dξ^6+c_dξ^d$; for $d=10$, $f_{10}(ξ)\simeq a_{10}ξ^2+b_{10}ξ^6+c_{10}ξ^{10}\lnξ$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/ρ(r)\simeq t^{-1/2}\ln t$.

cond-mat↗

arXiv1996

Crossover from directed percolation to compact directed percolation

We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical exponents switch from the compact directed percolation class to ordinary directed percolation. We conclude that the nonuniversality observed in models with multiple absorbing configurations cannot be explained as a simple surface effect.

cond-mat↗

arXiv1996

Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions (repulsive or attractive) are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is payed to the thermodynamic properties of bosons and their condensation.

cond-mat↗

arXiv1996

On the VC-dimension of neural networks with binary weights

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that are too large for enumerations, number theoretic arguments give lower bounds for the VC-dimension. For the Ising perceptron, the VC-dimension is probably larger than $N/2$.

cond-mat↗

arXiv1996

Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.

adap-org↗

arXiv1992

Exact Solution of a Phase Separation Model with Conserved Order Parameter Dynamics

Pairwise particle-exchange model on a linear lattice is solved exactly by a new rate-equation method. Lattice sites are occupied by particles A and B which can exchange irreversibly provided the local energy in reduced. Thus, the model corresponds to a zero-temperature Kawasaki-type phase separation process. Due to local order-parameter conservation, the dynamics reaches a frozen state at large times, the structure of which depends on the initial conditions.

cond-mat↗

arXiv2025

Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System

We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2 $ family of interactions. The algebra consists of the commutation between a ``Super- Hamiltonian'', and two other operators, in a Hilbert space that is an enlargement of the original one by introducing fermions. The commutation relations reduce to quantal Ordered Lax equations when projected to the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator. These in turn lead to a highly automatic proof of the integrability of these models. In the case of the discrete $SU(n)-1/r^2$ model, the `` Super-Hamiltonian'' is again an $SU(m)-1/r^2$ model with a related $m$, providing an interesting hierarchy of models.

cond-mat↗

arXiv2025

What Does The Korringa Ratio Measure?

We present an analysis of the Korringa ratio in a dirty metal, emphasizing the case where a Stoner enhancement of the uniform susceptibilty is present. We find that the relaxation rates are significantly enhanced by disorder, and that the inverse problem of determining the bare density of states from a study of the change of the Knight shift and relaxation rates with some parameter, such as pressure, has rather constrained solutions, with the disorder playing an important role. Some preliminary applications to the case of chemical substitution in the Rb$_{3-x}$K$_x $C$_{60}$ family of superconductors is presented and some other relevant systems are mentioned.

cond-mat↗

arXiv1995

Kondo Effect in a Luttinger Liquid: Exact Results from Conformal Field Theory

We report on exact results for the low-temperature thermodynamics of a spin-$\frac{1}{2}$ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: {\em either} a local Fermi liquid, {\em or} a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of back scattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.

cond-mat↗

arXiv1995

On Synchronization in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same than the obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.

cond-mat↗

arXiv1996

Finite-temperature Fermi-edge singularity in tunneling studied using random telegraph signals

We show that random telegraph signals in metal-oxide-silicon transistors at millikelvin temperatures provide a powerful means of investigating tunneling between a two-dimensional electron gas and a single defect state. The tunneling rate shows a peak when the defect level lines up with the Fermi energy, in excellent agreement with theory of the Fermi-edge singularity at finite temperature. This theory also indicates that defect levels are the origin of the dissipative two-state systems observed previously in similar devices.

cond-mat↗

arXiv1995

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.

cond-mat↗

arXiv1995

A New Phase of Tethered Membranes: Tubules

We show that fluctuating tethered membranes with {\it any} intrinsic anisotropy unavoidably exhibit a new phase between the previously predicted ``flat'' and ``crumpled'' phases, in high spatial dimensions $d$ where the crumpled phase exists. In this new "tubule" phase, the membrane is crumpled in one direction but extended nearly straight in the other. Its average thickness is $R_G\sim L^{ν_t}$ with $L$ the intrinsic size of the membrane. This phase is more likely to persist down to $d=3$ than the crumpled phase. In Flory theory, the universal exponent $ν_t=3/4$, which we conjecture is an exact result. We study the elasticity and fluctuations of the tubule state, and the transitions into it.

cond-mat↗

arXiv1996

Grazing Incidence Infrared Reflectivity of La$_{1.85}$Sr$_{0.15}$CuO$_4$ and NbN

Infrared reflectivity measurements, using p-polarized light at a grazing angle of incidence, show an increased sensitivity to the optical conductivity of highly reflecting superconducting materials. We demonstrate that when this measurement technique is applied to the conventional s-wave superconductor NbN, the results are in perfect agreement with BCS theory. For the in-plane response of a La$_{1.85}$Sr$_{0.15}$CuO$_4$ single crystal, in the superconducting state, we find a reduction of the optical conductivity in the frequency range below 20 meV. The observed frequency dependence excludes an isotropic s-wave gap, but agrees well with model calculations assuming a d-wave order parameter.

cond-mat↗

arXiv1995

Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.

cond-mat↗

arXiv1996

New magnetic coherence effect in superconducting La_{2-x}Sr_{x}CuO_{4}

We have used inelastic neutron scattering to examine the magnetic fluctuations at intermediate frequencies in the simplest high temperature superconductor, La_{2-x}Sr_{x}Cu_{4}. The suppression of the low energy magnetic response in the superconducting state is accompanied by an increase in the response at higher energies. Just above a threshold energy of ~7 meV there is additional scattering present below T_{c} which is characterised by an extraordinarily long coherence length, in excess of 50 Å.

cond-mat↗