Fermi liquid theory of ultra-cold trapped Fermi gases: Implications for Pseudogap Physics and Other Strongly Correlated Phases

We show how Fermi liquid theory can be applied to ultra-cold Fermi gases, thereby expanding their "simulation" capabilities to a class of problems of interest to multiple physics sub-disciplines. We introduce procedures for measuring and calculating position dependent Landau parameters. This lays the ground work for addressing important controversial issues: (i) the suggestion that thermodynamically, the normal state of a unitary gas is indistinguishable from a Fermi liquid (ii) that a fermionic system with strong repulsive contact interactions is associated with either ferromagnetism or localization; this relates as well to $^3$He and its p-wave superfluidity.Comment: 4 pages, 2 figures, revised versio

Spin waves in quasi-equilibrium spin systems

Using the Landau Fermi liquid theory we have discovered a new regime for the propagation of spin waves in a quasi-equilibrium spin systems. We have determined the dispersion relation for the transverse spin waves and found that one of the modes is gapless. The gapless mode corresponds to the precessional mode of the magnetization in a paramagnetic system in the absence of an external magnetic field. One of the other modes is gapped which is associated with the precession of the spin current around the internal field. The gapless mode has a quadratic dispersion leading to some interesting thermodynamic properties including a $T^{3/2}$ contribution to the specific heat. We also show that these modes make significant contributions to the dynamic structure function.Comment: 4 pages, 3 figure

Lognormal scale invariant random measures

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic versio

Multi-parameter generalization of nonextensive statistical mechanics

We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to fit experimental results which cannot be reproduced within the Boltzmann's or Tsallis' formalism.Comment: ReVTex 4.0, 4 eps figure

The random case of Conley's theorem

The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where $\mathcal{CR}(\phi)$ denotes the chain recurrent set of $\phi$, $A$ stands for an attractor and $B(A)$ is the basin determined by $A$. In this paper we show that by appropriately selecting the definition of random attractor, in fact we define a random local attractor to be the $\omega$-limit set of some random pre-attractor surrounding it, and by considering appropriate measurability, in fact we also consider the universal $\sigma$-algebra $\mathcal F^u$-measurability besides $\mathcal F$-measurability, we are able to obtain the random case of Conley's theorem.Comment: 15 page

Plume motion and large-scale circulation in a cylindrical Rayleigh-B\'enard cell

We used the time correlation of shadowgraph images to determine the angle $\Theta$ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-B\'enard cell of aspect ratio $\Gamma \equiv D/L = 1$ ($D$ is the diameter and $L \simeq 87$ mm the height) in the Rayleigh-number range $7\times 10^7 \leq R \leq 3\times 10^{9}$ for a Prandtl number $\sigma = 6$. We expect that $\Theta$ gives the direction of the large-scale circulation. It oscillates time-periodically. Near the top and bottom plates $\Theta(t)$ has the same frequency but is anti-correlated.Comment: 4 pages, 6 figure

Organisation of joints and faults from 1-cm to 100-km scales revealed by optimized anisotropic wavelet coefficient method and multifractal analysis

International audienceThe classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes

Smooth stable and unstable manifolds for stochastic partial differential equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's method. Then, we prove the smoothness of these invariant manifolds

Finite size scaling in the solar wind magnetic field energy density as seen by WIND

Statistical properties of the interplanetary magnetic field fluctuations can provide an important insight into the solar wind turbulent cascade. Recently, analysis of the Probability Density Functions (PDF) of the velocity and magnetic field fluctuations has shown that these exhibit non-Gaussian properties on small time scales while large scale features appear to be uncorrelated. Here we apply the finite size scaling technique to explore the scaling of the magnetic field energy density fluctuations as seen by WIND. We find a single scaling sufficient to collapse the curves over the entire investigated range. The rescaled PDF follow a non Gaussian distribution with asymptotic behavior well described by the Gamma distribution arising from a finite range Lévy walk. Such mono scaling suggests that a Fokker-Planck approach can be applied to study the PDF dynamics. These results strongly suggest the existence of a common, nonlinear process on the time scale up to 26 hours