Mapping spiral waves and other radial features in Saturn's rings

We have analyzed the highest-quality images to be obtained by Cassini of Saturn's main rings after the Saturn Orbit Insertion (SOI) and before the Ring Grazing Orbits (RGO) and Grand Finale (GF). These images are comparable to those of SOI in fidelity, though not in nominal resolution, due to their high signal-to-noise. We have systematically searched for radial structure in these images by reducing them to a single dimension (distance from Saturn's center) and using the continuous wavelet transform technique. We discuss the resonant theory of spiral waves and discuss the proper method for deriving the local surface density from the wavelet signature of a spiral wave. We present 1) individual features of interest found in our data, including several classes of waves that have not previously been reported; 2) a radial profile of surface density in Saturn's rings, which is more definitive for the A ring than any previously presented and which corrects some errors in previous profiles; and 3) an atlas of resonant features that indicates whether each feature is or is not expressed in the rings and that is organized graphically by resonance strength.Comment: 169 pages, 160 figures (body text 29 pages, 20 figures; appendix 140 pages, 140 figures); Submitted to Icaru

Quantum Hall effect anomaly and collective modes in the magnetic-field-induced spin-density-wave phases of quasi-one-dimensional conductors

We study the collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family. In phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly), the coexistence of two spin-density waves gives rise to additional collective modes besides the Goldstone modes due to spontaneous translation and rotation symmetry breaking. These modes strongly affect the charge and spin response functions. We discuss some experimental consequences for the Bechgaard salts.Comment: Final version (LaTex, 8 pages, no figure), to be published in Europhys. Let

Effect of umklapp scattering on the magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors

We study the effect of umklapp scattering on the magnetic-field-induced spin-density-wave (FISDW) phases which are experimentally observed in the quasi-one-dimensional organic conductors of the Bechgaard salts family. Within the framework of the quantized nesting model, we show that the transition temperature is determined by a modified Stoner criterion which includes the effect of umklapp scattering. We determine the SDW polarization (linear or circular) by analyzing the Ginzburg-Landau expansion of the free energy. We also study how umklapp processes modify the quantum Hall effect (QHE) and the spectrum of the FISDW phases. We find that umklapp scattering stabilizes phases which exhibit a sign reversal of the QHE, as experimentally observed in the Bechgaard salts. These ``negative'' phases are characterized by the simultaneous existence of two SDWs with comparable amplitudes. As the umklapp scattering strength increases, they may become helicoidal (circularly polarized SDWs). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect appears. These two characteristic properties may be utilized to detect the magnetic-field-induced helicoidal SDW phases experimentally.Comment: Revtex, 27 pages, 9 figure

Boundary-induced spin density waves in linear Heisenberg antiferromagnetic spin chains with S≥1\mathbf{S \ge 1}

Linear Heisenberg antiferromagnets (HAFs) are chains of spin-$S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground state energy in the thermodynamic limit, but not the same spin $S_G$ when $S \ge 1$. The ground state of open chains of N spins has $S_G = 0$ or $S$, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities $\rho(r,N)$ of edge states in HAFs with $S = 1$, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $\rho(r,N)\propto(-1)^{r-1}$ for $r=1,2,\ldots N$. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy $\Gamma(N)$ that decreases exponentially with N for integer $S$ and faster than 1/N for half integer $S$. The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5 \xi$ spins by two parameters, the correlation length $\xi$ and the SDW amplitude, with $\xi = 6.048$ for $S = 1$ and 49.0 for $S = 2$. The BI-SDWs of $S = 3/2$ chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases $|\Gamma(N)|$ and weakens the size dependence. The nonlinear sigma model (NL$\sigma$M) has been applied the HAFs, primarily to $S = 1$ with even N, to discuss spin densities and exchange between localized states at the ends as $\Gamma(N) \propto (-1)^N \exp(-N/\xi)$...Comment: 11 pages, 10 figure

Recent results on energy relaxation in disordered charge and spin density waves

We briefly review different approaches used recently to describe collective effects in the strong pinning model of disordered charge and spin density waves, in connection with the CRTBT very low temperature heat relaxation experiments.Comment: 4 pages, invited talk at ECRYS-200