Dynamical transitions in incommensurate systems

In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model. A remarkable difference is that, while in the static case the two regimes are separated by a single transition (the Aubry transition), in the dynamical case the transition is characterized by a critical region, in which different phenomena take place at different times. In this paper, the generalized angular momentum we have previously introduced, and the dynamical modulation function are used to begin a characterization of this critical region. We further elucidate the relation between these two quantities, and present preliminary results about the order of the dynamical transition.Comment: 7 pages, 6 figures, file 'epl.cls' necessary for compilation provided; subm. to Europhysics Letter

Atomic quasi-Bragg diffraction in a magnetic field

We report on a new technique to split an atomic beam coherently with an easily adjustable splitting angle. In our experiment metastable helium atoms in the |{1s2s}^3S_1 M=1> state diffract from a polarization gradient light field formed by counterpropagating \sigma^+ and \sigma^- polarized laser beams in the presence of a homogeneous magnetic field. In the near-adiabatic regime, energy conservation allows the resonant exchange between magnetic energy and kinetic energy. As a consequence, symmetric diffraction of |M=0> or |M=-1> atoms in a single order is achieved, where the order can be chosen freely by tuning the magnetic field. We present experimental results up to 6th order diffraction (24 \hbar k momentum splitting, i.e., 2.21 m/s in transverse velocity) and present a simple theoretical model that stresses the similarity with conventional Bragg scattering. The resulting device constitutes a flexible, adjustable, large-angle, three-way coherent atomic beam splitter with many potential applications in atom optics and atom interferometry.Comment: 4 pages, 5 figure

Biodiversity and decomposition in experimental grassland ecosystems

We examined the impact of biodiversity on litter decomposition in an experiment that manipulated plant species richness. Using biomass originating from the experimental species richness gradient and from a species used as a common substrate, we measured rates of decomposition in litterbags in two locations: in situ in the experiment plots and in an adjacent common garden. This allowed us to separate the effects of litter quality and decomposition location on decomposition. We found that plant species richness had a significant, but minor negative effect on the quality (nitrogen concentration) of the biomass. Neither litter type nor location had a consistent effect on the rate of carbon and nitrogen loss over a 1-year period. Thus, the increased productivity and corresponding lower soil available nitrogen levels observed in high diversity plots do not lead to faster litter decomposition or faster nitrogen turnover. This supports the hypothesis that increased productivity corresponding with higher species richness results in increased litter production, higher standing litter pools and a negative feedback on productivity, because of an increased standing nitrogen pool in the litter

The Role of Litter Quality Feedbacks in Terrestrial Nitrogen and Phosphorus Cycling

Many studies in ecosystem ecology argue for strong control of litter quality over nitrogen (N) cycling. We developed a model for temperate grasslands to test the importance of litter quality in decomposition for N and phosphorus (P) cycling based on the following premises. First, terrestrial N and P cycling differ fundamentally because N is a structural component of the soil organic matter (SOM), whereas P is not. Secondly, SOM has a much lower C:N ratio than litter inputs. Thirdly, litter decomposition follows an exponential decay with 20% of the original litter mass turning into SOM. Fourth, litter N concentration shows an exponential increase during decomposition, whereas P does not change and is released proportionally to the litter mass. Based on these premises we constructed a model which shows that 0.75% N is a critical initial litter concentration at which concentration all N is immobilized and no N is released from the litter. Thus at 0.75% N of the litter all net N mineralization is through SOM decomposition and not through litter decomposition. Phosphorus, in contrast, is primarily released in the early stages of litter decomposition. Empirical tests of these model predictions support the applicability of the model to temperate grassland ecosystems. This model predicts that N mineralization from SOM is much more important than mineralization from litter and that plant litter quality differences alone cannot explain ecosystem N cycling patterns. Phosphorus, in contrast, does cycle largely through litter decomposition, and plant litter quality differences are the dominant factor in determining ecosystem P cycling feedbacks

Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-cComment: RevTeX style, 20 pages, 12 figure

Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals

The staggered 6-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully-packed loop-gas line. We prove that the reconstruction and roughening transitions cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.Comment: 31 pages, 9 figure

Breakdown of a conservation law in incommensurate systems

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel Kontorova model, imply the existence of a generalized angular momentum which is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the non-linear couplings of our model cause parametric phonon excitations which lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signalling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction which can take place when the system is still floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E Replaced 27-03-2001: changes to text, minor revision of figure

Correlated percolation and the correlated resistor network

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.Comment: 16 pages, REVTeX, 6 figures include

Berry phase and adiabaticity of a spin diffusing in a non-uniform magnetic field

An electron spin moving adiabatically in a strong, spatially non-uniform magnetic field accumulates a geometric phase or Berry phase, which might be observable as a conductance oscillation in a mesoscopic ring. Two contradicting theories exist for how strong the magnetic field should be to ensure adiabaticity if the motion is diffusive. To resolve this controversy, we study the effect of a non-uniform magnetic field on the spin polarization and on the weak-localization effect. The diffusion equation for the Cooperon is solved exactly. Adiabaticity requires that the spin-precession time is short compared to the elastic scattering time - it is not sufficient that it is short compared to the diffusion time around the ring. This strong condition severely complicates the experimental observation.Comment: 16 pages REVTEX, including 3 figure

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.Comment: 7 pages, 4 figure