Simulation of large deviation functions using population dynamics

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardin\`a \emph{et al.} for discrete time processes and that of Lecomte \emph{et al.} for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.Comment: Proceedings of the 10th Granada Seminar on Computational and Statistical Physic

Temperature-induced crossovers in the static roughness of a one-dimensional interface

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian Variational Method (GVM), we explore the consequences of a finite interface width $\xi$ on the small-lengthscale fluctuations. We compute analytically the static roughness $B(r)$ of the interface as a function of the distance $r$ between two points on the interface. We focus on the case of short-range elasticity and random-bond disorder. We show that for a finite width $\xi$ two temperature regimes exist. At low temperature, the expected thermal and random-manifold regimes, respectively for small and large scales, connect via an intermediate `modified' Larkin regime, that we determine. This regime ends at a temperature-independent characteristic `Larkin' length. Above a certain `critical' temperature that we identify, this intermediate regime disappears. The thermal and random-manifold regimes connect at a single crossover lengthscale, that we compute. This is also the expected behavior for zero width. Using a directed polymer description, we also study via a second GVM procedure and generic scaling arguments, a modified toy model that provides further insights on this crossover. We discuss the relevance of the two GVM procedures for the roughness at large lengthscale in those regimes. In particular we analyze the scaling of the temperature-dependent prefactor in the roughness B(r)\sim T^{2 \text{\thorn}} r^{2 \zeta} and its corresponding exponent \text{\thorn}. We briefly discuss the consequences of those results for the quasistatic creep law of a driven interface, in connection with previous experimental and numerical studies

Using geophysics on a terminal moraine damming a glacial lake: the Flatbre debris flow case, Western Norway

A debris flow occurred on 8 May 2004, in Fjǽrland, Western Norway, due to a Glacial Lake Outburst Flood and a natural terminal moraine failure. The site was investigated in 2004 and 2005, using pre- and post-flow aerial photos, airborne laser scanning, and extensive field work investigations, resulting in a good understanding of the mechanics of the debris flow, with quantification of the entrainment and determination of the final volume involved. However, though the moraine had a clear weak point, with lower elevation and erosion due to overflowing in the melting season, the sudden rupture of the moraine still needs to be explained. As moraines often contain an ice core, a possible cause could be the melting of the ice, inducing a progressive weakening of the structure. Geophysical investigations were therefore carried out in September 2006, including seismic refraction, GPR and resistivity. All methods worked well, but none revealed the presence of ice, though the depth to bedrock was determined. On the contrary, the moraine appeared to be highly saturated in water, especially in one area, away from the actual breach and corresponding to observed water seepage at the foot of the moraine. To estimate future hazard, water circulation through the moraine should be monitored over time

Observation of resonance trapping in an open microwave cavity

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.Comment: to be published in Phys. Rev. Let

Thermodynamics of histories for the one-dimensional contact process

The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity coexist. We study this transition in the one-dimensional contact process by weighting its histories by exp(sK(t)). We determine the phase diagram and the critical exponents of this model using a recently developed approach to the thermodynamics of histories that is based on the density matrix renormalisation group. We find that for every value of the infection rate, there is a phase transition at a critical value of s. Near the absorbing state phase transition of the contact process, the generating function of the activity shows a scaling behavior similar to that of the free energy in an equilibrium system near criticality.Comment: 16 pages, 7 figure

Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.Comment: 22 pages, 4 figure

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page

Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Simulation of high brightness tapered lasers

Tapered semiconductor lasers have demonstrated both high power and good beam quality, and are of primary interest for those applications demanding high brightness optical sources. The complex non-linear interaction between the optical field and the active material requires accurate numerical simulations to improve the device design and to understand the underlying physics. In this work we present results on the design and simulation of tapered lasers by means of a Quasi- 3D steady-state single-frequency model. The results are compared with experiments on Al-free active region devices emitting at 1060 nm. The performance of devices based on symmetric and asymmetric epitaxial designs is compared and the influence of the design on the beam properties is analyzed. The role of thermal effects on the beam properties is experimentally characterized and analyzed by means of the numerical simulations. Tapered lasers with separate electrical contacts in the straight and tapered sections, based on symmetrical and asymmetrical epitaxial designs are also presented and analyze