Loschmidt echoes in two-body random matrix ensembles

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting e.g. from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze''. Numerical calculations confirm this result and show, that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.Comment: 9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications following referees' suggestion

Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.Comment: RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Let

Understanding coastal change using shoreline trend analysis supported by cluster-based segmentation

Shoreline change analysis is a well defined and widely adopted approach for the examination of trends in coastal position over different timescales. Conventional shoreline change metrics are best suited to resolving progressive quasi-linear trends. However, coastal change is often highly non-linear and may exhibit complex behaviour including trend-reversals. This paper advocates a secondary level of investigation based on a cluster analysis to resolve a more complete range of coastal behaviours. Cluster-based segmentation of shoreline behaviour is demonstrated with reference to a regional-scale case study of the Suffolk coast, eastern UK. An exceptionally comprehensive suite of shoreline datasets covering the period 1881 to 2015 is used to examine both centennial- and intra-decadal scale change in shoreline position. Analysis of shoreline position changes at a 100 m alongshore interval along 74 km of coastline reveals a number of distinct behaviours. The suite of behaviours varies with the timescale of analysis. There is little evidence of regionally coherent shoreline change. Rather, the analyses reveal a complex interaction between met-ocean forcing, inherited geological and geomorphological controls, and evolving anthropogenic intervention that drives changing foci of erosion and deposition

Large-scale spatial variability in the contemporary coastal sand and gravel resource, Suffolk, eastern UK

The response of coastal systems to changes in sea level and storm events is often dependent on the availability of sediment and sustainability of sediment supply. This paper analyses the changing sediment resource of a driftaligned shoreline in eastern England, UK, over centennial and decadal timescales. Spatial variability in cross-shore extent and elevational distribution of this mixed sand and gravel system exerts a significant control on the ability of different stretches of this shoreline to respond dynamically to changes in marine forcing. Furthermore, anthropogenic interference has led to the development of unnaturally high beach ridges in some places, which contrasts with the absence of intertidal or supratidal sediment along stretches dominated by seawalls

Seabed dynamics in a large coastal embayment: 180 years of morphological change in the outer Thames estuary

This article analyses the morphological history of the outer Thames seabed, covering over 3,000 km 2 from Aldeburgh (Suffolk), to Southend-on-Sea (Essex) and Margate (Kent). The region has been depicted on bathymetric charts since the sixteenth century, and has been formally charted since the eighteenth century. Charts published since the early 1800s incorporate sufficient grid reference or ground control detail for georectification onto a common coordinate system (British National Grid). The morphological history of the outer seabed was thus reconstructed through the digitisation and interpolation of soundings onto a regular grid (3D surface). The evolution of seabed morphology was examined using transects, bathymetric change maps and spatial statistics. The results show considerable spatial variability in seabed behaviour. Within the central Thames, banks have experienced significant depth changes can be associated with lateral shifts in individual banks. Some of the outer banks in this region exhibit progressive elongation. Shifts in bank position across the Suffolk shoreface appear to be more subtle, and there is evidence here of both onshore and offshore migration. There is no clear evidence of any regionally coherent response to large-scale historical forcing such as sea-level rise

1/f noise in the Two-Body Random Ensemble

We show that the spectral fluctuations of the Two-Body Random Ensemble (TBRE) exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent \alpha in the 1/f^{\alpha} noise for the individual members of the ensemble. Almost all the exponents lie inside a narrow interval around \alpha=1 suggesting that also individual members exhibit 1/f noise, provided they are individually unfoldedComment: 4 pages, 3 figures, Accepted for publication in Phys. Rev.

Ultra-fast mission analysis routine for Apollo Block 2 environmental control system radiators Final report

Computer program for rapid mission analysis of Apollo Block 2 environmental control system radiator

Clustering of equine grass sickness cases in the United Kingdom: a study considering the effect of position-dependent reporting on the space-time K-function

Equine grass sickness (EGS) is a largely fatal, pasture-associated dysautonomia. Although the aetiology of this disease is unknown, there is increasing evidence that Clostridium botulinum type C plays an important role in this condition. The disease is widespread in the United Kingdom, with the highest incidence believed to occur in Scotland. EGS also shows strong seasonal variation (most cases are reported between April and July). Data from histologically confirmed cases of EGS from England and Wales in 1999 and 2000 were collected from UK veterinary diagnostic centres. The data did not represent a complete census of cases, and the proportion of all cases reported to the centres would have varied in space and, independently, in time. We consider the variable reporting of this condition and the appropriateness of the space–time K-function when exploring the spatial-temporal properties of a ‘thinned’ point process. We conclude that such position-dependent under-reporting of EGS does not invalidate the Monte Carlo test for space–time interaction, and find strong evidence for space–time clustering of EGS cases (P<0.001). This may be attributed to contagious or other spatially and temporally localized processes such as local climate and/or pasture management practices