Quantisations of piecewise affine maps on the torus and their quantum limits

For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the so called quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, and examples of non-ergodic maps where arbitrary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking

Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical limit almost all eigenstates converge to the volume measure of the torus. Nevertheless, we show that for each of the invariant submanifolds, there are also eigenstates which localize and converge to the volume measure of the corresponding submanifold.Comment: 17 page

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result

A review of hyperfibrinolysis in cats and dogs

The fibrinolytic system is activated concurrently with coagulation; it regulates haemostasis and prevents thrombosis by restricting clot formation to the area of vascular injury and dismantling the clot as healing occurs. Dysregulation of the fibrinolytic system, which results in hyperfibrinolysis, may manifest as clinically important haemorrhage. Hyperfibrinolysis occurs in cats and dogs secondary to a variety of congenital and acquired disorders. Acquired disorders associated with hyperfibrinolysis, such as trauma, cavitary effusions, liver disease and Angiostrongylus vasorum infection, are commonly encountered in primary care practice. In addition, delayed haemorrhage reported in greyhounds following trauma and routine surgical procedures has been attributed to a hyperfibrinolytic disorder, although this has yet to be characterised. The diagnosis of hyperfibrinolysis is challenging and, until recently, has relied on techniques that are not readily available outside referral hospitals. With the recent development of point‐of‐care viscoelastic techniques, assessment of fibrinolysis is now possible in referral practice. This will provide the opportunity to target haemorrhage due to hyperfibrinolysis with antifibrinolytic drugs and thereby reduce associated morbidity and mortality. The fibrinolytic system and the conditions associated with increased fibrinolytic activity in cats and dogs are the focus of this review article. In addition, laboratory and point‐of‐care techniques for assessing hyperfibrinolysis and antifibrinolytic treatment for patients with haemorrhage are reviewed

Long-Distance Relationships: Use of Technology Advances in Communication, Idealization and Satisfaction

Long distance romantic relationships are becoming more and more common nowadays. There can be various concrete reasons that are the causes for this occurrence, among the most common, the pursuit of career opportunities, educational goals, military service, and migratory issues. The aim of this study is answering the question: how is possible to maintain this kind of relationship? This is explained from two variables: the first one refers to the technology advances which help the communication and the second one studied from the psychological periscope, the romantic idealization. It is approach the perception of this new type of relationships in the general population. Understanding technology influences in human life could help to develop more technological advances to the people to feel closer and to keep healthy relationships with themselves and the others, as well, it could bring lights to counseling and psychological therapy