Pure Stationary States of Open Quantum Systems

Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems. We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems. Open quantum systems with pure stationary states of linear oscillator are suggested. We consider stationary states for the Lindblad equation. We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX

Physics in the Real Universe: Time and Spacetime

The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible microphysical laws and does not represent macro-physical behaviour and the development of emergent complex systems, including life, which do indeed exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world linesComment: 28 pages, including 9 Figures. Major revision in response to referee comment

Stability of Non-Abelian Black Holes

Two types of self-gravitating particle solutions found in several theories with non-Abelian fields are smoothly connected by a family of non-trivial black holes. There exists a maximum point of the black hole entropy, where the stability of solutions changes. This criterion is universal, and the changes in stability follow from a catastrophe-theoretic analysis of the potential function defined by black hole entropy.Comment: 4 Figures to be sent on request,8 pages, WU-AP/33/9

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

In this paper, we derive a frequency detuning method for multi-degree-of-freedom oscillators with nonlinear stiffness. This approach includes a matrix of detuning parameters, which are used to model the amplitude dependent variation in resonant frequencies for the system. As a result, we compare three different approximations for modeling the affect of the nonlinear stiffness on the linearized frequency of the system. In each case, the response of the primary resonances can be captured with the same level of accuracy. However, harmonic and subharmonic responses away from the primary response are captured with significant differences in accuracy. The detuning analysis is carried out using a normal form technique, and the analytical results are compared with numerical simulations of the response. Two examples are considered, the second of which is a two degree-of-freedom oscillator with cubic stiffnesses

Urolitíase: estudo comparativo em bovinos Guzerá oriundos de propriedades com e sem o problema

Diversos fatores podem contribuir para a formação de cálculos urinários, dentre estes, o desequilíbrio nutricional e a dureza da água consumida pelos ruminantes. O objetivo deste estudo foi identificar as características de propriedades que predispõem à urolitíase, através da avaliação da água, da dieta e determinações séricas e urinárias de cálcio, fósforo, magnésio, cloretos, sódio, potássio, cálculo da excreção fracionada (EF) dos eletrólitos, e da creatinina, proteína total, albumina e globulinas séricas. Foram colhidas amostras de sangue e urina de bovinos, Guzerá, criados semi intensivamente, distribuídos por dois grupos. O primeiro denominado grupo urolitíase (Gu), composto de animais com histórico, sinais clínicos e confirmação ultrassonográfica que apresentavam urolitíase; o segundo: grupo controle (Gc), sem histórico, nem sintomas da doença. Os bovinos do grupo urolitíase consumiam água com dureza total na concentração de 166,0mg CaCO3/L. A dieta dos animais do Gu apresentava maior concentração de fósforo e relação Ca:P inadequada. Os teores de fósforo sérico e urinário dos animais do Gu foram maiores do que os do Gc, assim como a concentração sérica de magnésio (p0,05), mas houve diminuição significativa nas EFs de magnésio, cloretos e de potássio do grupo urolitíase (p<0,05). A união destes fatores contribuiu para a ocorrência da urolitíase, sendo dureza total da água e a alta concentração de fósforo na dieta os principais fatores na gênese dos cálculos em bovinos