ترغب بنشر مسار تعليمي؟ اضغط هنا

Multiple phase transitions on compact symbolic systems

65   0   0.0 ( 0 )
 نشر من قبل Christian Wolf
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Let $phi:Xto mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:Xto X$ over a finite alphabet. Introducing a parameter $beta>0$ (interpreted as the inverse temperature) we study the regularity of the pressure function $betamapsto P_{rm top}(betaphi)$ on an interval $[alpha,infty)$ with $alpha>0$. We say that $phi$ has a phase transition at $beta_0$ if the pressure function $P_{rm top}(betaphi)$ is not differentiable at $beta_0$. This is equivalent to the condition that the potential $beta_0phi$ has two (ergodic) equilibrium states with distinct entropies. For any $alpha>0$ and any increasing sequence of real numbers $(beta_n)$ contained in $[alpha,infty)$, we construct a potential $phi$ whose phase transitions in $[alpha,infty)$ occur precisely at the $beta_n$s. In particular, we obtain a potential which has a countably infinite set of phase transitions.



قيم البحث

اقرأ أيضاً

106 - Yuri Lima 2019
This survey describes the recent advances in the construction of Markov partitions for nonuniformly hyperbolic systems. One important feature of this development comes from a finer theory of nonuniformly hyperbolic systems, which we also describe. Th e Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.
We study rank-two symbolic systems (as topological dynamical systems) and prove that the Thue-Morse sequence and quadratic Sturmian sequences are rank-two and define rank-two symbolic systems.
We consider the natural definition of DLR measure in the setting of $sigma$-finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of conformal measures associated with Walters potentials. In the BIP case, or when the potential normalizes the Ruelles operator, we prove that the notions of DLR and conformal coincide. On the standard renewal shift, we study the problem of describing the cases when the set of the eigenmeasures jumps from finite to infinite measures when we consider high and low temperatures, respectively. For this particular shift, we prove that there always exist finite DLR measures, and we have an expression to the critical temperature for this volume-type phase transition, which occurs only for potentials with the infinite first variation.
Compact stars may contain quark matter in their interiors at densities exceeding several times the nuclear saturation density. We explore models of such compact stars where there are two first-order phase transitions: the first from nuclear matter to a quark-matter phase, followed at higher density by another first-order transition to a different quark matter phase [e.g., from the two-flavor color superconducting (2SC) to the color-flavor-locked (CFL) phase). We show that this can give rise to two separate branches of hybrid stars, separated from each other and from the nuclear branch by instability regions and, therefore, to a new family of compact stars, denser than the ordinary hybrid stars. In a range of parameters, one may obtain twin hybrid stars (hybrid stars with the same masses but different radii) and even triplets where three stars, with inner cores of nuclear matter, 2SC matter, and CFL matter, respectively, all have the same mass but different radii.
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct dimensionalities around the singularity where the phase transition physically exists. Here, we propose a method of detecting phase transitions and splitting the manifold into phase transitions free sub-manifolds. Therein, we utilize a relationship between curvature and singular value ratio of points sampled in a curve, and then extend the assertion into higher-dimensions using the shape operator. Then we attest that the same phase transition can also be approximated by singular value ratios computed locally over the data in a neighborhood on the manifold. We validate the phase transitions detection method using one particle simulation and three real world examples.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا