اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAperiodicity in equilibrium systems: Between order and disorder
263
0
0.0
(
0
)
تأليف
Aernout C.D.van Enter
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion and occurrence of aperiodic order in equilibrium statistical mechanics. In particular, we consider some spectral characterisations,and shortly review what is known about the occurrence of aperiodic order in lattice models at zero and non-zero temperatures. At the end some more speculative connections to the theory of (spin-)glasses are indicated.
قيم البحث
اقرأ أيضاً
We establish existence of order-disorder phase transitions for a class of non-sliding hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a fin
ite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee-Yang zeros lie in an annulus with finite positive radii.
The principle of maximum irreversible is proved to be a consequence of a stochastic order of the paths inside the phase space; indeed, the system evolves on the greatest path in the stochastic order. The result obtained is that, at the stability, the
entropy generation is maximum and, this maximum value is consequence of the stochastic order of the paths in the phase space, while, conversely, the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation at the stability.
In the setting of the principle of local equilibrium which asserts that the temperature is a function of the energy levels of the system, we exhibit plenty of steady states describing the condensation of free Bosons which are not in thermal equilibri
um. The surprising facts are that the condensation can occur both in dimension less than 3 in configuration space, and even in excited energy levels. The investigation relative to non equilibrium suggests a new approach to the condensation, which allows an unified analysis involving also the condensation of $q$-particles, $-1leq qleq 1$, where $q=pm1$ corresponds to the Bose/Fermi alternative. For such $q$-particles, the condensation can occur only if $0<qleq1$, the case 1 corresponding to the standard Bose-Einstein condensation. In this more general approach, completely new and unexpected states exhibiting condensation phenomena naturally occur also in the usual situation of equilibrium thermodynamics. The new approach proposed in the present paper for the situation of $2^text{nd}$ quantisation of free particles, is naturally based on the theory of the Distributions, which might hopefully be extended to more general cases
In this comprehensive study of Kitaevs abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement e
ntropy exactly and characterise the elementary anyonic excitations. The homology and cohomolgy groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterisations of topological order.
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. For large time t, one has regions with cons
tant and linearly decreasing density. The fluctuations on these two regions are given by the Airy_1 and Airy_2 processes, whose one-point distributions are the GOE and GUE Tracy-Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one-point distribution is a new interpolation between GOE and GUE edge distributions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
