Related papers: Critical Phenomena for Systems under Constraint
Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high temperature…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
Light is shown to exhibit critical and tricritical behavior in passive mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many body light-mode system. The phase…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing…
In this paper some critical aspects of the behaviour of breaking lattices subject to slow driving forces are briefly reviewed. In particular fluctuations in the response to the variation of external parameters are discussed.
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…
We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were…
Significant improvements have been achieved in motion control systems with the availability of high speed power switches and microcomputers on the market. Even though motor drivers are able to provide high torque control bandwidth under…
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the…
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…
In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…
The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…