Related papers: Complexity, Tunneling and Geometrical Symmetry
Obstructions influence the growth and expansion of bodies in a wide range of settings -- but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving…
The dynamics of a two-state system whose energies undergo a real crossing at some instant of time is studied. At this instant, both the coupling and the detuning vanish simultaneously, which leads to an exact degeneracy of the eigenenergies…
The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological…
Societal complexity may be at a historical peak. Distinct from entropy, complexity tends to rise as systems move away from order, crest at an intermediate state, and decline as entropy continues increasing. The use of a thermodynamic…
In a continuing effort to understand divergences which occur when quantum fields are confined by bounding surfaces, we investigate local energy densities (and the local energy-momentum tensor) in the vicinity of a wall. In this paper,…
Recently, level crossings in the energy bands of crystals have been identified as a key signature for topological phase transitions. Using realistic models we show that the parameter space controlling the occurrence of level coincidences in…
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite…
The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory…
Degeneracies in the spectrum of an adiabatically transported quantum system are important to determine the geometrical phase factor, and may be interpreted as magnetic monopoles. We investigate the mechanism by which constraints acting on…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
A two-level system subjected to a high-frequency driving field can exhibit an effect termed ``coherent destruction of tunneling'', in which the tunneling of the system is suppressed at certain values of the frequency and strength of the…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length…
A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organisation (more than the parts) what largely conditions most higher-level properties, which are not…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily…
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…