Related papers: Complexity, Tunneling and Geometrical Symmetry
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
We investigate tunneling decay in a magnetic field. Because of broken time-reversal symmetry, the standard WKB technique does not apply. The decay rate and the outcoming wave packet are found from the analysis of the set of the particle…
In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent)…
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and…
Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties…
It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…
The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
In recent years, twisting has emerged as a new degree of freedom that plays an increasingly important role in Bloch bands of various physical systems. However, there is currently a lack of reports on the non-trivial physics of topological…
Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. Using concurrence as the entanglement…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
The competition of depletion attractions and longer-ranged repulsions between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. For instance, gel networks, i.e., states where the…
The self-similarity of complex systems has been studied intensely across different domains due to its potential applications in system modeling, complexity analysis, etc., as well as for deep theoretical interest. Existing studies rely on…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
We study the effects of the environment on tunneling in an open system described by a static double-well potential. We describe the evolution of a quantum state localized in one of the minima of the potential at $t=0$, both in the limits of…