相关论文: Weyl law for open systems with sharply divided mix…

The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [G. Cz\'edli, The number of rectangular islands by means of distributive lattices, European J. Combin. 30 (2009), 208-215].…

We introduce a spectral notion of graph complexity derived from the Weyl's law. We experimentally demonstrate its correlation to how well the graph can be embedded in a low-dimensional Euclidean space.

We consider activated random walk (ARW), an interacting particle system and prototypical model of self-organized criticality in a setting which combines mean-field behavior with the geometry of an arbitrary graph, which we call the village…

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure…

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…

We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. We sketch a number of proofs so that the reader can get a…

For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…

The study of Weyl points in electronic systems has inspired many recent researches in classical systems such as photonic and acoustic lattices. Here we show how the Weyl physics can also inspire the design of novel elastic structures. We…

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the…

A clear signature of classical chaoticity in the quantum regime is the fractal Weyl law, which connects the density of eigenstates to the dimension $D_0$ of the classical invariant set of open systems. Quantum systems of interest are often…

Periodic orbit expressions for the density of states lead to spurious results when directly used to calculate quantities of thermodynamic interest. This is because the trace formula is usually valid only for large energies while the…

Weyl points (WP) are robust spectral degeneracies, which can not be split by small perturbations, as they are protected by their non-zero topological charge. For larger perturbations, WPs can disappear via pairwise annihilation, where two…

In this work we show that Weyl particles can exist at different states in zero electromagnetic field, either as free particles, or at localized states described by a parameter with dimensions of mass. We also calculate the electromagnetic…

We review `particle partitioning entanglement' for itinerant many-particle systems. This is defined as the entanglement between two subsets of particles making up the system. We identify generic features and mechanisms of particle…

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit.…

We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable…

Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and non-distillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely…

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as…

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea…