相关论文: Phases of Wave Functions and Level Repulsion

Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued…

Exceptional points are singularities of the spectrum and wave functions which occur in connection with level repulsion. They are accessible in experiments using dissipative systems. It is shown that the wave function at an exceptional point…

At high level density, two states avoid usually crossing at the critical value $a_{\rm cr}$ of the parameter $a$ by which the system is controlled. The wavefunctions of the two states are mixed in a finite parameter range around $a_{\rm…

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional…

In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…

The mechanism of avoided level crossings in quantum systems is studied. It is traced back to the existence of branch points in the complex plane which influence the properties of resonance states as well as of discrete states. An avoided…

Due to the absence of degeneracy in one dimension, when a parameter, $\lambda$, of a potential is varied slowly the discrete energy eigenvalue curves, $E_n(\lambda)$, cannot cross but they are allowed to come quite close and diverge from…

Branch points in the complex plane are responsible for avoided level crossings in closed and open quantum systems. They create not only an exchange of the wave functions but also a mixing of the states of a quantum system at high level…

We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a…

We present spectroscopic observation of an exceptional point or the transition point between diabatic crossing and avoided crossing of neighboring quasi-eigenmodes in a chaotic optical microcavity with a large size parameter. The transition…

Tunneling in the presence of an opaque barrier, part of which varies in time, is investigated numerically and analytically in one dimension. Clearly, due to the varying barrier a tunneling particle experiences spectral widening. However, in…

We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…

In this paper we consider the problem of avoided crossings (level repulsion) in phononic crystals and suggest a computationally efficient strategy to distinguish them from normal cross points. This process is essential for the correct…

We study the evolution with magnetic field of the single-particle energy levels high up in the energy spectrum of one dot as probed by the ground state of the adjacent dot in a weakly coupled vertical quantum dot molecule. We find that the…

The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them…

The authors examine graphical properties of eigenfunctions with stadium boundaries associated with avoided crossings of energy levels.

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…

An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…

Level repulsion - the opening of a gap between two degenerate modes due to coupling - is ubiquitous anywhere from solid state theory to quantum chemistry. In contrast, if one mode has negative energy, the mode frequencies attract instead.…

All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…