The degeneracy and spatial support of pseudo-Landau levels (pLLs) in strained honeycomb lattices systematically depends on the geometry -- for instance, in hexagonal and rectangular flakes the 0th pLL displays a twofold increased degeneracy, while th
e characteristic sublattice polarization of the 0th pLL is only fully realized in a zigzag-terminated triangle. These features are dictated by algebraic constraints in the atomistic theory, and signify a departure from the standard picture in which all qualitative differences between pLLs and Landau levels induced by a magnetic field trace back to the valley-antisymmetry of the pseudomagnetic field.
We investigate the nearest level spacing statistics of open chaotic wave systems. To this end we derive the spacing distributions for the three Wigner ensembles in the one-channel case. The theoretical results give a clear physical meaning of the mod
ifications on the spacing distributions produced by the coupling to the environment. Based on the analytical expressions obtained, we then propose general expressions of the spacing distributions for any number of channels, valid from weak to strong coupling. The latter expressions contain one free parameter. The surmise is successfully compared with numerical simulations of non-Hermitian random matrices and with experimental data obtained with a lossy electromagnetic chaotic cavity.
In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the s
tatistics of resonance states in an open 2D chaotic microwave cavity are investigated by solving the Maxwell equations with lossy boundaries subject to Ohmic dissipation. We successfully compare the statistics of its complex-valued resonance states and associated widths with analytical predictions based on a non-Hermitian effective Hamiltonian model defined by a finite number of fictitious open channels.
We report non-invasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements.
We investigate the crossover from real mode to complex-valued quasimode, when absorption is progressively increased on one edge of the wafer. The complexness parameter, which characterizes the degree to which a resonance state is complex-valued, is measured for non-overlapping resonances and is found to be proportional to the non-homogeneous contribution to the line broadening of the resonance. A simple two-level model based on the effective Hamiltonian formalism supports our experimental results.
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply the random m
atrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble, we reveal and discuss the r^ole of spectral fluctuations.
