Related papers: Random Block Operators
In this paper we solve a long standing open problem for Random Schr\"odinger operators on $L^2(\mathbb{R}^d)$ with i.i.d single site random potentials. We allow a large class of free operators, including magnetic potential, however our…
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…
First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum…
We describe procedures to obtain the electronic structure of disordered systems using either tight binding like models or quite directly from ab inito density functional band structure calculations. The band structure is calculated using…
Using the properties of random M\"{o}bius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the…
The subject of this work are random Schroedinger operators on regular rooted tree graphs $\T$ with stochastically homogeneous disorder. The operators are of the form $H_\lambda(\omega) = T + U + \lambda V(\omega)$ acting in $\ell^2(\T)$,…
We present a simple model of the local order in amorphous organic semiconductors which naturally produces a spatially correlated exponential density of states (DOS). The dominant contribution to the random energy landscape is provided by…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation.Surprisingly we find patterns reminiscent of more orderly interactions,…
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a…
The evolution of a complex multi-state system is often interpreted as a continuous-time Markovian process. To model the relaxation dynamics of such systems, we introduce an ensemble of random sparse matrices which can be used as generators…
We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are…
Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
The long-range spectral density correlations (spectral rigidities $\bar{\Delta}_3(\bar n)$ and related spectral compressibilities) of the $E\otimes (b_1+b_2)$ Jahn-Teller model are found strongly nonuniversal with respect to the Hamiltonian…
Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
The eigenvectors of the particle number operator in second quantization are characterized by the block sparsity of their matrix product state representations. This is shown to generalize to other classes of operators. Imposing block…
The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those…
In this paper we establish a connection between the bulk topological structure and the magnetic properties of drumhead surface states of nodal loop semimetals. We identify the magnetic characteristics of the surface states and compute the…