相关论文: Unitary Random-Matrix Ensemble with Governable Lev…

We analyze the behavior of families $(u_\alpha)_{\alpha>0}$ of solutions to the high-order critical equation $P_\alpha u_\alpha=\Delta_g^k u_\alpha +\hbox{lot}=|u_\alpha|^{2^\star-2}u_\alpha$ on a Riemannian manifold $M$, with a uniform…

We study an ensemble of diverse (inhomogeneous) thermostatically controlled loads aggregated to provide the demand response (DR) services in a district-level energy system. Each load in the ensemble is assumed to be equipped with a random…

We present an analysis of the spectral density of the adjacency matrix of large random trees. We show that there is an infinity of delta peaks at all real numbers which are eigenvalues of finite trees. By exact enumerations and Monte-Carlo…

We study theoretically and numerically how hard frictionless particles in random packings can rearrange. We demonstrate the existence of two distinct unstable non-linear modes of rearrangement, both associated with the opening and the…

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ . We show that the eigenvector…

In this paper the feasibility of funnel control techniques for the Fokker-Planck equation corresponding to a multi-dimensional Ornstein-Uhlenbeck process on an unbounded spatial domain is explored. First, using weighted Lebesgue and Sobolev…

Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…

We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families…

We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…

Low temperature scanning tunneling microscope images and spectroscopic data have been obtained on subnanometer size Pb clusters fabricated using the technique of buffer layer assisted growth. Discrete energy levels were resolved in…

Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the…

The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of $N$ particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically…

The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the two-point correlation function are…

We study fermions on a finite chain, interacting repulsively when residing on the same and on nearest-neighbor sites, and subjected to a Wannier-Stark linearly-varying potential. Using the density matrix renormalization-group numerical…

We present exact analytical results revealing the existence of a countable infinity of unusual single particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond shaped loops as the…

The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…

The reduced density matrix of a given subsystem, denoted by $\rho_A$, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called…

We prove that large Boltzmann stable planar maps of index $\alpha \in (1;2)$ converge in the scaling limit towards a random compact metric space $\mathcal{S}_{\alpha}$ that we construct explicitly. They form a one-parameter family of random…