相关论文: Quantitative concentration inequalities for the un…
We define a linear functional, the DOS functional, on spaces of holomorphic functions on the unit disk which is associated with random ergodic contraction operators on a Hilbert space, in analogy with the density of state functional for…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to…
The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is…
We prove that the density function of the gradient of a sufficiently smooth function $S : \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is…
The Boltzmann-Shannon Index (BSI) for clustered continuous data is introduced as a normalized measure that captures the relationship between geometry-based and frequency-based probability distributions defined over the clusters. In essence,…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
We extend our results in \cite{hislop_marx_1} on the quantitative continuity properties, with respect to the single-site probability measure, of the density of states measure and the integrated density of states for random Schr\"odinger…
By using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated…
We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…
Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schr\"odinger operators, and established a quantitative form of continuity in…
Environmental noise on a controlled quantum system is generally modeled by a dissipative Lindblad equation. This equation describes the average state of the system via the density matrix $\rho$. One way of deriving this Lindblad equation is…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
A collective description of density matrix is presented for identical multi-level atoms, which are either excited initially, driven coherently or pumped incoherently. The density matrix is defined as expectation value of projection or…
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…
This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a half-filled…
We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…