Related papers: Quantum states in disordered media. I. Low-pass fi…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
The local density of states (LDOS) of the adsorbate induced two-dimensional electron system (2DES) on n-InAs(110) is studied by low-temperature scanning tunneling spectroscopy. The LDOS exhibits irregular structures with fluctuation lengths…
The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that…
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as $\mathcal{O}(\frac{N}{L})$, where $N$ is the number of volume unknowns, and $L$ is…
Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and…
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically…
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…
This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts the problem reduces to stochastic…
High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a…
We develop an effective computational tool for simulating the scattering of 1D waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media,…
The Schr\"odinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues…
Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this…
This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential $V$. The main concern is treating nonlinearities whose degree is low…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or…
Subspace diagonalization techniques based on quantum sampling, such as quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD), have recently emerged as promising quantum-centric approaches for…
Entanglement is a key resource for quantum computing, sensing, and communication, however it is highly susceptible to decoherence. To address this, quantum optics has explored filtering techniques like photon ancillas and Rydberg atom…