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We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We construct a model of cooperative superradiant emission from a highly relativistic multi-particle source. We revise an existing model of the literature for a relativistic two-level particle, and construct from it a Hamiltonian describing…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
The configuration-interaction shell model approach provides an attractive framework for the calculation of nuclear level densities in the presence of correlations, but the large dimensionality of the model space has hindered its application…
A method of deriving the Hamiltonian of the interacting boson model, that is based on the microscopic framework of the nuclear energy density functional, is presented. The constrained self-consistent mean-field calculation with a given…
Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$ drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with density $f$. We compute the asymptotic rate of convergence towards 0 of the volume of the…
A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the…
Using a Hubbard-Stratonovich transformation coupled with Fourier path integral methods, expressions are derived for the numerical evaluation of the microcanonical density of states for quantum particles obeying Boltzmann statistics. A…
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on…
A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…