Related papers: Bootstrapping Simple QM Systems
We study the energy landscape near the ground state of a model of a single particle in a random potential with trivial topology. More precisely, we find the large dimensional limit of the Hessian spectrum at the global minimum of the…
We present a new exactly solvable (classical and quantum) model that can be interpreted as the generalization to the two-dimensional sphere and to the hyperbolic space of the two-dimensional anisotropic oscillator with any pair of…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
We examine the performance of various time propagation schemes using a one-dimensional model of the hydrogen atom. In this model the exact Coulomb potential is replaced by a soft-core interaction. The model has been shown to be a reasonable…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of the Stark-Hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
In this note we address the problem of solving for the positronium mass spectrum. We use front-form dynamics together with the method of flow equations. For a special choice of the similarity function, the calculations can be simplified by…
Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the…
The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…
Signatures of heavy particles during inflation are exponentially suppressed by the Boltzmann factor when the masses are far above the Hubble scale. In more realistic scenarios, however, scale-dependent features may change this conventional…
An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline…
We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb…
Bootstrap inference is a powerful tool for obtaining robust inference for quantiles and difference-in-quantiles estimators. The computationally intensive nature of bootstrap inference has made it infeasible in large-scale experiments. In…