Related papers: A Small Parameter Method for Few-Body Problems
Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
We describe kinetic simulations of transient problems in partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
We consider the evolution of narrow-band wave trains of finite amplitude in a nonlinear dispersive system which is described by the Klein--Gordon equation with arbitrary polynomial nonlinearity. We use a new perturbative technique which…
Reduced basis methods for approximating the solutions of parameter-dependant partial differential equations (PDEs) are based on learning the structure of the set of solutions - seen as a manifold ${\mathcal S}$ in some functional space -…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the…
The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three…
In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy $s$-wave correlated pair and spectator particles, while terms that include energy…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…
We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body…
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is…
In order to treat low-energy heavy-ion reactions, we make an extension of quantum molecular dynamics method. A phenomenological Pauli potential is introduced into effective interactions to approximate the nature of the Fermion many-body…
The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
Quantum computing offers several new pathways toward finding many-body eigenstates, with variational approaches being some of the most flexible and near-term oriented. These require particular parameterizations of the state, and for solving…