Related papers: Use of the Discrete Variable Representation Basis …
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
Gravitational wave detector technology provides high-precision measurement apparatuses that, if combined with a modulated particle source, have the potential to measure and constrain particle interactions in a novel way, by measuring the…
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit…
Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of…
A summary of recent researches on nuclear dynamics with realistic microscopic quantum approaches is presented. The Balian-V\'en\'eroni variational principle is used to derive the time-dependent Hartree-Fock (TDHF) equation describing the…
Selected resonance states of the deuterated formyl radical in the electronic ground state ($\widetilde{X}\,{}^2A'$) are computed using our recently introduced dynamically pruned discrete variable representation (DP-DVR) [H. R. Larsson, B.…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue…
Reinforcement learning (RL) agents make decisions using nothing but observations from the environment, and consequently, heavily rely on the representations of those observations. Though some recent breakthroughs have used vector-based…
An unusual regime for liquid-state nuclear magnetic resonance (NMR) where the magnetic field strength is so low that the $J$-coupling (intramolecular spin-spin) interactions dominate the spin Hamiltonian opens a new paradigm with…
Because of the rotational invariance of the nuclear Hamiltonian, there exists a density functional for nuclei that depends only on two scalar densities. Practical calculations boil down to radial, one-dimensional ones.
Photonic quantum computation refers to quantum computation that uses photons as the physical system for doing the quantum computation. The field is largely divided between discrete-variable (DV) and continuous-variable (CV) photonic quantum…
We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions,…
The variation after projection (VAP) method is expected to be an efficient way of getting the optimized nuclear wave functions, so that they can be as close as possible to the exact shell model ones. However, we found there are two…
Covariant density functional theory, which has so far been applied only within the framework of static and time dependent mean field theory is extended to include Particle-Vibration Coupling (PVC) in a consistent way. Starting from a…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We present a new realization of relativistic hadronic me- chanics and its underlying iso-Poincar'e symmetry specifically constructed for nuclear physics which: 1) permits the representation of nucleons as ex- tended, nonspherical and…
Applications of relativistic light front dynamics to computing wave functions of heavy nuclei are reviewed. The motivation for this is the desire to find wave functions, expressed in terms of the plus-momentum variable, that simplify the…
The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…