Related papers: Efficient $6j$ symbol evaluations for atomic calcu…
Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum…
On basis of generalized 6j-symbols we give a formulation of topological quantum field theories for 3-manifolds including observables in the form of coloured graphs. It is shown that the 6j-symbols associated with deformations of the…
Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open-shell atoms and ions. While, for instance, relativistic computations are traditionally…
As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge…
Nucleation rate computations are of broad importance in particle physics and cosmology. Perturbative calculations are often used to compute the nucleation rate $\Gamma$, but these are incomplete. We perform nonperturbative lattice…
We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…
A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
We discuss an initial implementation of the coupled-cluster method for nuclear structure calculations and apply our method to He-4. We will discuss the future directions that this research will take as we move from method testing and…
Copulas are mathematical tools for modeling joint probability distributions. Since copulas enable one to conveniently treat the marginal distribution of each variable and the interdependencies among variables separately, in the past 60…
Accurate calculations of the nucleation rate $\Gamma$ for first order phase transitions are important for determining their observable consequences in particle physics and cosmology. Perturbative calculations are often used, but they are…
The full exploitation of non-abelian symmetries in tensor network states (TNS) derived from a given lattice Hamiltonian is highly attractive in various aspects. From a theoretical perspective, it can offer deep insights into the…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any…
Accurate atomic structure calculations of complicated atoms with 4 or more valence electrons begin to push the memory and time limits of supercomputers. This paper presents a robust method of decreasing the size of \textit{ab initio}…
We calculate excitation energies for low states of nobelium, including states with open $5f$ subshell. An efficient version of the many-electron configuration-interaction method for treating the atom as a sixteen external electrons system…
Symbolic computation systems suffer from memory inefficiencies due to redundant storage of structurally identical subexpressions, commonly known as expression swell, which degrades performance in both classical computer algebra and emerging…
The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
In this work we introduce novel numerical schemes for a penalized version of the ternary Cahn-Hilliard system for the purpose of creating accurate and efficient numerical schemes of interfacial dynamics with three components as well as some…
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is,…