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We study topological properties of bound pairs of photons in spatially-modulated qubit arrays (arrays of two-level atoms) coupled to a waveguide. While bound pairs behave like Bloch waves, they are topologically nontrivial in the parameter…

Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…

The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead…

In this work, we construct and quantify asymptotically in the limit of large mass a variety of edge-localized stationary states of the focusing nonlinear Schr\"odinger equation on a quantum graph. The method is applicable to general bounded…

We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such…

We introduce a new method to calculate Franck-Condon factors in polyatomic molecules that is based on the tomographic probability approach to quantum mechanics. This approach is implemented to calculate transition probabilities in various…

We have investigated bound modes in finite linear chains of dielectric particles of various lengths, interparticle spacing and particle materials. Through a unique application of the multisphere Mie scattering formalism, we have developed…

By using the \emph{Rydberg--Klein--Rees} (RKR) formulas to solve the inverse Schr\"{o}dinger problem, we found a confining bottom-up potential from a given eigenvalue spectrum. To illustrate this methodology, we consider the vector meson…

The ground and excited state calculations at key geometries, such as the Frank-Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy…

We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a…

Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and…

Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited…

In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method incorporates validated truncation error bounds, and…

A challenge for molecular quantum dynamics (QD) calculations is the curse of dimensionality with respect to the nuclear degrees of freedom. A common approach that works especially well for fast reactive processes is to reduce the…

The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function.…

We present a (proto) Foundation Model for Nuclear Physics, capable of operating on low-level detector inputs from Imaging Cherenkov Detectors at the future Electron Ion Collider. Building upon established next-token prediction approaches,…

A model of dense plasmas relying on the superconfiguration approximation is presented. In each superconfiguration the nucleus is totally screened by the electrons in a Wigner-Seitz sphere (ion-sphere model). Superconfigurations of the same…

We propose an excited-state molecular dynamics simulation method based on variational quantum algorithms at a computational cost comparable to that of ground-state simulations. We utilize the feature that excited states can be obtained as…

We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy.…

An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green's 3rd identity…