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Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy,…
We formulate a time-dependent density functional theory for the coupled dynamics of electrons and nuclei that goes beyond the Born-Oppenheimer (BO) approximation. We prove that the time-dependent marginal nuclear probability density…
We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral…
Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical…
We have investigated the wave-function feature of Rydberg sodium in a uniform electric field and found that the core-induced interaction of non-hydrogenic atom in electric field can be directly visualized in the wave-function. As is well…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as…
This study addresses the effect of the magnetic hyperfine interaction on the relativistic H1s wave functions. These are used to calculate the electric, magnetic, and confinement force densities acting on the 1s electron. The magnetic field…
We investigate the impact of the quantum effects of protons on the electronic structure of high-pressure H$_3$S, a benchmark hydrogen-rich superconductor with a critical temperature ($T_c$) exceeding 200 K. Using Nuclear-Electronic Orbital…
It is generally assumed that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models have also suggested that compressed hydrogen may form an unusual two-component…
Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (4He and Ne), molecular solids (H2 and CH4), and some ionic (LiH), covalent (graphite), and…
We investigate the possibility of ultracold neutron (UCN) storage in quantum states defined by the combined potentials of the Earth's gravity and the neutron optical repulsion by a horizontal surface of liquid helium. We analyse the…
We present new ab initio calculations of the electronic structure of various atoms and molecules in strong magnetic fields ranging from B=10^12 G to 2x10^15 G, appropriate for radio pulsars and magnetars. For these field strengths, the…
Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wavefunction…
An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The…
Quantum simulations with ultracold atoms typically create atomic wavefunctions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological…
New type of radiation in crystals is predicted and investigated in computer simulation. It is shown that process of volume reflection of electrons and positrons in bent crystals is accomplished with high-power radiation of photons. Volume…
We hypothesize that in a non-metallic crystalline structure under extreme pressures, atomic wavefunctions deform to adopt a reduced rotational symmetry consistent with minimizing interstitial space in the crystal. We exemplify with a simple…
We analyze the entanglement between electronic and nuclear motions in molecular wave functions, by using different widely used ansatzes in molecular Hamiltonian models (H$^+_2$ in 1D and the Shin-Metiu model); namely, i) Born-Oppenheimer…
In a two-dimensional approximation, the probability density and current for a photoelectron near the localization of a quantum vortex are theoretically investigated. The wave function in the momentum representation, which we found earlier,…