Nonrelativistic Atom Research Articles

Looking for Carroll particles in two time spacetime

We make an attempt to describe Carroll particles with a nonvanishing value of energy (i.e. the Carroll particles which always stay in rest) in the framework of two time physics, developed in the series of papers by I. Bars and his coauthors. In the spacetime with one additional time dimension and one additional space dimension one can localize the symmetry which exists between generalized coordinate and their conjugate momenta. Such a localization implies the introduction of the gauge fields, which in turn implies the appearance of some first-class constraints. Choosing different gauge-fixing conditions and solving the constraints one obtain different time parameters, Hamiltonians, and generally, physical systems in the standard one time spacetime. In this way such systems as nonrelativistic particle, relativistic particles, hydrogen atoms, and harmonic oscillators were described as dual systems in the framework of two time physics. Here, we find a set of gauge fixing conditions which provides as with such a parametrization of the phase-space variables in the two time world which gives the description of Carroll particle in the one time world. Besides, we construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999. Published by the American Physical Society 2024

Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas.

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.

Density functional applications of jellium with a local gap model correlation energy functional.

We develop a realistic density functional approximation for the local gap, which is based on a semilocal indicator that shows good screening properties. The local band model has remarkable density scaling behaviors and works properly for the helium isoelectronic series for the atoms of the Periodic Table, as well as for the non-relativistic noble atom series (up to 2022 e-). Due to these desirable properties, we implement the local gap model in the jellium-with-gap correlation energy, developing the local-density-approximation-with-gap correlation functional (named LDAg) that correctly gives correlation energies of atoms comparable with the LDA ones but shows an improvement for ionization potential of atoms and molecules. Thus, LDAg seems to be an interesting and useful tool in density functional theory.

Shifting physics of vortex particles to higher energies via quantum entanglement

Physics of structured waves is currently limited to relatively small particle energies as the available generation techniques are only applicable to the soft X-ray twisted photons, to the beams of electron microscopes, to cold neutrons, or non-relativistic atoms. The highly energetic vortex particles with an orbital angular momentum would come in handy for a number of experiments in atomic physics, nuclear, hadronic, and accelerator physics, and to generate them one needs to develop alternative methods, applicable for ultrarelativistic energies and for composite particles. Here, we show that the vortex states of in principle arbitrary particles can be generated during photon emission in helical undulators, via Cherenkov radiation, in collisions of charged particles with intense laser beams, in such scattering or annihilation processes as emu rightarrow emu , ep rightarrow ep, e^-e^+ rightarrow pbar{p}, and so forth. The key element in obtaining them is the postselection protocol due to entanglement between a pair of final particles and it is largely not the process itself. The state of a final particle – be it a gamma -ray, a hadron, a nucleus, or an ion – becomes twisted if the azimuthal angle of the other particle momentum is measured with a large error or is not measured at all. As a result, requirements to the beam transverse coherence can be greatly relaxed, which enables the generation of highly energetic vortex beams at accelerators and synchrotron radiation facilities, thus making them a new tool for hadronic and spin studies.

Motion induced excitation and electromagnetic radiation from an atom facing a thin mirror

We evaluate the probability of (de-)excitation and photon emission from a neutral, moving, non-relativistic atom, coupled to the quantum electromagnetic field and in the presence of a thin, perfectly conducting plane ("mirror"). These results extend, to a more realistic model, the ones we had presented for a scalar model, where the would-be electron was described by a scalar variable, coupled to an (also scalar) vacuum field. The latter was subjected to either Dirichlet or Neumann conditions on a plane. In our evaluation of the spontaneous emission rate produced when the accelerated atom is initially in an excited state, we pay attention to its comparison with the somewhat opposite situation, namely, an atom at rest facing a moving mirror.

Towards a Novel Super Current

For nonrelativistic two-electron atoms, we employ a phase-amplitude method to derive an energy-dependent three-body force which controls the dynamics of the atom near the threshold for double escape. Its potential energy has been taken into account to derive beyond a static adiabatic basis a novel partial differential equation that replaces an adiabatic basis. That equation whose solutions span a Banach space has been solved exactly in the energy window near threshold. In that energy range, we find the formation of unstable electron pairs, comparable to Cooper pairs. In contrast to Cooper pairs, our pairs are bound by dominant correlation rather than by the coupling to a phonon field. These ingredients are suspected to allow for a super current independent of the temperature.

Analysis of atomic Pauli potentials and their large-Z limit.

Modeling the Pauli energy, the contribution to the kinetic energy caused by Pauli statistics, without using orbitals is the open problem of orbital-free density functional theory. An important aspect of this problem is correctly reproducing the Pauli potential, the response of the Pauli kinetic energy to a change in density. We analyze the behavior of the Pauli potential of non-relativistic neutral atoms under Lieb-Simon scaling-the process of taking nuclear charge and particle number to infinity, in which the kinetic energy tends to the Thomas-Fermi limit. We do this by mathematical analysis of the near-nuclear region and by calculating the exact orbital-dependent Pauli potential using the approach of Levy and Ouyang for closed-shell atoms out to element Z = 976. In rough analogy to Lieb and Simon's own findings for the charge density, we find that the potential does not converge smoothly to the Thomas-Fermi limit on a point-by-pointbasis but separates into several distinct regions of behavior. Near the nucleus, the potential approaches a constant given by the difference in energy between the lowest and highest occupied eigenvalues. We discover a transition region in the outer core where the potential deviates unexpectedly and predictably from both the Thomas-Fermi potential and the gradient expansion correction to it. These results may provide insight into the semi-classical description of Pauli statistics and new constraints to aid the improvement of orbital-free density functional theory functionals.

A new method of construction of resonances that applies to critical models

We introduce a new method of multi-scale analysis that can be used to study the spectral properties of operators in non-relativistic quantum electrodynamics with critical coupling functions. We utilize our method to prove the existence of resonances of nonrelativistic atoms which are minimally coupled to the quantized (ultraviolet-regularized) radiation field and construct them together with the corresponding resonance eigenvector in case of critical coupling, i.e., without any infrared regularization. This result was first proved in [19] with the ingredient of a suitable Pauli-Fierz transformation. The purpose of the present paper, however, is to demonstrate the power of our new method for the estimation of resolvents that is based on the isospectral Feshbach-Schur map [8]. The reconstruction formula for the resolvent of an operator in terms of the resolvent of its image under the Feshbach-Schur map allows us to use a fixed projection and to compare two resolvents without actually decimating the degrees of freedom. This is in contrast to the renormalization group based on Feshbach-Schur map, developed in [8,5], that uses a decreasing sequence of ever-smaller projections and successively decimates the degrees of freedom. It is this new method that allows us to treat the critical and physically relevant Standard model of non-relativistic quantum electrodynamics[7] which is intractable by standard methods.

Nonrelativistic treatment of hydrogen-like and neutral atoms subjected to the generalized perturbed Yukawa potential with centrifugal barrier in the symmetries of noncommutative quantum mechanics

We have obtained the approximate analytical solutions of the nonrelativistic Hydrogen-like atoms such as [Formula: see text] and [Formula: see text] and neutral atoms such as ([Formula: see text] and [Formula: see text]) atoms with a newly proposed generalized perturbed Yukawa potential with centrifugal barrier (GPYPCB) model using the generalized Bopp’s shift method and standard perturbation theory in the symmetries of noncommutative three-dimensional real space phase (NC: 3D-RSP). By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and generalized Hamiltonian operator for all orbital quantum numbers [Formula: see text] in the symmetries of NC: 3D-RSP. The potential is a superposition of the perturbed Yukawa potential and new terms proportional with [Formula: see text]) appear as a result of the effects of noncommutativity properties of space and phase on the perturbed Yukawa potential model. The obtained energy eigenvalues appear as functions of the generalized Gamma function, the discreet atomic quantum numbers [Formula: see text], two infinitesimal parameters [Formula: see text], which are induced by (position–position and phase–phase). In addition, the dimensional parameters [Formula: see text] of perturbed Yukawa potential with centrifugal barrier model in NC: 3D-RSP. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of perturbed Yukawa potential model and the two operators are modified spin–orbit interaction and the modified Zeeman operator for the previous Hydrogenic and neutral atoms.

Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

Is the Hartree-Fock prediction that the chemical potential µ of non-relativistic neutral atoms is equal to minus the ionisation potential I sensitive to electron correlation?

Numerical estimates of the chemical (µ) and ionisation (I) potentials from natural orbital functional (NOF) theory of one of us are presented for neutral atoms ranging from H to Kr, and compared with the corresponding experimental ionisation energies. The semi-empirical treatment by Vela et al. relates µ approximately to the measured I. By a physical argument based on the concept of the Pauli potential, we thereby derive in the fully correlated ground states of atoms. The predicted vertical I by means of the extended Koopmans' theorem is in good agreement with the corresponding experimental data. However, the NOF theory of µ lowers the experimental values considerably though oscillatory behaviour is again in evidence. This comparison has prompted us to reopen the Hartree-Fock prediction by Alonso and March that .

Numerical solution of elliptic boundary-value problems for Schrödinger-type equations using the Kantorovich method

Calculation schemes for numerical solution of elliptic boundary-value problems for Schrodinger-type equations based on Kantorovich method that reduces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are presented. The reduced boundaryvalue problems are discretized using the high-accuracy finite element method and implemented in the form of program complexes in Fortran 77. The efficiency of the calculation schemes and programs is demonstrated by the analysis of benchmark calculations of a boundary-value problem with 3D Schrodinger equation, describing the bound states in the nonrelativistic helium atom. Physical results of the symbolic-numeric analysis of low-dimensional quantum models using the developed method and software are discussed.

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z 1/3. This improves Lieb’s upper bound N c < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, $${\limsup_{Z \to \infty}N_c/Z \le 1.22}$$ .

Communication: Ionization potentials in the limit of large atomic number

By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.

Functional renormalization group and conformal invariance in cold atoms

We present an application of a field-theoretic functional renormalization group technique to fewbody (vacuum) physics of nonrelativistic atoms near a Feshbach resonance. We consider and compare a onecomponent bosonic system with a two-component fermionic system, focusing on the scale-free unitarity limit of an infinite scattering length. While the two-body problem is consistent with nonrelativistic conformal symmetry for the two considered systems, a conformal anomaly, manifested through a renormalization group limit cycle with the Efimov parameter s0 ≈ 1.006, is found for bosons in the three-body problem.

Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields

The scaling properties of various composite information-theoretic measures (Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher–Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by s 1 = B ħ 3 ( 4 π ϵ 0 ) 2 Z 2 m 2 e 3 and s 2 = F ħ 4 ( 4 π ϵ 0 ) 3 Z 3 e 5 m 2 . Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behavior is discussed.

Spin-Dependent Bohmian Electronic Trajectories for Helium

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates.

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization-group technique to the few-body (vacuum) physics of nonrelativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with a U(1) symmetry, two-component fermions with a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{SU}(2)$ symmetry, and three-component fermions with a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{SU}(3)$ symmetry. We focus on the scale-invariant unitarity limit of an infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed-point behavior of the considered systems. Nevertheless, the numerical three-body solution in the $s$-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be $s\ensuremath{\approx}1.006$, consistent with the result of Efimov.

Infrared-finite algorithms in QED II. The expansion of the groundstate of an atom interacting with the quantized radiation field

In this paper, we present an explicit and constructive algorithm enabling us to calculate the groundstate and the groundstate energy of a non-relativistic atom minimally coupled to the quantized radiation field up to an error of arbitrary finite order in the fine structure constant. Because of infrared divergences, which invalidate a straightforward Taylor expansion, an iterative construction is employed to remove the infrared cut-off in photon momentum space and to produce a convergent algorithm.

Spontaneous emission of a moving atom in vacuum

Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.