Short-range Interaction Potential Research Articles

Collisions of ultracold molecules in bright and dark optical dipole traps

Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photoexcitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood and provide a benchmark for the development of new theories.

Universal relations for dipolar quantum gases

We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential. We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function. These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement. For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction. We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.

The validity of the local density approximation for smooth short range interaction potentials

In the full quantum theory, the energy of a many-body quantum system with a given one-body density is described by the Levy–Lieb functional. It is exact but very complicated to compute. For practical computations, it is useful to introduce the local density approximation that is based on the local energy of constant densities. The aim of this paper is to make a rigorous connection between the Levy–Lieb functional theory and the local density approximation. Our justification is valid for fermionic systems with a general class of smooth short range interaction potentials, in the regime of slowly varying densities. We follow a general approach developed by Lewin, Lieb, and Seiringer for Coulomb potential [M. Lewin et al., Pure Appl. Anal. 2(1), 35–73 (2020)] but avoid using any special properties of the potential including the scaling property and screening effects for the localization of the energy.

The Hartree and Vlasov equations at positive density

We consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider time-dependent solutions which have a finite relative energy with respect to the reference translation-invariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semi-classical limit and obtain as a by-product global well-posedness of the Vlasov equation in the (relative) energy space.

Inverse scattering in the Stark effect

We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder (1995 J. Math. Phys. 36 3902–21), we prove that the high-velocity limit of the scattering operator uniquely determines the short-range interaction potentials. Moreover, we prove that, when a long-range interaction potential is given, the high-velocity limit of the Dollard-type modified scattering operator uniquely determines the short-range part of the interactions. We allow the potential functions to belong to very broad classes. These results are improvements on the previous results obtained by Adachi and Maehara (2007 J. Math. Phys. 48 042101; Adachi et al 2013 Inverse Problems 29 085012).

From the Coulomb to Effective Interaction: Application to Bose—Einstein Condensation

The expression for the short-range effective interaction potential of "quasinulei"\, is derived based on the model of the "pure"\, Coulomb interaction. This model represents the equilibrium Coulomb system (CS) of interacting electrons and the identical nuclei, using the adiabatic approximation for nuclei and an arbitrary strong (in general) interaction for the electronic subsystem. On the basis of general properties of Coulomb interaction it is shown that the Fourier-component of the pair effective potential between "quasinuclei" possesses discontinuity at the wave vector $q=0$. This discontinuity is essential for the Bose condensed systems as HeII and the rarified Alkali metals at temperatures lower than the Bose condensation transition, since there are macroscopic quantity of quasiparticles with the momentum $q=0$. In particular, it is shown that for the single-particle excitations can exist the gap which disappears in the normal state. The value of this gap is estimated. The problem of generalization of the obtained results for the case of a strong electron-nuclei (or electron-point ion system) is discussed.

Analysis of electrical double layer structure in molten salts.

This paper reports the results of analysis of the electrical double layer (EDL) phenomenon in molten salts to provide information on the influence of short range interaction type on the shape of charge distribution and the effect of the charge distribution shape on capacitance values. A new method of analysis is proposed, which allows a quantitative discussion. It is assumed that EDL can be modelled as a number of capacitor plates connected in series. This paper reports the application of the proposed method in quantitative analysis of the molten salt capacitance data obtained for different short range potentials. The data to be analysed were obtained from the Monte Carlo simulations of the symmetrical molten salt electrolyte for the following short range interaction potentials: hard spheres, Lennard-Jones repulsions, and full Lennard-Jones. The new analysis method gives a more detailed understanding of EDL in molten salts and can become an inspiration for new researches in this field.

Two-dimensional structures formed in a binary system of DNA nanoparticles with a short-range interaction potential

Covering nanoparticles with DNA strands is one of the useful methods of controlling the interaction between particles because DNA strands can be easily designed according to our specifications. Obtaining an idea from the two-dimensional structures formed by the nanoparticles covered with DNA strands, which we call DNA nanoparticles, we carry out Brownian dynamics simulations and study the formation of two-dimensional structures in a binary system. We assume that the different types of particles attract each other with Morse potential, which is minimum when their distance is σ′. When the types of particles are the same and their distance is smaller than σ, the particles are repulsive. The mixture of both square and triangular lattices is formed when σ′/σ = 1. With decreasing σ′/σ, a square lattice, a honeycomb lattice, and string-shaped clusters are formed. The coexistence of both square and triangular lattices with large σ′/σ and the formation of stringlike clusters with small σ′/σ occur because we neglect the attraction between the same types of particles and use a short-range attraction between different types of particles.

Rheological behavior of colloidal suspension with long-range interactions

In this work, we study the constitutive behavior of interacting colloidal suspensions for moderate and high concentrations. Specifically, using a lattice Boltzmann solver, we numerically examine suspensions flowing through narrow channels, and explore the significance of the interaction potential strength on the system's macroscopic response. When only a short-range interaction potential is considered, a Newtonian behavior is always recovered and the system's effective viscosity mostly depends on the suspension concentration. However, when using a Lennard-Jones potential we identify two rheological responses depending on the interaction strength, the volume fraction, and the pressure drop. Exploiting a model proposed in the literature we rationalize the simulation data and propose scaling relations to identify the relevant energy scales involved in these transport processes. Moreover, we find that the spatial distribution of colloids in layers parallel to the flow direction does not correlate with changes in the system macroscopic response; but, interestingly, the rheology changes do correlate with the spatial distribution of colloids within individual layers. Namely, suspensions characterized by a Newtonian response display a cubiclike structure of the colloids within individual layers, whereas for suspensions with non-Newtonian response colloids organize in a hexagonal structure.

On the analytic smoothing effect for the Hartree equation with a short range interaction potential

We consider the Cauchy problem for the Hartree equation in space dimension d≥2. We assume that the interaction potential V(x) is short range. More precisely, we consider the case where V belongs to the weak Ld/σ space with 1<σ<d. We prove that if 2≤σ<d (resp. 1<σ<2), the initial data ϕ is small in the sense of the homogeneous Sobolev space H˙σ/2−1 (resp. the homogeneous weighted Sobolev space FH˙1−σ/2) and the Fourier transform Fϕ satisfies a real-analytic condition, then the corresponding solution u(t) is also real-analytic for any t≠0. We remark that no H˙σ/2−1 (resp. FH˙1−σ/2) smallness condition is imposed on first and higher order partial derivatives of Fϕ when 2≤σ<d (resp. 1<σ<2).

On statistical theory of rarefied gas in the Coulomb model of matter. Particle identity and effective interaction potential of initial atoms

The free energy of a Coulomb system of interacting electrons and nuclei is studied in the adiabatic approximation for nuclei with allowance for particle identity effects. An explicit expression is found for the effective short-range interaction potential of “identical” initial atoms in the self-consistent Hartree–Fock approximation for the electron subsystem and the first-order perturbation theory in a small parameter defined via the ratio of the atomic size to the mean distance between initial atoms.

The creation, destruction, and transfer of multipole moments in electron–ion three-body recombination using the Gell-Mann–Goldberger–Watson method

We use the Gell-Mann–Goldberger–Watson (GGW) method to further develop and elaborate on our earlier investigation of electron–ion three-body scattering. The GGW method is used to obtain multipole moment creation, destruction, and transfer rate formulae by the three-body recombination of electrons with ions assuming short-range interaction potentials. This approach leads to the derivation of the rate coefficient formula obtained previously via the alternative wave-packet propagation method. We show how to include exchange effects into the formalism, allowing extension of its validity to lower incident electron energies, and also introduce the Liouville-space formulation. Furthermore, we indicate that this method makes the relevance of the formulae to relativistic systems more transparent, demonstrating its validity for high incident electron energies and heavy ions. The Liouville-space formulation is used to facilitate the derivation of a selection rule for the rate coefficients for cylindrically symmetric plasmas, which is of practical importance for the proper formulation of population-alignment collisional-radiative modeling.

Coarse-Grained Molecular Dynamics Approach to Simulating Clay Behavior

AbstractA unique simulation was developed within the large-scale atomic/molecular massively parallel simulator (LAMMPS) open source molecular dynamics environment to model kaolinite clay during one-dimensional consolidation. The simulation was composed of a coarse-grained representation of the mineral with long-range and short-range interaction potentials. Additionally, the simulation allows for the edge-to-edge and edge-to-face attractions to develop through use of two subparticle types. Periodic simulation boundaries were created and thus allowed for consolidation to proceed without any wall effects distorting the resulting fabric. By following the parallel processing paradigm of the LAMMPS code, the number of particles simulated was limited only by the hardware on which the simulation was run. The results of the simulation showed remarkable consistency with previous published studies over all the void ratios explored and the transition from overconsolidated to normally consolidated behavior was capture...

On the discrete spectrum of the Hamiltonians of n-particle systems with n → ∞ in function spaces with various permutation symmetries

The restrictions of the nonrelativistic energy operators H n of the relative motion of a system of n identical particles with short-range interaction potentials to subspaces M of functions with various permutation symmetries are considered. It is proved that, for each of these restrictions, there exists an infinite increasing sequence of numbers N j , j = 1, 2, …, such that the discrete spectrum of each operator \(H_{N_j }\) on M is nonempty. The family {M} of considered subspaces is, apparently, close to maximal among those which can be handled by the existing methods of study.

Linear instability of a zigzag pattern.

Interacting particles confined in a quasi-one-dimensional channel are physical systems which display various equilibrium patterns according to the interparticle interaction and the transverse confinement potential. Depending on the confinement, the particles may be distributed along a straight line, in a staggered row (zigzag), or in a configuration in which the linear and zigzag phases coexist (distorted zigzag). In order to clarify the conditions of existence of each configuration, we have studied the linear stability of the zigzag pattern. We find an acoustic transverse mode that destabilizes the zigzag configuration for short-range interaction potentials, and we calculate the interaction range above which this instability disappears. In particular, we recover the unconditional stability of zigzag patterns for Coulomb interactions. We show that the domain of existence for the distorted zigzag patterns is accurately described by our linear stability analysis. We also emphasize the complexity of finite size effects. Last, we provide a criterion for the onset of instability in the thermodynamic limit and propose a biphasic model that explains some characteristics of the distorted zigzag patterns.

The creation, destruction and transfer of multipole moments in electron–ion three-body recombination

We use the wave-packet propagation scheme of Goldberger and Watson to define multipole moment creation, destruction, and transfer rates for the three-body recombination (TBR) of electrons with ions. We first assume short-range interaction potentials and then consider Coulomb interactions, for which we use Dollardʼs theory of multichannel scattering. We present the multipole moment rate coefficients in terms of the TBR amplitudes. Finally, we discuss time-reversal invariance and the reciprocity relations, both for the short-range case and for the Coulomb-interaction case, and show that the multipole moment rate coefficients can be expressed in terms of electron-impact ionization amplitudes.

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

We show local and global well-posedness results for the Hartree equation $$i\partial_t\gamma=[-\Delta+w*\rho_\gamma,\gamma],$$ where $\gamma$ is a bounded self-adjoint operator on $L^2(\R^d)$, $\rho_\gamma(x)=\gamma(x,x)$ and $w$ is a smooth short-range interaction potential. The initial datum $\gamma(0)$ is assumed to be a perturbation of a translation-invariant state $\gamma_f=f(-\Delta)$ which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state $\gamma(t)$, counted relatively to the stationary state $\gamma_f$. We indeed use a general notion of relative entropy, which allows to treat a wide class of stationary states $f(-\Delta)$. Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

Positron and electron scattering on atoms and molecules–modified effective range theory revisited

New experiments on the very low-energy electron and positron scattering allow to verify the old question on applicability of modified effective range theory (MERT). We perform it using an analytical solution of the Schrodinger equation with the long-range polarization potential. In this work two atomic (He, Ar) and molecular (H2, CH4) target are studied using this approach. Total cross sections were used for obtaining parameters characterizing the scattering phase shifts related to the short-range interaction potential; differential cross sections were used for comparison. Differently from previous works, we conclude that MERT with few (2-3) partial waves applies very well up to energies of few eV in all four targets studied. For positrons, reliable experimental data indicate occurrence of zeros in the s-wave phase shifts for all four targets. This should be recognized as Ramsauer-Townsend minima.

Three-Body Bound States in Atomic Mixtures With Resonantp-Wave Interaction

We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a nonzero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long range; namely, it decreases as the third power of the interatomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states, are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.

Huge-scale molecular dynamics simulation of multibubble nuclei

We have developed molecular dynamics codes for a short-range interaction potential that adopt both the flat-MPI and MPI/OpenMP hybrid parallelizations on the basis of a full domain decomposition strategy. Benchmark simulations involving up to 38.4 billion Lennard-Jones particles were performed on Fujitsu PRIMEHPC FX10, consisting of 4800 SPARC64 IXfx 1.848 GHz processors, at the Information Technology Center of the University of Tokyo, and a performance of 193 teraflops was achieved, which corresponds to a 17.0% execution efficiency. Cavitation processes were also simulated on PRIMEHPC FX10 and SGI Altix ICE 8400EX at the Institute of Solid State Physics of the University of Tokyo, which involved 1.45 billion and 22.9 million particles, respectively. Ostwald-like ripening was observed after the multibubble nuclei. Our results demonstrate that direct simulations of multiscale phenomena involving phase transitions from the atomic scale are possible and that the molecular dynamics method is a promising method that can be applied to petascale computers.