Two-particle Configurations Research Articles

Correlated metallic two-particle bound states in Wannier-Stark flatbands

Tight-binding single-particle models on simple Bravais lattices in space dimension $d \geq 2$, when exposed to commensurate DC fields, result in the complete absence of transport due to the formation of Wannier--Stark flatbands [Phys. Rev. Res. $\textbf{3}$, 013174 (2021)]. The single-particle states localize in a factorial manner, i.e., faster than exponential. Here, we introduce interaction among two such particles that partially lifts the localization and results in metallic two-particle bound states that propagate in the directions perpendicular to the DC field. We demonstrate this effect using a square lattice with Hubbard interaction. We apply perturbation theory in the regime of interaction strength $(U)$ $\ll$ hopping strength $(t)$ $\ll$ field strength $(\mathcal{F})$, and obtain estimates for the group velocity of the bound states in the direction perpendicular to the field. The two-particle group velocity scales as $U {(t/\mathcal{F})}^\nu$. We calculate the dependence of the exponent $\nu$ on the DC field direction and on the dominant two-particle configurations related to the choices of unperturbed flatbands. Numerical simulations confirm our predictions from the perturbative analysis.

The influence of Stefan flow on the flow and heat-transfer characteristics of spherical-particle pair in supercritical water

For any flow process of mixtures containing dispersed reactive particles, especially highly concentrated particles, the particle-particle, and fluid-particle interactions are very complex and affect the overall flow. Supercritical water gasification technology is a complex multiphase-flow process that occurs in high-temperature reactors. Under these conditions, the components of the particle surface are heated and gasify to form a Stefan flow (i.e., a mass flow), which modifies fluid-particle interactions. The interaction between particles and the influence of Stefan flow cannot be ignored. In this work, we consider the simplest case of two identical spherical particles with different relative orientations and particle distances and discuss the flow and fluid-particle heat-transfer characteristics by numerical simulation of supercritical water flowing around the fixed two-particle system. We are particularly interested in the fluid-particle interactions with different particle configurations under the influence of Stefan flow. Three particle configurations are possible: tandem, cross, and parallel. The flow field, Nusselt number, drag coefficient, and temperature distribution around the particles are all analyzed. In comparison with a single particle, the two-particle configurations significantly affect the drag coefficient, Nusselt number, and vortex structure and Stefan flow strongly affects the wake vortex structure of two particles with small particle distance, reducing the drag coefficient and Nusselt number.

Charge symmetry broken complex coacervation

Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve as a proxy for simple coacervation. First, a low-density density-functional calculation reveals the dominance of two-particle configurations coupled by ion adsorption on neighboring macroions. Then a binary cell model, solved on the Debye-H\"uckel as well as the full nonlinear Poisson-Boltzmann level, unveils the charge-symmetry breaking as inducing the phase separation between low- and high-density phases as a function of pH. These results can be identified as a charge symmetry broken complex coacervation between chemically identical macroions.

Exact solution of U(5)–O(6) transitional description in interacting boson model with two-particle and two-hole configuration mixing * * Support from the National Natural Science Foundation of China (11675071, 11975009, 11575076), the Liaoning Provincial Universities Overseas Training Program (2019-46), the U. S. National Science Foundation (OIA-1738287 and ACI-1713690), U. S. Department of Energy (DE-SC0005248), the Southeastern Universities Research Association, and the

The exact solution of the U(5)-O(6) transitional description in the interacting boson model with two-particle and two-hole configuration mixing is derived based on the Bethe ansatz approach. The Bethe ansatz equations are provided to determine the model's eigenstates and corresponding eigen-energies. N= 2 and N= 4 cases are considered as examples to demonstrate the solution features. As an example of the application, some low-lying level energies and B(E2) ratios of 108Cd are fitted and compared with the corresponding experimental data.

Rotational bands in neutron-rich Mo, Ru, and Pd nuclei * * Supported by the National Key R&D Program of China (2018YFA0404401), the National Natural Science Foundation of China (11835001, 11575007, 11847203) and the China Postdoctoral Science Foundation (2018M630018)

The collective rotations of the configuration in neutron-rich Mo, Ru and Pd isotopes were systematically investigated by the configuration-constrained cranking shell model based on the Skyrme Hartree-Fock method with pairing treated by shell-model diagonalization. The calculations efficiently reproduce the experimental moments of inertia of both the ground-state and side bands. Rotational bands built on two-particle configurations have been the subject of intense study. Possible configurations were assigned to the observed bands in 102-106Mo, 108-112Ru and 112-114Pd. We predict the existence of the bands in 108,110Mo. These results provide deep insights into the structure of neutron-rich nuclei, and provide useful information for future experiments.

On Bound Electron Pairs on the Half-Line

Based on the quantum two-body problem introduced in [arXiv:1604.06693] we consider bound pairs of electrons moving on the positive half-line. The analysis is motivated by the ground-breaking work of Cooper who identified the pairing of electrons as a possible explanation for superconducting behaviour in metals. In this paper we are interested in the connection between the topologies of the underlying one- and two-particle configuration spaces and spectral properties of the Hamiltonian linked to a condensation of pairs. We derive explicit estimates for the energy gap and prove condensation for a gas of non-interacting pairs. Finally, we add some disorder to the system and prove destruction of the condensate.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

Simulated Microstructural Evolution and Design of Porous Sintered Wicks

Porous structures formed by sintering of powders, which involves material-bonding under the application of heat, are commonly employed as capillary wicks in two-phase heat transport devices such as heat pipes. These sintered wicks are often fabricated in an ad hoc manner, and their microstructure is not optimized for fluid and thermal performance. Understanding the role of sintering kinetics—and the resulting microstructural evolution—on wick transport properties is important for fabrication of structures with optimal performance. A cellular automaton model is developed in this work for predicting microstructural evolution during sintering. The model, which determines mass transport during sintering based on curvature gradients in digital images, is first verified against benchmark cases, such as the evolution of a square shape into an area-preserving circle. The model is then employed to predict the sintering dynamics of a side-by-side, two-particle configuration conventionally used for the study of sintering. Results from previously published studies on sintering of cylindrical wires are used for validation. Randomly packed multiparticle configurations are then considered in two and three dimensions. Sintering kinetics are described by the relative change in overall surface area of the compact compared to the initial random packing. The effect of sintering parameters, particle size, and porosity on fundamental transport properties, viz., effective thermal conductivity and permeability, is analyzed. The effective thermal conductivity increases monotonically as either the sintering time or temperature is increased. Permeability is observed to increase with particle size and porosity. As sintering progresses, the slight increase observed in the permeability of the microstructure is attributed to a reduction in the surface area.

A fictitious domain approach for the simulation of dense suspensions

Low Reynolds number concentrated suspensions do exhibit an intricate physics which can be partly unraveled by the use of numerical simulation. To this end, a Lagrange multiplier-free fictitious domain approach is described in this work. Unlike some methods recently proposed, the present approach is fully Eulerian and therefore does not need any transfer between the Eulerian background grid and some Lagrangian nodes attached to particles. Lubrication forces between particles play an important role in the suspension rheology and have been properly accounted for in the model. A robust and effective lubrication scheme is outlined which consists in transposing the classical approach used in Stokesian Dynamics to our present direct numerical simulation. This lubrication model has also been adapted to account for solid boundaries such as walls. Contact forces between particles are modeled using a classical Discrete Element Method (DEM), a widely used method in granular matter physics. Comprehensive validations are presented on various one-particle, two-particle or three-particle configurations in a linear shear flow as well as some O(103) and O(104) particle simulations.

Discrete Morse functions for graph configuration spaces

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear.

Enhancement of thermoelectric efficiency in a two-level molecule

Electron and energy transport through a two-level molecule (quantum dot) with intra- andinter-level Coulomb correlations is studied using the non-equilibrium Green functionformalism. Thermoelectric coefficients are determined in the regime of linear transport for awide range of gate voltages and temperature. At low temperatures Coulomb blockadeeffects lead to oscillations of thermal conductance which are well correlated withoscillations in electron conductance. Due to different probabilities of particularone- and two-particle configurations, the intensities of the peaks corresponding toresonant states are different, which results in the selection of channels active in thetransport. Additional selection can be obtained for molecules with level-dependenttunnelling rates to external electrodes. In such systems, channels with stronglyreduced heat transfer can appear, which results in an enhancement of the thermalefficiency.

Probabilistic analysis of transport–reaction processes over catalytic particles: Theory and experimental testing

We developed a probabilistic theory of transport–reaction processes over various types of configurations of catalytic particles, particularly for a single particle. The theory describes a single pulse–response experiment which is similar to the single pulse temporal analysis of products (TAP) experiment. The analysis is based on the general theory of Brownian motion with “killing” and the Feynman–Kac formula. Different diffusion–reaction problems, particularly the problem “diffusion–very fast reaction” (infinite rate reaction), have been analyzed. In the latter case, the probability for a reactant to be converted equals a purely geometric characteristic, namely, the probability for a reactant molecule to hit at least one catalyst particle in a configuration of particles. Solving a boundary value problem, the probability of conversion can be found as a function of the apparent kinetic parameter. Based on experimental data on exit flow and conversion this parameter can be extracted. Experimental data in studies of CO oxidation over a single particle of Pt catalyst show a qualitative agreement with data from computational experiments based on the developed probabilistic theory. For two-particle catalyst configurations, it was found computationally a non-trivial dependence of the reactant conversion on some geometric characteristics, especially the distance between particles. A distance was found for which conversion is highest.

Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations

Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along a contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the membrane. Symmetric two-particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime; in particular, the problem may be solved exactly in the case of two membrane-bound parallel cylinders. This apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane-mediated interactions.

Dynamic simulation using a multipolar model of particles under dielectrophoretic force

This article presents the simulation of an electrorheological (ER) fluid system by using a multipole model that includes multipolar interactions between particles. The model uses the multipole re-expansion and the method of images for calculating electric field and force. The highest order of multipoles ( N mp) and the number of iterations ( N iter) used in the method of images can be chosen for the accuracy of the force approximation and the simulation time required. Study of a two-particle configuration shows that the force does not increase linearly with increasing N mp and N iter. The specific case N mp=4 and N iter=2 is chosen for dynamic simulation. We have performed the simulation of a system of 20 particles, and compared the formulation of particle chains with that obtained using the dipole model. The results imply that the response time for the change in viscosity of real-ER fluids is significantly shorter than that predicted by the dipole model.

Resonances of the helium atom in a strong magnetic field

We present an investigation on the resonances of a doubly excited helium atom in a strong magnetic field covering the regime B = 0-100 a.u. A full-interaction approach which is based on an anisotropic Gaussian basis set of one-particle functions being nonlinearly optimized for each field strength is employed. Accurate results for a total of 17 resonances below the threshold of consisting of He+ in the N=2 state are reported in this work. This includes states with total magnetic quantum numbers M=0,-1,-2 and even z-parity. The corresponding binding energies are compared to approximate energies of two-particle configurations consisting of two hydrogen-like electrons in the strong field regime, thereby providing an understanding of the behavior of the energies of the resonances with varying field strength.

Interface-mediated interactions between particles: A geometrical approach

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy-based approach.

Toward isovector M1 transitions in odd-odd N = Z nuclei

IsovectorM1 transitions between low-lying T=1 and T=0 states in odd-odd N = Z nuclei are discussed. The data on low-spin states in the odd-odd nuclei 46V and 50Mn investigated with the 46Ti(p, nγ)46V and 50Cr(p, nγ)50Mn fusion evaporation reactions at the FN-TANDEM accelerator in Cologne are reported. A simple explanation of the enhancement of the M1 transitions is given in terms of quasideuteron configurations. The fragmentation of the strong M1 transitions is shown to be due to the coupling of the two-particle configurations to the rotating core.

The flow characteristics of an interactive particle at low Reynolds numbers

For any flow process of mixtures containing dispersed reactive particles, especially highly concentrated particles, the particle-particle, and fluid-particle interactions are very complex and affect the overall flow. Supercritical water gasification technology is a complex multiphase-flow process that occurs in high-temperature reactors. Under these conditions, the components of the particle surface are heated and gasify to form a Stefan flow (i.e., a mass flow), which modifies fluid-particle interactions. The interaction between particles and the influence of Stefan flow cannot be ignored. In this work, we consider the simplest case of two identical spherical particles with different relative orientations and particle distances and discuss the flow and fluid-particle heat-transfer characteristics by numerical simulation of supercritical water flowing around the fixed two-particle system. We are particularly interested in the fluid-particle interactions with different particle configurations under the influence of Stefan flow. Three particle configurations are possible: tandem, cross, and parallel. The flow field, Nusselt number, drag coefficient, and temperature distribution around the particles are all analyzed. In comparison with a single particle, the two-particle configurations significantly affect the drag coefficient, Nusselt number, and vortex structure and Stefan flow strongly affects the wake vortex structure of two particles with small particle distance, reducing the drag coefficient and Nusselt number.

A New Interpretation of Bethe Ansatz Solutions for Massive Thirring Model

We reexamine Bethe ansatz solutions of the massive Thirring model. We solve equations of periodic boundary conditions numerically without referring to the density of states. It is found that there is only one bound state in the massive Thirring model. The bound state spectrum obtained here is consistent with Fujita–Ogura's solutions of the infinite momentum frame prescription. Further, it turns out that there exist no solutions forstring-like configurations. Instead, we find boson–boson scattering states in two-particle two-hole configurations where all the rapidity variables turn out to be real.

New 0 + states in 146Sm from a (p,t) experiment and the particle-core coupling model

The reaction 148Sm(p,t) 146Sm was studied at E p = 26 MeV. Fifty-six excited states in the final N = 84 nucleus were observed below E exc = 4.2 MeV and their angular distributions were measured at 8 angles. Spin and parity assignments are made for 37 of them, based on the determination of the transferred angular momentum L. Ten excited J π = 0 + states were identified. The emerging excitation energies of the J π = 0 + states and the monopole strength distribution in 146Sm are compared with those observed in nearby nuclei and with results of calculations done in the framework of the Particle-Core Coupling Model. The main features of the experimental results are interpreted using a superposition of two types of configurations: two-particle states coupled to the collective excitations of the N = 82 core and two holes coupled to the collective excitations of the N = 86 core. Calculations show also that two-phonon⊗two-particle configurations are spread over many states and their identification becomes difficult.