Two-particle System Research Articles

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.

Strange hadron correlations in heavy-ion collisions at RHIC energies and below

Geometry and dynamics of the particle-emitting source in heavy-ion collisions can be inferred via the femtoscopy method. Two-particle correlations at small relative momentum exploit Quantum Statistics and the Final State Interactions (Coulomb and strong), which allow one to study the space-time characteristics of the source of the order of 10−15 m and 10−23 s. Femtoscopic measurements allow one also to study FSI, especially the strong one, which is unknown for many two-particle systems. The RHIC program covers a significant part of the QCD phase diagram using collisions of Au nuclei for several beam energies from 7.7 to 200 GeV for which baryon-rich region is studied via femtoscopy. These measurements complement those obtained from AGS, SPS, and SIS experiments. Strange hadron measurements together with nonstrange ones provide complementary information about source characteristics. Strangeness is a significant observable for many regimes of collision energies providing a complete view of strangeness production in heavy-ion collisions. These proceedings shows the femtoscopic measurements of various strange particle combinations at different collision energies and centralities of the collision.

Solvable two-particle systems with time-asymmetric interactions in de Sitter space

The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.

Numerical investigation of movement patterns of particles falling in a viscous fluid

To study the movement patterns of particles, the long-term sedimentation of multiple circular particles in a narrow channel filled with a viscous fluid is investigated numerically. The attention is focused firstly on the equilibrium movement pattern of particles at an intermediate terminal Reynolds number (Ret), and then on its connection with behaviors of multiple particles. For three particles released in a symmetric pattern, at the first stage, all particles tend to fall at the same speed, then after a dramatic interaction, particles split into two groups (1 + 2). The single particle moves steadily with a faster velocity along the central line, while the other two particles self-organize into a two-particle system, moving as a steady oblique doublet, periodic oscillation pair, or a steady symmetrical doublet. For the sedimentation of six particles, there are more separations after the first stage. The small groups owning 1, 2 and 3-particle move in their own typical equilibrium movement patterns. It seems that at intermediate Reynolds numbers multiple particles tend to break up into small groups that can maintain their own equilibrium movement patterns. It is shown that the study on the movement patterns of one/two particles can provide essential information for the self-organization behavior of multiple particles.

ON THE SPECTRUM OF THE TWO-PARTICLE SCHRÖDINGER OPERATOR WITH POINT POTENTIAL: ONE DIMENTIONAL CASE

In the paper a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schr\"{o}\-dinger operator (energy operator) $h_\varepsilon$ depending on $\varepsilon,$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The main results of the work are based to the study of the operator $h_\varepsilon.$ First the essential spectrum is described. The existence of unique negative eigenvalue of the Schr\"{o}dinger operator is proved. Further, this eigenvalue and corresponding eigenfunction are found.

Lattice Boltzmann modeling of particle dynamics in rotating coordinate system

Centrifugal rotation is one of the most important techniques for separating and purifying particles or cells, which enables broad applications in biomedicine and chemistry. To study the separation mechanism of the rotating flow, a lattice Boltzmann method is developed to simulate particulate flows in the rotating coordinate system, where the centrifugal and Coriolis forces are exerted not only on the fluid but also on the particles. This method is first validated by simulation of two benchmark cases, namely, the external force driven flow in the rotating coordinate system and the motion of a single particle in a rotating fluid disk. It is then used to investigate the dynamics of a single particle, two particles and a particle cluster in a rotating channel. Results show that the centrifugal force and Coriolis force drive the particle to move toward the outlet and toward the bottom wall, respectively, and decreasing particle size can reduce the hydrodynamic resistance, thus making the particle move faster. In the two-particle system, the particle-particle interaction is found to play an important role, which could cause the downstream particle to move first downward and then upward when the particle mass is small, or to exhibit a damped oscillation behavior when the particle mass is large. By simulating the motion of a particle cluster, we demonstrate the capability of the rotating channel to screen particles with different sizes or masses.

Anderson Localization of Composite Particles.

We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice. We illustrate that the coupling has a dramatic effect on localization properties, even with a small number of internal states participating in quantum dynamics.

Trapped two-nucleon system in energy-dependent effective field theory

We discuss how to connect the energy levels of two-particle systems trapped by a harmonic-oscillator force to scattering amplitudes, with nucleon-nucleon scattering phase shifts in uncoupled channels as the application. At the center of the proposed framework is the energy-dependent effective field theory that aims to expand observables in a neighborhood around each reference energy, often taken to be one of the energy levels. We also investigate how to disentangle the trapping force at short distances and the intrinsic interaction between the particles.

Contact interactions: the two-dimensional case

We prove that in two dimensions the contact interaction of two wave functions is represented by a self-adjoint operator. Together with a confining potential, this provides a stable condensate of two-particle systems. Recall that in three dimensions one has a condensate of four wave functions in contact interaction (the Bose–Einstein condensate).

Interplay and competition between disorder and flat band in an interacting Creutz ladder

We clarify the interplay and competition between disorder and flat band in the Creutz ladder with interparticle interactions focusing on the system's dynamics. Without disorder, the Creutz ladder exhibits flat-band many-body localization (FMBL). In this work, we find that disorder generates drastic effects on the system, i.e., addition of it induces a thermal phase first and further increase of it leads the system to the conventional many-body-localized (MBL) phase. The competition gives novel localization properties and unconventional quench dynamics to the system. We first draw the global sketch of the localization phase diagram by focusing on the two-particle system. The thermal phase intrudes between the FMBL and MBL phases, the regime of which depends on the strength of disorder and interactions. Based on the two-particle phase diagram and the properties of the quench dynamics, we further investigate finite-filling cases in detail. At finite-filling fractions, we again find that the interplay and competition between the interactions and disorder in the original flat-band Creutz ladder induces a thermal phase, which separates the FMBL and MBL phases. We also verify that the time evolution of the system coincides with the static phase diagrams. For suitable fillings, the conservation of the initial-state information and low-growth entanglement dynamics are also observed. These properties depend on the strength of disorder and interactions.

Lipkin model on a quantum computer

Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. We present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods.

Grain growth in sintering: A discrete element model on large packings

Sintering is a high temperature process used for ceramic or metallic powder consolidation that consists of concurrent densification and grain growth. This work presents a coupled solid-state sintering and grain growth model capable of studying large packings of particles within the Discrete Element Method (DEM) framework. The approach uses a refinement for large particle size ratios of previously established contact laws to model shrinkage. In addition, mass transfer between neighboring particles is implemented to model grain growth by surface diffusion and grain-boundary migration. The model assumptions are valid for initial and intermediate stage sintering. The model is validated on a two-particle system by comparing neck and particle size evolutions with those obtained by phase-field and meshed-based methods. Simulations on large packings (up to 400 000 particles) with particle size distributions originating from experiments are performed. The results of these simulations using physical data from the literature are compared to experimental data with good accordance of the key features of the microstructure evolution (densification kinetics, grain size-density trajectory, evolution of the mean grain size and of the size distribution). The simulations show that even at an early stage of sintering, hardly detectable grain growth actually affects the sintering kinetics to a non-negligible extent and that the realism of DEM simulations of sintering is improved when grain growth is considered. Taking advantage of the possibility to simulate large packings, the model elucidates the influence of the initial particle size distribution on the grain growth kinetics.

On-shell representations of two-body transition amplitudes: Single external current

This work explores scattering amplitudes that couple two-particle systems via a single external current insertion, $2+\mathcal{J}\ensuremath{\rightarrow}2$. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD.

Coulomb corrections to two-particle interactions in artificial traps

In present work, we discuss the effect of Coulomb interaction to the dynamics of two-particle system bound in various traps. The strategy of including Coulomb interaction into the quantization condition of trapped system is discussed in a general and non-perturbative manner. In most cases, Coulomb corrections to quantization condition largely rely on numerical approach or perturbation expansion. Only for some special cases, such as the spherical hard wall trap, a closed-form of quantization condition with all orders of Coulomb corrections can be obtained.

Bound Entanglement from Randomized Measurements.

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, we present the optimal inequalities if entanglement in a bipartition of a multiqubit system shall be analyzed in terms of these moments. Finally, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework.

Мeson resonances in the relativistic quark model

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons.

A Two-Body Problem for a Class of Coupling Potentials with Harmonic Oscillator Interaction in Noncommutative Phase Space: Path Integral Approach

Recently Gnatenko et al. (J Phys Stud 21:4002, 2017) have treated the two-body problem with harmonic oscillator interaction in noncommutative phase space. According to the path integral formulation, we generalize this process by adding the coupling potentials ( $$\kappa {\mathbf {P}} ^{\left( a\right) }\cdot {\mathbf {P}}^{\left( b\right) }$$ and $${\tilde{\kappa }} {\mathbf {X}}^{\left( a\right) }\cdot {\mathbf {X}}^{\left( b\right) }$$ ) together with a Harmonic oscillator interaction in noncommutative phase space. Moreover, in order to convert this problem into a one-particle system, we have added a third condition along with what this paper provided. As well as, when $$ \kappa $$ and $${\tilde{\kappa }}$$ equal to zero exact expressions for the energy levels of a two-particle system with harmonic oscillator interaction in noncommutative phase space have been found.

Genesis of electric field assisted microparticle assemblage in a dielectric fluid

Abstract

Direct numerical simulation of magneto-Archimedes separation of spherical particles

Abstract

The EPR paradox and the uncertainty principle

The EPR paradox appears when measurement results of some properties of two distantly entangled particles are correlated in a way that cannot be explained classically, and apparently violate locality. The resolution of the paradox depends on one’s interpretation of quantum mechanics. Explanations from quantum mechanics remain commonplace today, but they fail to explain the EPR (Einstein, Podolsky and Rosen) paradox totally in a way than can be accepted by the whole community. Here, we present a simple resolution to this paradox in which the uncertainty in the energy of the two-particle system is reduced by its lack of interaction during the journey so that the uncertainty in time becomes greater than the time they have been separating. Consequently, the present and past become indistinguishable because when we measure an observable in the system its value is the same as if the two particle were still together or very close. It is also argued that the destruction of information as the present and past become identical should release heat by Landauer’s principle, and this might make this proposal testable.