Two-particle System Research Articles

Rydberg excitons in cuprous oxide: A two-particle system with classical chaos.

When an electron in a semiconductor gets excited to the conduction band, the missing electron can be viewed as a positively charged particle, the hole. Due to the Coulomb interaction, electrons and holes can form a hydrogen-like bound state called the exciton. For cuprous oxide, a Rydberg series up to high principle quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343 (2014)] with the extension of excitons up to the μm-range. In this region, the correspondence principle should hold and quantum mechanics turn into classical dynamics. Due to the complex valence band structure of Cu2O, classical dynamics deviates from a purely hydrogen-like behavior. The uppermost valence band in cuprous oxide splits into various bands resulting in yellow and green exciton series. Since the system exhibits no spherical symmetry, the angular momentum is not conserved. Thus, the classical dynamics becomes non-integrable, resulting in the possibility of chaotic motion. Here, we investigate the classical dynamics of the yellow and green exciton series in cuprous oxide for two-dimensional orbits in the symmetry planes as well as fully three-dimensional orbits. Our analysis reveals substantial differences between the dynamics of the yellow and green exciton series. While it is mostly regular for the yellow series, large regions in phase space with classical chaos do exist for the green exciton series.

Aligned colloidal clusters in an alternating rotating magnetic field elucidated by magnetic relaxation

Precise control at the colloidal scale is one of the most promising bottom-up approaches to fabricating new materials and devices with tunable and precisely engineered properties. Magnetically driven colloidal assembly offers great versatility because of the ability to externally tune particle-particle interactions and to construct a host of particle arrangements. However, despite previous efforts to probe the parameter space, global orientational control in conjunction with two-dimensional microstructural control has remained out of reach. Furthermore, the magnetic relaxation time of superparamagnetic beads has been largely overlooked despite being a key feature of the magnetic response. Here, we take advantage of the magnetic relaxation time of superparamagnetic beads in an alternating rotating magnetic field and show how harnessing this feature facilitates the formation of oriented clusters. The orientation of these clusters can be controlled by field parameters. Using experiments, simulations, and theory, we probe a two-particle system (dimer) under this alternating rotating magnetic field and use its dynamics to provide insights into the collective response that forms clusters. We find that the type of field has significant implications for the dipolar interactions between the colloids because of the nonnegligible magnetic relaxation. Moreover, we find that the competing time scales of the magnetic relaxation and the alternating field generate an anisotropic interaction potential that drives cluster alignment. By exploiting the magnetic relaxation time of magnetic systems, we can tailor new types of interparticle interactions, thereby expanding the capabilities of colloidal assembly in engineering unique materials and devices.

Gluon generalized TMDs and Wigner distributions in boost invariant longitudinal space

We present the gluon generalized TMDs for non-zero skewness and Wigner distributions in the boost invariant longitudinal space. The boost-invariant longitudinal space is defined as σ=12b−Δ+ and is conjugate to the skewness variable ξ. We use the dressed quark model, where a high-energetic quark is dressed by a gluon. This two-particle system has the advantage of addressing both the gluon and the quark sectors. The different contributions in Wigner distributions coming from different polarization of gluon and the dressed quark system are investigated.

Three-dimensional FSI simulation of cell entrapment utilizing acoustic interparticle force in a standing acoustic field

Abstract In recent years, there has been significant development in microfluidic devices for cell separation and sorting using acoustic methods in biomedical applications. The acoustic interparticle force (AIF) arises from particle interactions with the scattered field of other particles, influencing particle motion at close ranges and facilitating optimal trapping and separation. This study analyzes a two-particle system consisting of a fixed particle and a white blood cell (WBC) within a standing acoustic field and creeping flow using fluid-structure interaction (FSI). To reduce computational costs by decoupling the acoustics and FSI, the acoustic pressure equation (AcPr) was solved on the frequency domain to calculate the total acoustic radiation force in each time step. Model accuracy was assessed by evaluating interparticle (AIF) and primary acoustic radiation forces (ARF) on a polystyrene particle and comparing simulation results to analytical and experimental data. Results demonstrate precise ARF performance, with discrepancies in acoustic interparticle force attributed to viscous losses near the particle surface. Moreover, the higher density of the fixed particle compared to WBCs induces significant acoustic interparticle attraction at close distances. Consequently, cell entrapment occurs through strong attraction and collision with fixed aluminum and silicon particles in creeping flow in all three Reynolds numbers 1.4E-3, 2.1E-3, and 3E-3. Increasing Reynolds numbers augment the likelihood of cell separation from the fixed particle. These findings contribute to optimizing cell isolation and entrapment strategies.

Analyzing Quantum Entanglement with the Schmidt Decomposition in Operator Space.

Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically relies on the observation that quantum states with a high fidelity to some entangled target state are entangled, too. We introduce a general method to construct entanglement witnesses based on the Schmidt decomposition of observables. The method works for two-particle and multiparticle systems and is strictly stronger than fidelity-based constructions. The resulting witnesses can also be used to quantify entanglement and to characterize its dimensionality. Finally, we present experimentally relevant examples, where our approach improves entanglement detection significantly.

Hard confinement of a two-particle quantum system using the variational method

Hard confinement of a two-particle quantum system using the variational method

Electrochemical grand potential-based phase-field simulation of electric field-assisted sintering

An electrochemical grand potential functional was proposed to describe the sintering of an ionic ceramic green body. The resultant phase-field description enables simulation of the consolidation of an arbitrary number of granular particles and their interactions with the surrounding void phase. The model includes the effects of charged vacancies and the associated interactions between internal and applied electric fields. Defect segregation to grain boundaries is also accounted for, as well as enhanced interfacial defect mobilities. The model was parameterized for Y2O3. Simulations of two-particle systems showed that the applied electric field had an increasingly important impact on neck growth as particle size increased. A sudden rapid increase in temperature occurred for larger field strengths, which has been reported to be correlated to the onset of a flash event in flash sintering. Simulations of many particles showed that internal heat generation by Joule heating was localized at particle–particle contacts (grain boundaries), even though their conductivities were lower than nearby internal particle-void interfaces. A percolative path for ionic charge across the green body and the ceramic sintered solid was thus defined, accelerating the Joule heating process as the porosity of the green body is removed.

Application of the quantum model of the rotating wave approximation to the generation of spin waves in nanowires

The paper simulates systems in which two types of spin waves can occur, propagating in opposite directions. To achieve this, the quantum slow-wave approximation is employed, allowing for the determination of the probability distribution of occupied states in a quantum two-particle system subjected to perturbations, commonly referred to as Rabi oscillations. This model is specifically applied to a configuration of parallel nanowires exposed to an external electromagnetic wave within the microwave range. The study explores a potential application of the investigated nanostructures in the development of a device for detecting electromagnetic fields.

Three-Body Entanglement in Particle Decays.

Quantum entanglement has long served as a foundational pillar in understanding quantum mechanics, with a predominant focus on two-particle systems. We extend the study of entanglement into the realm of three-body decays, offering a more intricate understanding of quantum correlations. We introduce a novel approach for three-particle systems by utilizing the principles of entanglement monotone concurrence and the monogamy property. Our findings highlight the potential of studying deviations from the standard model and emphasize its significance in particle phenomenology. This work paves the way for new insights into particle physics through multiparticle quantum entanglement, particularly in decays of heavy fermions and hadrons.

Study of thermodynamic properties of N particles in one-dimensional harmonic oscillator potential

We have calculated the partition function and hence the energy and the specific heat of a two-particle system in n numbers of finite nondegenerate energy levels of equal spacing distributed according to classical and quantum statistics. We have then extended our study for N identical particles placed in 1D harmonic oscillator potential. It is observed that the specific heat of bosons and fermions are exactly the same in this potential at any temperature, and at high temperature the results are similar to that for the classical particles. The partition function of a system of two particles placed in 2D harmonic oscillator potential has also been determined as comparison.

Entanglement in a complex plasma

Quantum mechanical approach is extended to the interaction of dust particles in a complex plasma. Massive and highly charged dust particles interact each other through the exchange of quasi-particles (virtual waves) in a quantum mechanical viewpoint. The interaction is described by the Hamiltonian, which describes the two-particle system as uncoupled harmonic oscillators. When the pair of dust particles are embedded in the injected plasma wave, the Hamiltonian is found to show the presence of coupled harmonic oscillator indicating the emergence of the entanglement in semiclassical nature. The entanglement of a pair of dust particles is encapsulated in the Hamiltonian, which is formulated by the method of second quantization. The frequency of the wave to trigger the emergence of the entanglement is found to be one-half of the dust plasma frequency. The interaction between a pair of dust particles is formulated as a scattering process and is described by the transition probability. Measure of the semiclassical entanglement is shown by the entropy, and the resulting entropy is found to increase with time.

Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

We investigate the entanglement in a two-particle system with continuous degree of freedom constituted by trapped neutral atoms interacting via tunable dipole-dipole interaction. We describe the system in the quantum Wigner phase space representation. The atom entanglement is measured in terms of violation of the non separability condition or of some Bell inequalities. By an optimal control procedure, we design the control parameters that steer the system toward a maximally entangled state. We estimate the robustness of the control by considering the presence of an external source of noise weakly interacting with the atoms.

Probing quantum entanglement from quantum correction to newtonian potential energy

Inspired by string theory ideas, we probe quantum entanglement from the gravitational potential energy. Concretely, we reconsider the study of quantum corrections to the Newtonian potential energy by treating a massive two-particle system m 1 and m 2 with size dimensions r 1 ad r 2 where the two particles separated by a distance d are under only their mutual classical gravitational interaction Vrr1,r2 . Exploring such a size-dependent gravitational behavior and taking the limit r 1, r 2 ≪ d, we investigate the associated quantum biparticle state and express its evolution after an interaction time τ. Among others, we show that the two masses cannot be separable due to the induced gravitational entanglement in terms of the accumulated quantum phase δ ϕ = δ V g τ/ℏ. By analogy with the classical gravity, we derive the expression of the resulting extremely weak entanglement force from the corresponding gravitational entanglement energy. Then, we provide certain entanglement diagnostics.

Sedimentation of two circular particles with different sizes in a vertical channel at low Reynolds numbers

In this study, the generalized finite-difference with singular value decomposition method for fluid–structure interaction problems is used to simulate the sedimentation of the two circular particles with different sizes in a vertical channel. The effects of the Reynolds number (8 ≤ Re ≤ 70) and the size difference (0 ≤ β ≤ 0.1) on the final motions of the two particles are analyzed. Over the ranges of the parameters investigated, three modes in the final state of the two-particle system are identified, i.e., the steady state, the periodic oscillation state, and the period-doubling bifurcation (PDB) state. Depending on the importance of the inertial force, the steady state can be classified as the steady state I and the steady state II. Similarly, the periodic oscillation state can be categorized into the periodic motion I (PMI) and the periodic motion II (PMII) based on the influence of the wake between the two particles. The directions of the limit cycles corresponding to PMI and PMII are counterclockwise and clockwise, respectively. In PMI, the limit cycle at 8 ≤ Re ≤ 9 decreases in size with increasing β, while the limit cycle at 12 ≤ Re < 70 behaves oppositely. The limit cycle in PMII always increases in size with β. PDB, characterized by the limit cycle with two branches, mainly appears at 14 ≤ Re ≤ 30.

$ \mathcal{N} = 2 $ double graded supersymmetric quantum mechanics via dimensional reduction

<abstract><p>We presented a novel $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-graded supersymmetric quantum mechanics ($ {\mathbb{Z}_2^2} $-SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and was the first example of the quantum mechanical realization of an eight-dimensional irreducible representation (irrep) of the $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-supersymmetry algebra. The $ {\mathbb{Z}_2^2} $-SQM was obtained by quantizing the one-dimensional classical system derived by dimensional reduction from the two-dimensional $ {\mathbb{Z}_2^2} $-supersymmetric Lagrangian of $ \mathcal{N} = 1 $, which we constructed in our previous work. The ground states of the $ {\mathbb{Z}_2^2} $-SQM were also investigated.</p></abstract>

Laser-induced heating for the experimental study of critical Casimir forces with optical trapping

Critical Casimir interactions represent a perfect example of bath-induced forces at mesoscales. These forces may have a relevant role in the living systems as well as a role in the design of nanomachines fueled by environmental fluctuations. Since the thermal fluctuations are enhanced in the vicinity of a demixing point of a second-order phase transition, we can modulate the magnitude and range of these Casimir-like forces by slight changes in the temperature. Here, we consider two optical trapped colloidal beads inside a binary mixture. The Casimir interaction is controlled by warming the mixture by laser-induced heating, whose local application ensures high reproducibility. Once this two-particle system is warmed, the critical behavior of different observables allows the system to become its self-thermometer. We use this experimental scheme for analyzing the energetics of a critical colloidal system under a non-equilibrium-driven protocol. We quantify how the injected work can be dissipated to the environment as heat or stored as free energy. Indeed, our system allows us to use the fluctuation theorems framework for analyzing the performance of this critically driven toy model. Our work paves the way for future experimental studies on the non-equilibrium features of bath-induced forces and the design of critically driven nanosystems.

Kinematic Calculation of the 16O(γ,4α) Reaction

The event distribution over the excitation energy of a system of two α-particles (Ex) is measured for the reaction 16O(γ,4α). It is found that an intermediate excited 8Be nucleus is formed, and the channels of the 8Be nucleus ground state (GS) formation are extracted. After the separation of the GS 8Be nucleus, a broad maximum with a center at ∼ 3 MeV appears in the distribution of Ex, which may correspond to the first excited state of the 8Be nucleus. There are two possible channels for the formation of this state in the reaction - γ + 16O → α1 + 12C* → α1 + α2 + 8Be* →α1 + α2 + α3 + α4 and γ + 16O → 8Be* + 8Be* → (α1 + α2) + (α3 + α4). Each decay mode is reduced to several two-particle systems. For a comprehensive study of the channel for the formation of the first excited state of the 8Be nucleus in the 16O(γ,4α) reaction, a kinematic model for calculating the parameters of α-particles has been developed. The model is based on the assumption of a sequential two-particle decay with the formation of intermediate excited states of 8Be and 12C nuclei. For the kinematic model of the 16O(γ,4α) reaction, a graphical application was created in the Python programming language. The matplotlib library is used for data visualization. To generate random values, a set of functions from the standard random library of the Python programming language is used. Monte Carlo simulations of several distributions for one parameter with a given numerical function were performed. Several excited states of the 12C and 8Be nuclei can contribute to the reaction. The created scheme allows us to choose the relative contribution for each channel of decay, as well as the contribution of a separate level in each channel. To correctly comparison of the experimental data and the results of the kinematic calculation, the α-particles were sorted by energy in such a way that T1sort > T2sort > T3sort > T4sort. As a result of comparing the experimental and calculated data, it was determined that predominantly occurs the process γ + 16O → α1 + 12C* → α1 + α2 + 8Be* → 4α with the formation of the 12C nucleus in states with E0 = 13.3 MeV, E0 = 15.44 MeV, and the 1st excited state of the 8Be nucleus with E0 = 3.04 MeV. The conditions for the identification of α-particles in the experiment for each decay of the stage are determined.

On the relation between nodal structures in quantum wave functions and particle correlation

We study the influence of nodal structures in two-dimensional quantum mechanical densities on wave packet entanglement. This is motivated by our recent study [Entropy, 25, 970 (2023)], which showed that the mutual information derived from the momentum-space probability density of a coupled two-particle system exhibits an unusual time dependence, which is not encountered if the position-space density is employed in the calculation. In studying a model density, here, we identify cases where the mutual information increases with the number of nodes in the wave function and approaches a finite value, whereas in this limit, the linear correlation vanishes. The results of the analytical model are then applied to interpret the correlation measures for coupled electron-nuclear dynamics, which are treated by numerically solving the time-dependent Schrödinger equation.

Kinetic modeling of fluid-induced interactions in compressible, rarefied gas flows for aerodynamically interacting particles

In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2<Ma∞<2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or “hypersonic-surfing”, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.

Balanced loss-gain induced chaos in a periodic Toda lattice

We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable. The three-particle equal-mass periodic Toda lattice is considered in presence of balanced loss-gain and velocity mediated coupling. The system is Hamiltonian for specific values of the coupling constants. The generalized momentum is the second integral of motion and study of Poincaré section indicates its integrability in certain region of the parameter-space. The generic model admits both non-chaotic and chaotic solutions. The chaos in the system with vanishing velocity mediated coupling is solely induced due to the presence of balanced loss-gain, since undriven equal-mass Toda lattice is non-chaotic. The chaotic behavior is studied in detail for the generic system.