Статті в журналах: "Interacting particles systems"

1

Karmanov, Vladimir A. "Abnormal Bound Systems." Universe 8, no. 2 (February 3, 2022): 95. http://dx.doi.org/10.3390/universe8020095.

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It is taken for granted that bound systems are made of massive constituents that interact through particle exchanges (charged particles interacting via photon exchanges, quarks in elementary particles interacting via gluon exchanges, and nucleons in nuclei interacting via meson exchanges). However, as was recently theoretically found, there exist systems dominated by exchange particles (at least for the zero exchange masses). In these systems, the contribution of massive constituents is negligible. These systems have a relativistic nature (since they are mainly made of massless particles moving at the speed of light), and therefore, they cannot be described by the Schrödinger equation. Though these results were found so far in the simple Wick–Cutkosky model (spinless constituents interacting via the ladder of spinless massless exchanges), the physical ground for their existence seems to be rather general.

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2

Abadi, Noam, and Franco Ruzzenenti. "Complex Networks and Interacting Particle Systems." Entropy 25, no. 11 (October 27, 2023): 1490. http://dx.doi.org/10.3390/e25111490.

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Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems.

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3

Sudbury, Aidan. "The survival of various interacting particle systems." Advances in Applied Probability 25, no. 4 (December 1993): 1010–12. http://dx.doi.org/10.2307/1427804.

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Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.

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4

Sudbury, Aidan. "The survival of various interacting particle systems." Advances in Applied Probability 25, no. 04 (December 1993): 1010–12. http://dx.doi.org/10.1017/s0001867800025878.

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Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.

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5

Itoh, Yoshiaki, Colin Mallows, and Larry Shepp. "Explicit sufficient invariants for an interacting particle system." Journal of Applied Probability 35, no. 3 (September 1998): 633–41. http://dx.doi.org/10.1239/jap/1032265211.

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We introduce a new class of interacting particle systems on a graph G. Suppose initially there are Ni(0) particles at each vertex i of G, and that the particles interact to form a Markov chain: at each instant two particles are chosen at random, and if these are at adjacent vertices of G, one particle jumps to the other particle's vertex, each with probability 1/2. The process N enters a death state after a finite time when all the particles are in some independent subset of the vertices of G, i.e. a set of vertices with no edges between any two of them. The problem is to find the distribution of the death state, ηi = Ni(∞), as a function of Ni(0).We are able to obtain, for some special graphs, the limiting distribution of Ni if the total number of particles N → ∞ in such a way that the fraction, Ni(0)/S = ξi, at each vertex is held fixed as N → ∞. In particular we can obtain the limit law for the graph S2, the two-leaf star which has three vertices and two edges.

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6

Itoh, Yoshiaki, Colin Mallows, and Larry Shepp. "Explicit sufficient invariants for an interacting particle system." Journal of Applied Probability 35, no. 03 (September 1998): 633–41. http://dx.doi.org/10.1017/s0021900200016284.

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We introduce a new class of interacting particle systems on a graph G. Suppose initially there are N i (0) particles at each vertex i of G, and that the particles interact to form a Markov chain: at each instant two particles are chosen at random, and if these are at adjacent vertices of G, one particle jumps to the other particle's vertex, each with probability 1/2. The process N enters a death state after a finite time when all the particles are in some independent subset of the vertices of G, i.e. a set of vertices with no edges between any two of them. The problem is to find the distribution of the death state, η i = N i (∞), as a function of N i (0). We are able to obtain, for some special graphs, the limiting distribution of N i if the total number of particles N → ∞ in such a way that the fraction, N i (0)/S = ξ i , at each vertex is held fixed as N → ∞. In particular we can obtain the limit law for the graph S 2, the two-leaf star which has three vertices and two edges.

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7

METZNER, WALTER, and CLAUDIO CASTELLANI. "TWO PARTICLE CORRELATIONS AND ORTHOGONALITY CATASTROPHE IN INTERACTING FERMI SYSTEMS." International Journal of Modern Physics B 09, no. 16 (July 20, 1995): 1959–83. http://dx.doi.org/10.1142/s021797929500080x.

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The wave function of two fermions, repulsively interacting in the presence of a Fermi sea, is evaluated in detail. We consider large but finite systems in order to obtain an unambiguous picture of the two-particle correlations. As recently pointed out by Anderson, in d≤2 dimensions the particles may be correlated even when situated on the Fermi surface. The “partial exclusion principle” for two particles with opposite spin on the same Fermi point is discussed, and related to results from the T-matrix approximation. Particles on different Fermi points are shown to be uncorrelated in d>1. Using the results for the two-particle correlations we find that the orthogonality effect induced by adding an extra particle to a (tentative) two-dimensional Fermi liquid is finite.

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8

Morvan, A., T. I. Andersen, X. Mi, C. Neill, A. Petukhov, K. Kechedzhi, D. A. Abanin, et al. "Formation of robust bound states of interacting microwave photons." Nature 612, no. 7939 (December 7, 2022): 240–45. http://dx.doi.org/10.1038/s41586-022-05348-y.

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AbstractSystems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2–9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

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9

SKOROHOD, A. V. "Infinite systems of randomly interacting particles." Random Operators and Stochastic Equations 1, no. 1 (1993): 1–14. http://dx.doi.org/10.1515/rose.1993.1.1.1.

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10

Karwowski, Jacek, and Kamil Szewc. "Quasi-Exactly Solvable Models in Quantum Chemistry." Collection of Czechoslovak Chemical Communications 73, no. 10 (2008): 1372–90. http://dx.doi.org/10.1135/cccc20081372.

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A separable model of N interacting particles, in which disjoint pairs of particles interact by arbitrary two-particle potentials while the remaining interactions obey the Hooke law, is discussed from a perspective of its applications in quantum chemistry. In particular, properties of three- and four-particle Hookean systems modeling He-like atoms, H2+ and H2 molecules and many exotic systems are analyzed. The energy spectra and the structure of the wavefunctions of quasi-exactly solvable Schrödinger equations which result from this analysis are investigated in some detail.

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11

LEV, B. I. "CELLULAR STRUCTURE IN CONDENSED MATTER." Modern Physics Letters B 27, no. 28 (October 24, 2013): 1330020. http://dx.doi.org/10.1142/s0217984913300202.

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In this paper, general description of a cellular structure formation in a system of interacting particles has been proposed. Analytical results are presented for such structures in colloids, systems of particles immersed into a liquid crystal and gravitational systems. It is shown that physical nature of formation of cellular structures in all systems of interacting particles is identical. In all cases, a characteristic of the cellular structure, depending on strength of the interaction, concentration of particles and temperature, can be obtained.

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12

KONDRATIEV, YURI, EUGENE LYTVYNOV, and MICHAEL RÖCKNER. "EQUILIBRIUM KAWASAKI DYNAMICS OF CONTINUOUS PARTICLE SYSTEMS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 02 (June 2007): 185–209. http://dx.doi.org/10.1142/s0219025707002695.

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We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the a priori explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).

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13

Stefanovich, Eugene V. "Moving Unstable Particles and Special Relativity." Advances in High Energy Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/4657079.

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In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

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14

Keim, Nathan C., and Joseph D. Paulsen. "Multiperiodic orbits from interacting soft spots in cyclically sheared amorphous solids." Science Advances 7, no. 33 (August 2021): eabg7685. http://dx.doi.org/10.1126/sciadv.abg7685.

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When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots—locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.

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15

Çamkıran, John, Fabian Parsch, and Glenn D. Hibbard. "A local orientational order parameter for systems of interacting particles." Journal of Chemical Physics 156, no. 9 (March 7, 2022): 091101. http://dx.doi.org/10.1063/5.0079985.

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Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we introduce a quantity E that captures the amount of pairwise informational redundancy among the bonds formed by a particle. Particles with larger E have less diversity in bond angles and thus simpler neighborhoods. We show that E possesses a number of intuitive mathematical properties, such as increasing monotonicity in the coordination number of Platonic polyhedral geometries. We demonstrate analytically that E is, in principle, able to distinguish a wide range of structures and conjecture that it is maximized by the icosahedral geometry under the constraint of equal sphere packing. An algorithm for computing E is described and is applied to the structural characterization of crystals and glasses. The findings of this study are generally consistent with existing knowledge on the structure of such systems. We compare E to the Steinhardt order parameter Q6 and polyhedral template matching (PTM). We observe that E has resolution comparable to Q6 and robustness similar to PTM despite being much simpler than the former and far more informative than the latter.

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16

Persson, B. N. J., and J. Biele. "Heat transfer in granular media with weakly interacting particles." AIP Advances 12, no. 10 (October 1, 2022): 105307. http://dx.doi.org/10.1063/5.0108811.

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We study the heat transfer in weakly interacting particle systems in vacuum. The particles have surface roughness with self-affine fractal properties, as expected for mineral particles produced by fracture, e.g., by crunching brittle materials in a mortar, or from thermal fatigue or the impact of micrometeorites on asteroids. We show that the propagating electromagnetic (EM) waves give the dominant heat transfer for large particles, while for small particles both the evanescent EM-waves and the phononic contribution from the area of real contact are important. As an application, we discuss the heat transfer in rubble pile asteroids.

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17

ALBEVERIO, SERGIO, HANNO GOTTSCHALK, and MINORU W. YOSHIDA. "SYSTEMS OF CLASSICAL PARTICLES IN THE GRAND CANONICAL ENSEMBLE, SCALING LIMITS AND QUANTUM FIELD THEORY." Reviews in Mathematical Physics 17, no. 02 (March 2005): 175–226. http://dx.doi.org/10.1142/s0129055x05002327.

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Euclidean quantum fields obtained as solutions of stochastic partial pseudo differential equations driven by a Poisson white noise have paths given by locally integrable functions. This makes it possible to define a class of ultra-violet finite local interactions for these models (in any space-time dimension). The corresponding interacting Euclidean quantum fields can be identified with systems of classical "charged" particles in the grand canonical ensemble with an interaction given by a nonlinear energy density of the "static field" generated by the particles' charges via a "generalized Poisson equation". A new definition of some well-known systems of statistical mechanics is given by formulating the related field theoretic local interactions. The infinite volume limit of such systems is discussed for models with trigonometric interactions using a representation of such models as Widom–Rowlinson models associated with (formal) Potts models at imaginary temperature. The infinite volume correlation functional of such Potts models can be constructed by a cluster expansion. This leads to the construction of extremal Gibbs measures with trigonometric interactions in the low-density high-temperature (LD-HT) regime. For Poissonian models with certain trigonometric interactions an extension of the well-known relation between the (massive) sine-Gordon model and the Yukawa particle gas connecting characteristic and correlation functionals is given and used to derive infinite volume measures for interacting Poisson quantum field models through an alternative route. The continuum limit of the particle systems under consideration is also investigated and the formal analogy with the scaling limit of renormalization group theory is pointed out. In some simple cases the question of (non-) triviality of the continuum limits is clarified.

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18

Fogarty, Thomás, Miguel Ángel García-March, Lea F. Santos, and Nathan L. Harshman. "Probing the edge between integrability and quantum chaos in interacting few-atom systems." Quantum 5 (June 29, 2021): 486. http://dx.doi.org/10.22331/q-2021-06-29-486.

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Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

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19

Feliachi, Ouassim, Marc Besse, Cesare Nardini, and Julien Barré. "Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (November 1, 2022): 113207. http://dx.doi.org/10.1088/1742-5468/ac9fc6.

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Abstract Kinetic and hydrodynamic theories are widely employed for describing the collective behavior of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the corresponding fluctuating hydrodynamics, for aligning self-propelled particles in the limit of dilute systems. We discover that fluctuations at kinetic level are not Gaussian and depend on the interactions among particles, but that only their Gaussian part survives in the hydrodynamic limit. At variance with fluctuating hydrodynamics for weakly interacting particles, we find that the noise variance at hydrodynamic level depends on the interaction rules among particles and is proportional to the square of the density, reflecting the binary nature of the aligning process. The results of this paper, which are derived for polar self-propelled particles with polar alignment, could be straightforwardly extended to polar particles with nematic alignment or to fully nematic systems.

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20

Alon, Ofir E. "Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles." Entropy 22, no. 12 (November 26, 2020): 1342. http://dx.doi.org/10.3390/e22121342.

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A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

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21

Li, Zhongyang, Fei Lu, Mauro Maggioni, Sui Tang, and Cheng Zhang. "On the identifiability of interaction functions in systems of interacting particles." Stochastic Processes and their Applications 132 (February 2021): 135–63. http://dx.doi.org/10.1016/j.spa.2020.10.005.

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22

Al-Nimr, M. A., and V. S. Arpaci. "Radiative Properties of Interacting Particles." Journal of Heat Transfer 114, no. 4 (November 1, 1992): 950–57. http://dx.doi.org/10.1115/1.2911906.

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Two statistical models for the radial distribution function are proposed. In terms of these models, analytical expressions for the radiation efficiency factors of random homogeneous systems are derived. The Planck and Rosseland mean absorption coefficients are evaluated and the ratio of dependent over independent mean absorption coefficients is given. The role of the far-field and the near-field effects on radiation is investigated. The near-field effect on the scattered radiation is found to be negligible compared to the far-field effect. The effect of particle interaction is demonstrated by a simple transport problem.

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23

Wagner, Caleb G., Michael F. Hagan, and Aparna Baskaran. "Steady states of active Brownian particles interacting with boundaries." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (January 1, 2022): 013208. http://dx.doi.org/10.1088/1742-5468/ac42cf.

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Abstract An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach nontrivial nonequilibrium steady states with intriguing phenomenology, such as accumulation at boundaries, ratchet effects, and long-range depletion interactions. Nevertheless, theoretical analysis of these phenomena has proven difficult. Here, we address this theoretical challenge in the context of non-interacting particles in two dimensions, basing our analysis on the steady-state Smoluchowski equation for the one-particle distribution function. Our primary result is an approximation strategy that connects asymptotic solutions of the Smoluchowski equation to boundary conditions. We test this approximation against the exact analytic solution in a 2D planar geometry, as well as numerical solutions in circular and elliptic geometries. We find good agreement so long as the boundary conditions do not vary too rapidly with respect to the persistence length of particle trajectories. Our results are relevant for characterizing long-range flows and depletion interactions in such systems. In particular, our framework shows how such behaviors are connected to the breaking of detailed balance at the boundaries.

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24

Tovbin, Yu K. "Kinetic Equations of Physicochemical Processes with Allowance for Multi-Particle Effects in the Lattice Gas Model." Russian Journal of Physical Chemistry A 96, no. 2 (February 2022): 278–92. http://dx.doi.org/10.1134/s0036024422020273.

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Abstract A way of deriving kinetic equations of physicochemical processes in dense phases is developed on the basis of the discrete–continuous description of the spatial distribution of components in the lattice gas model (LGM), with allowance for multi-particle effects. The emergence of multi-particle effects is associated with the simultaneous influence of all neighbors on the rate of the elementary stage with the participation of a given particle. They include multi-particle potentials of interaction, including quantum–chemical energy calculations, the effect the configurations of neighboring molecules have on the internal motion of the central particle, and the effects of the indirect correlation of interacting particles that occurs for any potential of pair interaction, assuming the internal motions of particles do not depend on the local configurations of neighbors. Multi-particle effects take models beyond the quasi-chemical approximation, which reflects direct correlations of interacting particles through pair distribution functions, and require the use of correlation functions for a larger number of particles in describing their kinetics. The rates of elementary one- and two-node stages are calculated within the theory of absolute rates of reactions in non-ideal reaction systems. Ways of calculating approximate rates of the elementary stages of mono- and bimolecular processes are discussed, along with the possibilities of generalizing the derived equations.

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25

Rallison, J. M. "Brownian diffusion in concentrated suspensions of interacting particles." Journal of Fluid Mechanics 186 (January 1988): 471–500. http://dx.doi.org/10.1017/s0022112088000230.

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In this paper we set out to calculate the self-diffusivity of a Brownian particle in a concentrated suspension. The problem is treated by regarding the neighbours of a test particle as forming a ‘cage’. For short time t < tc, say, the particle is partially constrained by the cage and an equation is proposed to describe the coupled dynamics of particle and cage. The equation is shown to be asymptotically exact in some cases and acceptably accurate for other simple systems by comparing with Monte Carlo simulations. For times t > tc, the particle diffuses sufficiently far to escape its original cage (and finds itself in a new one). A quantitative estimate for tc is proposed and verified for a system of rod-like particles by numerical simulation. By combining these two ingredients an estimate of the long-time (t [Gt ] tc) self-diffusivity of a particle is made. For rod-like particles tc is the reptation time, and the result here is compared with the theory of Doi & Edwards (1978a, b), and with experiment. For a system of spheres comparison is made with the tracer light-scattering experiments of Kops-Werkhoven & Fijnaut (1982). In both cases good agreement is found when the particle concentration is sufficiently high.

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26

Berlyand, Leonid, Robert Creese, Pierre-Emmanuel Jabin, and Mykhailo Potomkin. "Continuum Approximations to Systems of Correlated Interacting Particles." Journal of Statistical Physics 174, no. 4 (December 15, 2018): 808–29. http://dx.doi.org/10.1007/s10955-018-2205-8.

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27

MAZROUI, M'HAMMED, and YAHIA BOUGHALEB. "SURFACE DIFFUSION IN SYSTEMS OF INTERACTING BROWNIAN PARTICLES." International Journal of Modern Physics B 15, no. 16 (June 30, 2001): 2193–247. http://dx.doi.org/10.1142/s0217979201001649.

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The paper reviews recent results on diffusive phenomena in two-dimensional periodic potential. Specifically, static and dynamic properties are investigated by calculating different correlation functions. Diffusion process is first studied for one-dimensional system by using the Fokker–Planck equation which is solved numerically by the matrix continued fraction method in the case of bistable potential. The transition from hopping to liquid-like diffusion induced by variation of some parameters is discussed. This study will therefore serve to demonstrate the influence of this form of potential. Further, an analytical approximation for the dc-conductivity is derived for a wide damping range in the framework of the Linear Response Theory. On the basis of this expression, calculations of the ac conductivity of two-dimensional system with Frenkel–Kontorova pair interaction in the intermediate friction regime is performed by using the continued fraction expansion method. The dc-conductivity expression is used to determine the rest of the development. By varying the density of mobile ions we discuss commensurability effects. To get information about the diffusion mechanism, the full width at half maximum λω(q), of the quasi-elastic line of the dynamical structure factor S(q,ω) is computed. The calculations are extended up to large values of q covering several Brillouin zones. The analysis of λω(q) with different parameters shows that the most probable diffusion process in good two-dimensional superionic conductors consists of a competition between a back correlated hopping in one direction and forward correlated hopping in addition to liquid-like motions in the other direction.

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28

Song, T., and R. M. Roshko. "Preisach model for systems of interacting superparamagnetic particles." IEEE Transactions on Magnetics 36, no. 1 (2000): 223–30. http://dx.doi.org/10.1109/20.822533.

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29

Blank, M. L. "Self-consistent mappings and systems of interacting particles." Doklady Mathematics 83, no. 1 (February 2011): 49–52. http://dx.doi.org/10.1134/s1064562411010133.

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30

Ohtsuki, T., and T. Keyes. "Anomalous dynamics of interacting particles in random systems." Journal of Physics A: Mathematical and General 18, no. 3 (February 21, 1985): L171—L174. http://dx.doi.org/10.1088/0305-4470/18/3/013.

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31

Hubal, Halyna M. "The generalized kinetic equation for symmetric particle systems." MATHEMATICA SCANDINAVICA 110, no. 1 (March 1, 2012): 140. http://dx.doi.org/10.7146/math.scand.a-15201.

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Анотація:

The generalized kinetic equation is obtained for symmetric system of many particles interacting via a pair potential. A representation of a solution of the Cauchy problem for the BBGKY hierarchy is used in the form of an expansion over particle groups whose evolution is governed by the cumulants (semi-invariants).

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32

Euán-Díaz, Edith C., Salvador Herrera-Velarde, Vyacheslav R. Misko, François M. Peeters, and Ramón Castañeda-Priego. "Single-File Diffusion of Driven Interacting Colloids." Biophysical Reviews and Letters 09, no. 04 (December 2014): 413–34. http://dx.doi.org/10.1142/s1793048014400086.

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Анотація:

The dynamical properties of interacting colloids spatially restricted to move in one-dimensional channels [J. Chem. Phys. 133, 114902 (2010)] and subjected to external periodic energy landscapes [Phys. Rev. E 86, 081123 (2012)] have been recently reported in terms of the long-time self-diffusion behavior. However, the full description of the mean-square displacement, ranging from short times to long times, is still missing. Thus, by means of Brownian dynamics computer simulations, we revisit the process known as single-file diffusion in driven interacting colloidal systems at all time scales. In particular, we review three different pair potentials, namely, Weeks–Chandler–Andersen, Yukawa and superparamagnetic potentials. We mainly focus on the importance of the correlation between particles via the coupling among hydrodynamic interactions and the external periodic field, resulting in nontrivial particle dynamics along the file in systems composed of repulsively interacting particles. [Formula: see text] Special Issue Comments: This article reviews results on the dynamical properties of interacting colloids in a single file when they are subjected to external periodic energy landscapes presented before in [J. Chem. Phys. 33, 114902 (2010)] and [ Phys. Rev. E 86, 081123 (2012)]. We analyze different interactions that cover from short to long ranges of the interparticle potentials. We mainly focus on the importance of the correlation between particles via the coupling among the hydrodynamic interactions and the external periodic field. Note from Publisher: In the captions of Figs. 1 through 4, "??" has appeared where the number 9 should appear. In table 1, in the WCA section, the variable "φ" shows the values: 0.2,0.3,0.3,0.3,0.3,0.3. The correct values are: 0.2, 0.3, 0.4, 0.5 , 0.6 , 0.7.

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33

Melnikov, G. А., N. М. Ignatenko, V. V. Suchilkin, and А. S. Gromkov. "Formation of Cluster Systems in Chaotic Condensed Media." Proceedings of the Southwest State University. Series: Engineering and Technology 13, no. 2 (July 25, 2023): 164–76. http://dx.doi.org/10.21869/2223-1528-2023-13-2-164-176.

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Purpose. The study of cluster formation in a system of chaotically moving and interacting particles taking into account the Efimov effect and the "golden" section.Methods. Methods of mathematical modeling, quantum mechanics, a model of solid spheres, and a cluster model were used.Results. Within the framework of the proposed work, it is noted that in a three-particle system of particles, it is possible to form their spatial configuration in the form of a "golden" triangle, and in the case of an excited state of two particles, the third particle is far enough away from the other two, it is this configuration that corresponds to the conditions for the occurrence of the Efimov effect in a three-particle system.Based on the mathematical formalism of the description of self-organization processes in the work, it is shown that in chaotic environments within the framework of the Efimov model, with the involvement of the "golden" section in the mutual arrangement of three interacting particles, it is possible to form disk-shaped clusters containing a "magic" number of particles. In the structure of these clusters, the formation of quantum-dimensional regions in the form of a torus is possible. The parameters of such areas are defined.Conclusion. The described model of the formation and decay of disk-shaped clusters, taking into account the Efimov effect and the "golden" section rule, allows us, without resorting to a complex solution of equations in the three-body problem, to obtain important relations following from strict theories. The proposed approach implies the possibility of self-organization of clusters and the formation of quantum-dimensional regions in their structure, for example, in the form of a torus with a potential well, capable of capturing charged particles and determining their energy spectrum, as well as explaining the appearance of spectral bands in the IR spectra of substances.The proposed approach may be of practical importance, for example, for predicting the IR spectra of liquids, the presence of quantum dots in liquids with a wide spectrum of excitation from UV to IR radiation.

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34

Grotto, Francesco, Eliseo Luongo, and Mario Maurelli. "Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems." Nonlinearity 36, no. 12 (November 17, 2023): 7149–90. http://dx.doi.org/10.1088/1361-6544/ad0aab.

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Abstract We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.

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35

Wang, Yu-Qing, and Zi-Huan Zhang. "Cluster mean-field dynamics in one-dimensional TASEP with inner interactions and Langmuir dynamics." Modern Physics Letters B 33, no. 02 (January 20, 2019): 1950012. http://dx.doi.org/10.1142/s021798491950012x.

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In the area of statistical physics, totally asymmetric simple exclusion process (TASEP) is treated as one of the most important driven-diffusive systems. It contains profound non-equilibrium statistical physics mechanisms due to being the paradigm model like Ising model. Different with previous work, a one-dimensional TASEP coupled with inner interactions and Langmuir dynamics is taken into account. Weak coupled binding and unbinding rates are introduced in the proposed model. Bond breaking and making mechanisms of self-driven particles illustrating the unidirectional movement of protein motors are investigated by means of performing cluster mean-field analyses. Dynamics in the proposed system dominated by the competition between the attraction effect and the repulsion one are found to depend on the specific value of the interaction energy of these active particles. The research work will be helpful for understanding non-equilibrium statistical behaviors of interacting particle systems.

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36

CURILEF, SERGIO. "NONEXTENSIVE MICROSCOPIC BEHAVIOR OF LONG-RANGE INTERACTING PARTICLES IN PERIODIC MEDIA." International Journal of Modern Physics C 11, no. 03 (May 2000): 629–34. http://dx.doi.org/10.1142/s0129183100000547.

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This work presents a possible way to study the long-range interacting particles in finite-infinite (mesoscopic-macroscopic) systems with periodic boundary conditions. A symmetric lattice and their contributions over all space are used in the problem. In the present model, we assume that at long distances, the two-body attractive potential decays as a 1/rα law. We verified that the potential in any particle converges (diverges) when the interactions are short(long)-ranged. On the other hand, forces in any particle converge rapidly in all cases. However, we adopt a nonextensive scaling and we guarantee that the potential converges anywhere.

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37

Rieser, Jakob, Mario A. Ciampini, Henning Rudolph, Nikolai Kiesel, Klaus Hornberger, Benjamin A. Stickler, Markus Aspelmeyer, and Uroš Delić. "Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles." Science 377, no. 6609 (August 26, 2022): 987–90. http://dx.doi.org/10.1126/science.abp9941.

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Arrays of optically trapped nanoparticles have emerged as a platform for the study of complex nonequilibrium phenomena. Analogous to atomic many-body systems, one of the crucial ingredients is the ability to precisely control the interactions between particles. However, the optical interactions studied thus far only provide conservative optical binding forces of limited tunability. In this work, we exploit the phase coherence between the optical fields that drive the light-induced dipole-dipole interaction to couple two nanoparticles. In addition, we effectively switch off the optical interaction and observe electrostatic coupling between charged particles. Our results provide a route to developing fully programmable many-body systems of interacting nanoparticles with tunable nonreciprocal interactions, which are instrumental for exploring entanglement and topological phases in arrays of levitated nanoparticles.

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38

van Meurs, Patrick. "The continuum limit of interacting dislocations on multiple slip systems." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 102. http://dx.doi.org/10.1051/cocv/2020038.

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In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a Γ-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we consider n edge dislocations in multiple slip systems. Since the interaction potential of dislocations has a logarithmic singularity at zero with a sign that depends on the orientation of the slip systems, the interaction energy is unbounded from below. To make the minimization problem of this energy meaningful, we follow the common approach to regularise the interaction potential over a length-scale δ > 0. The novelty of our result is that we leave the type of regularisation general, and that we consider the joint limit n →∞ and δ → 0. Our result shows that the limit behaviour of the interaction energy is not affected by the type of the regularisation used, but that it may depend on how fast the size (i.e., δ) decays as n →∞.

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39

Yukalov, V. I. "Particle fluctuations in systems with Bose–Einstein condensate." Laser Physics 34, no. 11 (October 10, 2024): 113001. http://dx.doi.org/10.1088/1555-6611/ad8221.

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Abstract Particle fluctuations in systems, exhibiting Bose–Einstein condensation, are reviewed in order to clarify the basic points that attract high interest and often confront misunderstanding. It is explained that the so-called ‘grand canonical catastrophe’, claiming the occurrence of catastrophic particle fluctuations in the condensed phase, treated by grand canonical ensemble, does not exist. What exists is the incorrect use of the grand canonical ensemble, where gauge symmetry is not broken, while the correct description of the condensed phase necessarily requires gauge symmetry breaking. The ideal Bose gas has no catastrophic condensate fluctuations, and moreover there are no condensate fluctuations at all, as soon as gauge symmetry is broken. However it does have anomalous fluctuations of uncondensed particles, which implies its instability. For interacting particles, there are no condensate fluctuations, as soon as gauge symmetry is broken, and anomalous fluctuations of uncondensed particles, when correctly calculated, do not appear. Particle fluctuations in the systems of trapped atoms are discussed. Canonical ensemble and grand canonical ensemble with broken gauge symmetry are equivalent with respect to the number of particle scaling.

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40

CALSAMIGLIA, J., L. HARTMANN, W. DÜR, and H. J. BRIEGEL. "ENTANGLEMENT AND DECOHERENCE IN SPIN GASES." International Journal of Quantum Information 05, no. 04 (August 2007): 509–23. http://dx.doi.org/10.1142/s0219749907003018.

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We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non–Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non–collective decoherence processes are studied. We give quantitative results for the Boltzmann gas and also for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice. These models can be simulated efficiently for systems of mesoscopic sizes (N ~ 105).

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41

OITMAA, J. "RECENT DEVELOPMENTS IN STRONGLY INTERACTING LATTICE SYSTEMS." International Journal of Modern Physics B 13, no. 05n06 (March 10, 1999): 697–708. http://dx.doi.org/10.1142/s021797929900059x.

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I give an overview of areas of recent and current research in the theoretical study of strongly interacting lattice systems, in the areas of lattice spin models (magnetism), lattice electron models (superconductivity) and lattice gauge models (elementary particles). The emphasis is on novel and interesting physics, and recent results.

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42

Carinci, Gioia, Cristian Giardinà, and Frank Redig. "Exact formulas for two interacting particles and applications in particle systems with duality." Annals of Applied Probability 30, no. 4 (August 2020): 1934–70. http://dx.doi.org/10.1214/19-aap1548.

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43

Bertacchi, Daniela, Fábio Prates Machado, and Fabio Zucca. "Local and Global Survival for Nonhomogeneous Random Walk Systems on Z." Advances in Applied Probability 46, no. 1 (March 2014): 256–78. http://dx.doi.org/10.1239/aap/1396360113.

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We study an interacting random walk system on ℤ where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability ln. We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability pn ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases ½ - ln ~ ± 1 / nα, pn = 1 and ½ - ln ~ ± 1 / nα, 1 - pn ~ 1 / nβ (where α, β > 0).

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44

Bertacchi, Daniela, Fábio Prates Machado, and Fabio Zucca. "Local and Global Survival for Nonhomogeneous Random Walk Systems on Z." Advances in Applied Probability 46, no. 01 (March 2014): 256–78. http://dx.doi.org/10.1017/s0001867800007035.

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Анотація:

We study an interacting random walk system on ℤ where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability l n . We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability p n ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases ½ - l n ~ ± 1 / n α, p n = 1 and ½ - l n ~ ± 1 / n α, 1 - p n ~ 1 / n β (where α, β > 0).

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45

Delgado, Rosario, F. Javier López, and Gerardo Sanz. "Local conditions for the stochastic comparison of particle systems." Advances in Applied Probability 36, no. 4 (December 2004): 1252–77. http://dx.doi.org/10.1239/aap/1103662966.

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We study the stochastic comparison of interacting particle systems where the state space of each particle is a finite set endowed with a partial order, and several particles may change their value at a time. For these processes we give local conditions, on the rates of change, that assure their comparability. We also analyze the case where one of the processes does not have any changes that involve several particles, and obtain necessary and sufficient conditions for their comparability. The proofs are based on the explicit construction of an order-preserving Markovian coupling. We show the applicability of our results by studying the stochastic comparison of infinite-station Jackson networks and batch-arrival, batch-service, and assemble-transfer queueing networks.

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46

Delgado, Rosario, F. Javier López, and Gerardo Sanz. "Local conditions for the stochastic comparison of particle systems." Advances in Applied Probability 36, no. 04 (December 2004): 1252–77. http://dx.doi.org/10.1017/s0001867800013392.

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Анотація:

We study the stochastic comparison of interacting particle systems where the state space of each particle is a finite set endowed with a partial order, and several particles may change their value at a time. For these processes we give local conditions, on the rates of change, that assure their comparability. We also analyze the case where one of the processes does not have any changes that involve several particles, and obtain necessary and sufficient conditions for their comparability. The proofs are based on the explicit construction of an order-preserving Markovian coupling. We show the applicability of our results by studying the stochastic comparison of infinite-station Jackson networks and batch-arrival, batch-service, and assemble-transfer queueing networks.

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47

Bruna, Maria, Martin Burger, Antonio Esposito, and Simon M. Schulz. "Phase Separation in Systems of Interacting Active Brownian Particles." SIAM Journal on Applied Mathematics 82, no. 4 (August 2022): 1635–60. http://dx.doi.org/10.1137/21m1452524.

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48

Ignat’ev, Yu G. "Collisionless self-gravitating statistical systems of scalarly interacting particles." Gravitation and Cosmology 22, no. 1 (January 2016): 20–25. http://dx.doi.org/10.1134/s0202289316010072.

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49

Tomaselli, M. "Virtual particles versus superconductive vacuum polarizations in interacting systems." Physical Review C 48, no. 5 (November 1, 1993): 2290–301. http://dx.doi.org/10.1103/physrevc.48.2290.

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50

Wirth, S. "Magnetization reversal in systems of interacting magnetically hard particles." Journal of Applied Physics 77, no. 8 (April 15, 1995): 3960–64. http://dx.doi.org/10.1063/1.358578.

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