Many-particle Model Research Articles

Lowest-order relativistic interaction between lattice vibrations and internal degrees of freedom of a nucleus

A moving nucleus experiences a Lorentz contraction and spin rearrangement due to relativity. A nucleus that oscillates in a molecule or solid due to vibrations will undergo minor relativistic modifications which are a result of the vibrations, indicative of a relativistic phonon-nuclear interaction. The derivation of the lowest-order interaction from the many-particle Dirac model is reviewed. The Dirac model with a realistic potential model is not covariant, which is a source of concern. The lowest-order phonon-nuclear interaction obtained from a covariant two-body Bethe–Salpeter model is found to be similar to the interaction obtained from the Dirac model, supporting the notion that the interaction is not an artifact. Matrix elements of the lowest-order interaction are expressed in terms of one-body operators, which facilitates evaluation and allows for quantitative estimates of the magnitude.

Structure of low-lying states of 9Ве nucleus

Glauber's theory of multiple scattering is applied to the calculation of differential cross sections and polarization characteristics of particle scattering on light nuclei. All calculations were carried out within the framework of a reliable spectroscopic approach to nuclear reactions. Its essence consists in the use of nuclear models that reproduce practically all the spectroscopic characteristics of the nuclei under consideration. These include three-particle models of 6Li and 9Be nuclei, a many-particle shell model for nuclei with А = 6–14, and a particle-hole model of shells for nuclei with А = 15; three-body models for the 8Li and 9Li nuclei and a two-particle αt-model for the 7Li nucleus. As our experience shows, when implementing the spectroscopic approach, when the dominant mechanism of the process is also established, one can not only obtain a description of the main characteristics of the process, but also rely on the predictive nature of the theory. In the present work, the results obtained are supplemented by calculations of the structure of the low-lying 5/2+ and 5/2– levels. This allows us to draw a general conclusion: the negative parity levels in 9Be, in which the valence neutron is in the p state, do not have a halo structure; at the same time, low-lying levels of positive parity, in which the valence neutron passes into the next (2s-1d) shell, have such. A special place is occupied by our recent direct evidence of the halo structure of low-lying excited states of the 9Be nucleus with quantum numbers 1/2+ and 3/2+. Within the framework of the ααn model of the 9-Be nucleus, it was shown that a valence neutron with a high probability is located at 11 fm from the center of gravity of two α-particles, while in the 3/2- ground state this distance is several times smaller. The conclusions about the structure of low-lying levels of 9Be, obtained on the basis of the ααn model, are supported by calculations of p9Be scattering: only taking into account the halo structure makes it possible to reproduce the experimental data on inelastic scattering to positive parity levels.

Analyticity constraints bound the decay of the spectral form factor

Quantum chaos cannot develop faster than λ≤2π/(ℏβ) for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent λ is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponentη, that we introduce to characterize the early-time decay of the SFF, is bounded as η≤π/(2ℏβ). This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.

Kac’s Process with Hard Potentials and a Moderate Angular Singularity

We investigate Kac’s many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate independent of the number of particles N. As consequences, we obtain a wellposedness result for the corresponding Boltzmann equation and propagation of chaos in the many-particle limit Nrightarrow infty .

Quantum Hydrodynamics of Spinning Particles in Electromagnetic and Torsion Fields

We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial and torsion fields. The consistent hydrodynamical formulation is constructed for the many-particle quantum system of Dirac fermions on the basis of the nonrelativistic Pauli-like equation obtained via the Foldy–Wouthuysen transformation. With the help of the Madelung decomposition approach, the explicit relations between the microscopic and macroscopic fluid variables are derived. The closed system of equations of quantum hydrodynamics encompasses the continuity equation, and the dynamical equations of the momentum balance and the spin density evolution. The possible experimental manifestations of the torsion in the dynamics of spin waves is discussed.

Ellipsoidal inhomogeneity with anisotropic incoherent interface. Multipole series solution and application to micromechanics

The ellipsoidal inhomogeneity with transversely isotropic incoherent interface is considered in the conductivity and elasticity context. The general imperfect interface is modeled by the first order approximation of thin transversely isotropic interphase layer. This model expands the Gurtin et al. (1998) theory of curved deformable interfaces in solids with a nanometer-scale microstructure to the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface moduli. The rigorous analytical solution to the conductivity and elasticity problems has been obtained by the multipole expansion method in terms of ellipsoidal solid harmonics. An accurate fulfillment of the imperfect interface conditions reduces the model boundary value problem to the linear algebraic system for multipole strengths. These results apply equally to the inhomogeneities with anisotropic interphases and nano level incoherent interfaces. The obtained solutions are valid for the non-uniform far loading and are readily incorporated in the many-particle (finite cluster or representative unit cell) model of heterogeneous solid with anisotropic incoherent interface. The tensors of effective conductivity and elastic stiffness of composite with ellipsoidal inhomogeneities are evaluated using Maxwell homogenization scheme. The obtained accurate numerical data indicate that the effective properties of composite may vary widely due to shape of inhomogeneities and the interface anisotropy ratio. Taking the incoherency of interface into account may increase reliability of predicting the behavior of nanostructured solids.

Many-particle radiative heat transfer in a nonreciprocal graphene plasmonic cavity

Due to the presence of many-body interactions, strong enhancement effects of heat flux and rich thermophysical phenomena are possible. In this work, we build a many-particle radiative heat transfer model inside a cavity consisting of two graphene sheets. By introducing an additional particle and the graphene cavity in the near field, the heat transfer between two particles is discussed. We show that the mutual interactions greatly enhance the heat exchange and observe an interference fringe pattern. Moreover, the nonreciprocal plasmons on the drift-biased graphene provide a rotational degree of freedom to control the heat transfer and can be used to effectively rectify the thermal energy. Our findings extend recent progress in understanding and tailoring energy exchange in the many-body systems.

Спектр возбуждения ядра 10B при захвате реальных и виртуальных α-частиц

In this paper within the multi-particle shell model the excitation spectra of 10B nucleus in lithium reactions of triton and a-particle clusters transfer were calculated using the summation of the corresponding spectroscopic S-factors. It is shown that the difference between excitation spectra of 10B nucleus in lithium reaction of a-cluster transfer and in the reaction of radiation capture 6Li(a, g)10B is due to the structural peculiarities of the states of 10В nucleus in near threshold region. In (a, g) reaction on 6Li nucleus the resonance structure of cross sections is observed. The observable resonances are due to small a-widths of the excited states of 10B nucleus. As the wave functions of the ground state of 6,7Li nuclei, as well as the ground and excited states of the 10B nucleus, we used the well-known wave functions of the many-particle shell model calculated at the Scientific Research Institute of Nuclear Physics, M. Lomonosov Moscow State University. The large escape of resonance monochromatic g-quanta with energy Eg = 5.1639 and Eg = 6.025 МэВ in the process on 6Li nucleus confirms the possibility of use of the reaction for diagnostics of fusion plasma by adding a definite amount of lithium isotopes into the plasma.

Field-Induced Deformation and Structure Changes in a Magnetic Polymersome: Many-Particle Simulation

Coarse-grained molecular dynamics simulation is performed to analyse structure and deformation response of a magnetic polymersome – a submicron hollow capsule whose membrane is made of amphiphilic block-copolymer, and the intramembrane space is filled with magnetic nanoparticles. The major prospects of these objects are related to controlled drug release. The developed many-particle model is used to calculate equilibrium magnetized configurations of polymersomes with different intensity of magnetic interparticle coupling. The analysis of those data reveals that under external magnetic field, an initially spherical capsule stretches along the field direction assuming a spheroid-like shape. This behaviour is caused by the field-driven tendency of the nanoparticles to aggregate inside the polymersome membrane. At weak interparticle magnetic interaction no extended chains are observed. Accordingly, the deformation and density redistribution are relatively small. In a polymersome with strong interparticle coupling the nanoparticles self-organize in long chains aligned with the field, and this induces considerable elongation of the polymersome along with accumulation of the majority of the nanoparticles in the “equatorial” zone of the membrane of the capsule.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Comprehensive Study on Unusual Polarization Behaviors of the LiFePO4 Electrode Using Mathematical Modeling

LiFePO4 has been commercialized as a cathode material for high-power lithium-ion batteries for power-tools and hybrid-vehicles because of its low cost, high power, and thermal stability. The behavior of LiFePO4 electrodes, consisting of fine nanoparticles (30-150 nm), are influenced by the interactions between the constituent particles. In addition, the non-monotone potential profile of LiFePO4 single particles, which is characteristic of a many-particle model and originates from two-phase reactions, complicates the polarization behavior of the electrode's charge/discharge profile. One of the unique polarization behaviors of the LiFePO4 electrode is path-dependence[1], wherein the polarization during charge and discharge is influenced by the previous charge and discharge. In addition, the so-called memory-effect was recently reported as an unique polarization behavior of LiFePO4 electrode[2]. Here, an extra polarization bump appears in the (dis)charging profiles at around the SOC at which the previous partial (dis)charge was stopped. These unique polarization behaviors have been investigated in the past using mathematical simulations[3]. However, the detailed cause for the polarization has not been clarified yet. In this study, we investigated the polarization behavior of a LiFePO4 electrode by mathematical simulations using a many-particle model and deciphered the behavior using an active population[4]. It was clarified that the polarization of the memory-effect was caused by the reduction of the active population by relaxation during a previous rest. Through this mechanism, we suggested a new polarization behavior, so-called relaxation-induced-polarization (RIP), which affects the polarization in the (dis)charging profile after the rest. The RIP can be triggered by only the last rest, whereas the appearance of the memory-effect needs specific processes with at least three steps. We also investigated path-dependence behavior, which is a well-known but unusual polarization behavior of LiFePO4 electrodes, and suggested a mechanism for this behavior. Unlike the former two polarizations, the path-dependence was considered to be caused by kinetically inhomogeneous reactions for each particle. Using mathematical simulations incorporating a many-particle model, we further predicted that narrowing the particle size distribution was effective to reduce this polarization, but it cannot be fully erased. The comprehensive understanding of the three polarization behaviors by our model can give us more accurate estimation of the state-of-charge of Li-ion batteries with the LiFePO4 electrode.

Stochastic many-particle model for LFP electrodes

In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to $$\text {LiFePO}_{4}$$ (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage–current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage–charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.

Comprehensive Study of the Polarization Behavior of LiFePO4 Electrodes Based on a Many-Particle Model

The unique polarization behavior of LiFePO4 electrodes was investigated using mathematical simulations with a many-particle model, which have a non-monotonic potential profile for each LiFePO4 particle, and analyzed by the active population concept. The present simulations reveal two known polarization behaviors, namely the memory effect and path dependence. Notably, a hitherto unknown polarization behavior, the so-called relaxation-induced polarization (RIP), was also identified. The memory effect requires, at a minimum, a sequential four-step operation. By comparison, RIP is triggered only by a one-step operation, namely a long rest. In effect, the polarization associated with the memory effect and RIP was caused by a reduction of the active particles in the two-phase region via relaxation during a rest. The path-dependence mechanism was attributed to kinetically inhomogeneous reactions for each particle. We further found that narrowing the particle size distribution was an effective means to reduce polarization viz. the memory effect and path dependence of LiFePO4 electrodes. However, RIP could not be suppressed by narrowing the particle size distribution. A comprehensive understanding of these polarization behaviors with our model provides a more accurate way to estimate the state of charge in Li-ion batteries with LiFePO4 electrodes.

Hamiltonian formulation of systems with balanced loss–gain and exactly solvable models

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Classical many-particle systems with unique disordered ground states.

Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By contrast, the few previously known disordered classical ground states of many-particle systems are all high-entropy (highly degenerate) states. Here we show computationally that our recently proposed "perfect-glass" many-particle model [Sci. Rep. 6, 36963 (2016)10.1038/srep36963] possesses disordered classical ground states with a zero entropy: a highly counterintuitive situation . For all of the system sizes, parameters, and space dimensions that we have numerically investigated, the disordered ground states are unique such that they can always be superposed onto each other or their mirror image. At low energies, the density of states obtained from simulations matches those calculated from the harmonic approximation near a single ground state, further confirming ground-state uniqueness. Our discovery provides singular examples in which entropy and disorder are at odds with one another. The zero-entropy ground states provide a unique perspective on the celebrated Kauzmann-entropy crisis in which the extrapolated entropy of a supercooled liquid drops below that of the crystal. We expect that our disordered unique patterns to be of value in fields beyond glass physics, including applications in cryptography as pseudorandom functions with tunable computational complexity.

Explicit inclusion of electronic correlation effects in molecular dynamics

We design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for the inhomogeneity inherent in the process of quantum molecular dynamics (MD) simulation. We also propose an efficient algorithm based on the second-moment approximation to the electronic density of states for the search of the optimal variation parameters, from which the effective renormalized interatomic MD potentials are fully determined. By considering a minimal one-correlated-orbital Anderson many-particle model based on tight-binding hopping integrals, this fast GA-MD method is benchmarked with that using exact diagonalization to solve the GA variational parameters. In the infinite damping limit, the efficiency and accuracy are illustrated. This novel method will open up an unprecedented opportunity enabling large-scale quantum MD simulations of strongly correlated electronic materials.

Concurrent two-scale model for the viscoelastic behavior of elastomers filled with hard nanoparticles

A dynamic two-scale model is developed for describing the mechanical behavior of elastomers filled with hard nanoparticles. Using nonequilibrium thermodynamics, a closed system of evolution equations is derived, coupling continuum mechanics with a fine-scale description on the level of filler particles. So doing, a constitutive stress–strain relation emerges that is applicable to transient situations. In addition to the number density of filler particles, the particle arrangement is captured by the distribution of the difference vector between two representative interacting particles, which makes this model efficient in comparison with many-particle models. The two-particle model presented here is analyzed numerically in oscillatory deformation, for two purposes. First, the nonlinearity of the model is studied in detail, in terms of the Payne effect, that compares favorably with the literature. And second, the two-particle model is compared with a corresponding many-particle model in the literature.

Water vapor clustering in the field of Na+ cation inside a nanopore with hydrophilic walls. 2. Thermodynamic properties

The bicanonical statistical ensemble method has been used to calculate at the molecular level the free energy, entropy, and work of hydration of single-charged sodium cation in a model planar nanopore with structureless hydrophilic walls. The calculations have been performed in terms of a detailed many-particle model of intermolecular interactions calibrated with respect to experimental data on the free energy and enthalpy of the initial reactions of attachment in water vapor. In contrast to chlorine anion, at initial stages of formation, the hydration shell of sodium cation has a loose chain structure, which is reflected in the character of the interaction with pore walls and the behavior of entropy. Under the conditions of weakly hydrophilic walls, the system loses its stability; however, the stability remains preserved in a pore with strongly hydrophilic walls. Hydrophilic walls stabilize the system and shift the onset of hydration toward lower vapor pressures by several orders of magnitude.

Level densities of heavy nuclei in the shell model Monte Carlo approach

Nuclear level densities are necessary input to the Hauser-Feshbach theory of compound nuclear reactions. However, the microscopic calculation of level densities in the presence of correlations is a challenging many-body problem. The configurationinteraction shell model provides a suitable framework for the inclusion of correlations and shell effects, but the large dimensionality of the many-particle model space has limited its application in heavy nuclei. The shell model Monte Carlo method enables calculations in spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods and has proven to be a powerful tool in the microscopic calculation of level densities. We discuss recent applications of the method in heavy nuclei.

Anomalous Voltage Change in Charge and Discharge Curves for Electrode Materials Showing Plateau-like Behavior

An overvoltage phenomenon was investigated that occurs during partial charge-discharge experiments for LiFePO4 as electrode material showing a plateau-like behavior. The temperature was varied in order to determine the influence on the voltage change (overvoltage). This overvoltage effect was recently reported by another group and discussed in light of a many-particle model. However these measurements were carried out only at room temperature. Hence temperature influence was supposed to be worth of consideration. Indeed, an increased overvoltage was observed at lower temperature, while an opposite effect was obtained at higher temperature. Increasing the number of partial charge-discharge cycles leads to an interference of single voltage bumps, but the overvoltage seems to saturate at a given voltage level.