Range Effective Interaction Research Articles

Phase Diagram for Social Impact Theory in Initially Fully Differentiated Society

The study of opinion formation and dynamics is one of the core topics in sociophysics. In this paper, the results of computer simulation of opinion dynamics based on social impact theory are presented. The simulations are based on Latané theory in its computerised version proposed by Nowak, Szamrej and Latané. The active parameters of the model describe the volatility of the actors (social temperature T) and the effective range of interaction (governed by an exponent α in a scaling function of distance between actors). Initially, every actor i has his/her own opinion. Our results indicate that ultimately at least 90% of the initial opinions available are removed from the society. For a low social temperature and a long range of interaction, only one opinion survives. Also, a rough sketch of the system phase diagram is presented. It indicates a set of (α,T) leading either to (1) the dominance of the unanimity of the opinions or (2) mixtures of unanimity and polarisation, or (3) taking random opinions by actors, or (4) a mixture of the final fates of the systems. The drastic reduction of finally observed opinions vs. their initial variety may be generic for many sociophysical models of opinions formation but masked by assuming an initially small pool of available opinions (in the worst case, in models with only binary opinions).

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Adsorption and interaction mechanisms of Chi-g-P(AM-DMDAAC) assisted settling of kaolinite in a two-step flocculation process

Flocculation has been widely employed in treatment of mineral tailings and water management. In this study, a chitosan-graft-poly(acrylamide-dimethyl diallyl ammonium chloride) (Chi-g-P(AM-DMDAAC)) was synthesized in-house. The adsorption and interaction mechanisms of Chi-g-P(AM-DMDAAC) and an anionic polyacrylamide (APAM) in a two-step flocculation process of kaolinite were explored using settlement tests, zeta potential measurement, quartz crystal micro-balance with dissipation (QCM-D) and atomic force microscopy (AFM) technique. The type of primary flocculant was critical for the two-step flocculation process. The treatment of the kaolinite suspension using 1 mg/L of Chi-g-P(AM-DMDAAC) followed by adding 2 mg/L of APAM displayed more efficient flocculation performance. QCM-D results showed that three dissipative layers were assembled on model kaolinite surface after sequentially injecting 3.5 mg/L of Chi-g-P(AM-DMDAAC), 0.05 wt% kaolinite suspension and 2.5 mg/L of APAM. The above total adsorption amount (Δf of −64.9 Hz) was much higher than that of using the two flocculants in reverse order (Δf of −23.1 Hz). This result indicated that the adsorption layer of the positively charged Chi-g-P(AM-DMDAAC) on kaolinite surface provided active adsorption sites for APAM. Further AFM measurement confirmed that the average adhesion between the silicon tip adsorbed Chi-g-P(AM-DMDAAC) and model kaolinite surface in 2.5 mg/L APAM solution increased from 0.25 ± 0.1 nN to 4.2 ± 0.3 nN with the effective interaction range of 700 nm, which was stronger than that measured between a bare silicon tip and silica substrate in single-component-flocculant solutions. The highly efficient two-step flocculation process could be ascribed to the strong electrostatic attraction between the kaolinite and the oppositely charged Chi-g-P(AM-DMDAAC) and APAM. Findings in this study will benefit the development of environmentally friendly flocculant for mineral tailings and water treatment.

Effective-field-theory analysis of boson-trimer bond lengths to next-to-leading order

Cold Helium atoms are a unique system where a single excited three-body Efimov state occurs, naturally, without the need for an external magnetic field. While three-body bound state energies of cold Helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between Helium atoms leads to a helium-helium (dimer) scattering length, $a$, much larger than the helium-helium effective range of interaction, $r$. This feature is exploited in a theory that systematically expands observables in powers of $r/a$, known as short range effective field theory (srEFT), which has been used successfully to investigate properties of cold atom systems. Using srEFT we investigate the average bond length of atoms in the three-body ground state and excited Efimov state of cold Helium atoms. At leading-order (next-to-leading order) in srEFT, we find the average bond length of the $^4$He trimer ground state is 8.35(33) \r{A} (10.29(2) \r{A}) and the average bond length of the excited $^4$He trimer Efimov state is 103(4) \r{A} (105.3(2) \r{A}).

Nuclear symmetry energy parameters from neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni , 120Sn and 208Pb

Observables like neutron skin thickness and electric dipole polarizability in heavy nuclei are considered as most effective probes for the density dependence of nuclear symmetry energy at subsaturation density region. In the present work, within the framework of droplet model, we use finite range effective interactions to calculate the neutron skin thickness in 208Pb and the electric dipole polarizability in 68Ni, 120Sn and 208Pb. We correlate these quantities with the parameters of nuclear symmetry energy. Available experimental data on the neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni, 120Sn and 208Pb are used to deduce information on the density slope parameter of nuclear symmetry energy at saturation and at subsaturation densities. Constraints such as 35.2 ≤ L(ρ 0) ≤ 64.4 MeV and 43 ≤ L(ρ c ) ≤ 55 MeV are obtained using experimental values for neutron skin thickness.

Temperature-driven BCS-BEC crossover and Cooper-paired metallic phase in coupled boson-fermion systems

We propose a simple bose-fermi model in two dimensions, with a coupling that converts pairs of opposite spin fermions into localized bosons and vice versa. We show that tracing out one of the degrees, either the bosons or fermions, generates temperature-dependent long range effective interactions between bosons as well as effective attractive interactions between fermions. Using Monte Carlo techniques we obtain the thermodynamic properties and phase stiffness as a function of temperature, dominated by vortex-antivortex unbinding of the bosons. Remarkably in the fermion sector we observe a temperature-induced BCS-BEC crossover signaled by a distinct change of their spectral properties: the minimum gap locus moves from the Fermi wave vector to the $\Gamma$ point. Such a model is relevant for describing aspects of high $T_c$ superconductivity in cuprates and pnictides, superconducting islands on graphene, and bose-fermi mixtures in cold atomic systems.

On the phase transition in the sublattice TASEP with stochastic blockage

We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process with local deterministic bulk dynamics and a stochastic defect that mimicks a random blockage. Exact results are obtained for the compressibility and density correlations for a stationary grandcanonical ensemble given by the matrix product ansatz. At the critical density the static compressibility diverges while in the phase separated state above the critical point the compressibility vanishes due to strong non-local correlations. These correlations arise from a long range effective interaction between particles that appears in the stationary state despite the locality of the microscopic dynamics.

Nuclear symmetry energy and neutron skin thickness of 208Pb using a finite range effective interaction

We use a finite range simple effective interaction to construct nuclear equations of state for the study of the density dependence of the nuclear symmetry energy. The EoSs provide good descriptions of the nuclear symmetry energy at a subsaturation density ρc = 0.11 fm−3 and at a density around two times the saturation density ρ0. We obtain a correlation between the neutron skin thickness in 208Pb and the density slope parameter at the subsaturation density. A linear relation is obtained between the neutron skin thickness and the parameter , where Es(ρ0) and L(ρc) are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.

The Effect of Interaction Weight on Dipole Field Calculations to Reconstruct the La<sub>2</sub>CuO<sub>4</sub> μSR Spectrum

A modified dipole field equation proposed to reconstruct the μSR spectrum theoretically. Gaussian interaction weight added in dipole field calculation to investigate the effective interaction range between muon and its surrounding spin. The width of Gaussian interaction weight traced until the theoretical spectrum fit the data. The theoretical spectrum limited only to minima within the unit cell. By using the interaction weight the main peak spectrum can be reproduced without having a contradiction with the magnetic moment measured from neutron. Effective interaction between muon and surrounding spin estimated to be around which is relatively small.

Pseudogap regime of a strongly interacting two-dimensional Fermi gas with and without confinement-induced effective range of interactions

We investigate theoretically the many-body pairing of a strongly correlated two-dimensional Fermi gas with and without negative confinement-induced effective range. Using a strong-coupling effective field theory in the normal state, we show that the specific heat at constant volume can be used as a characteristic indicator of the crossover from the normal Fermi liquid to the pseudogap state in two dimensions. We calculate the pseudogap formation temperature through the specific heat at constant volume, examining the role of a negative confinement-induced effective range on many-body pairing above the superfluid transition. We compare our results with and without effective range to the recent experimental measurement performed with radio-frequency spectroscopy in Murthy et al.[Science359, 452-455 (2018)]. Although a good qualitative agreement is found, we are not able to discriminate the effect of the confinement-induced effect range in the experimental data.

Noise induced unanimity and disorder in opinion formation.

We propose an opinion dynamics model based on Latané’s social impact theory. Actors in this model are heterogeneous and, in addition to opinions, are characterised by their varying levels of persuasion and support. The model is tested for two and three initial opinions randomly distributed among actors. We examine how the noise (randomness of behaviour) and the flow of information among actors affect the formation and spread of opinions. Our main research involves the process of opinion formation and finding phases of the system in terms of parameters describing noise and flow of the information for two and three opinions available in the system. The results show that opinion formation and spread are influenced by both (i) flow of information among actors (effective range of interactions among actors) and (ii) noise (randomness in adopting opinions). The noise not only leads to opinions disorder but also it promotes consensus under certain conditions. In disordered phase and when the exchange of information is spatially effectively limited, various faces of disorder are observed, including system states, where the signatures of self-organised criticality manifest themselves as scale-free probability distribution function of cluster sizes. Then increase of noise level leads system to disordered random state. The critical noise level above which histograms of opinion clusters’ sizes loose their scale-free character increases with increase of the easy of information flow.

Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its equation of state and breathing mode frequency. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, in order to quantitatively explain recent experimental measurements at nonzero filling factor $N/N_{2D}$, where $N$ is the total number of atoms and $N_{2D}$ is the threshold number to reach the 2D limit. We therefore resolve in a satisfactory way the puzzling experimental observations of reduced equations of state and reduced quantum anomaly in breathing mode frequency, due to small yet non-negligible $N/N_{2D}$. We argue that a conclusive demonstration of the much-anticipated quantum anomaly is possible at a filling factor of a few percent. Our establishment of the minimal model for 2D ultracold atoms could be crucial to understanding the fermionic Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.

Model of level statistics for disordered interacting quantum many-body systems

We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent $\beta$ and range $h$ of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from ergodic to many-body localized phase. Analysis of higher order spacing ratios indicates that the considered $\beta$-$h$ model accounts even for long range spectral correlations and allows to obtain a clear picture of the flow of level statistics across the transition. Comparing spectral form factors of $\beta$-$h$ model and of a system in the ergodic-MBL crossover, we show that the range of effective interactions between eigenvalues $h$ is related to the Thouless time which marks the onset of quantum chaotic behavior of the system. Analysis of level statistics of random quantum circuit which hosts chaotic and localized phases supports the claim that $\beta$-$h$ model grasps universal features of level statistics in transition between ergodic and many-body localized phases also for systems breaking time-reversal invariance.

Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases

A quantum anomaly manifests itself in the deviation of the breathing mode frequency from the scale invariant value of 2ω in two-dimensional harmonically trapped Fermi gases, where ω is the trapping frequency. Its recent experimental observation with cold atoms reveals an unexpected role played by the effective range of interactions, which requires a quantitative theoretical understanding. Here we provide accurate, benchmark results on a quantum anomaly from a few-body perspective. We consider the breathing mode of a few trapped interacting fermions in two dimensions up to six particles and present the mode frequency as a function of scattering length for a wide range of effective range. We show that the maximum quantum anomaly gradually reduces as the effective range increases while the maximum position shifts towards the weak-coupling limit. We extrapolate our few-body results to the many-body limit and find a good agreement with the experimental measurements. Our results may also be directly applicable to a few-fermion system prepared in microtraps and optical tweezers.

Role of the confinement-induced effective range in the thermodynamics of a strongly correlated Fermi gas in two dimensions

We theoretically investigate the thermodynamic properties of a strongly correlated two-dimensional Fermi gas with a confinement-induced negative effective range of interactions, which is described by a two-channel model Hamiltonian. By extending the many-body T-matrix approach by Nozi\`eres and Schmitt-Rink to the two-channel model, we calculate the equation of state in the normal phase and present several thermodynamic quantities as functions of temperature, interaction strength, and effective range. We find that there is a non-trivial dependence of thermodynamics on the effective range. In experiment, where the effective range is set by the tight axial confinement, the contribution of the effective range becomes non-negligible as the temperature decreases down to the degenerate temperature. We compare our finite-range results with recent measurements on the density equation of state, and show that the effective range has to be taken into account for the purpose of a quantitative understanding of the experimental data.

Bose condensation of squeezed light

Light with a chemical potential and no mass is shown to possess a general phase-transition curve to Bose-Einstein condensation. This limiting density and temperature range is found by the diverging in-medium potential range of effective interaction. The inverse expansion series of the effective interaction from Bethe-Salpeter equation is employed exceeding the ladder approximation. While usually the absorption and emission with Dye molecules is considered, here it is proposed that squeezing can create also such a mean interaction leading to a chemical potential. The equivalence of squeezed light with a complex Bogoliubov transformation of interacting Bose system with finite lifetime is established with the help of which an effective gap is deduced where the squeezing parameter is related to an equivalent gap by $|\Delta(\omega)|={\hbar \omega/( \coth {2|z(\omega)|}-1)}$. This gap phase creates a finite condensate in agreement with the general limiting density and temperature range. In this sense it is shown that squeezing induces the same effect on light as an interaction leading to possible condensation. The phase diagram for condensation is presented due to squeezing and the appearance of two gaps is discussed.

The fourth-order symmetry energy of nuclear matter and symmetry energy coefficients of finite nuclei using extended semi-empirical mass formula

An extended nuclear mass formula has been used by considering the bulk, surface and coulomb contributions to the nuclear mass. In this mass formula, the fourth-order symmetry energy coefficient [Formula: see text] of finite nuclei and fourth-order symmetry energy [Formula: see text] of nuclear matter (NM) are related explicitly to the characteristic parameters of NM equation of state (EOS) using finite range effective interaction. The calculations are carried out with Yukawa form of exchange interaction having the same range but with different strengths for interaction between like and unlike nucleon. In this extended mass formula, by approximating [Formula: see text] to a constant [Formula: see text] an explicit relation between [Formula: see text] and fourth-order symmetry energy [Formula: see text] is obtained, which provides the possibility to extract information on [Formula: see text].

Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions.

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.

The Two-Particle Correlation Function for Systems with Long-Range Interactions

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable.

Effect of calcium ions on the interactions between surfaces end-grafted with weak polyelectrolytes.

We study the interactions between two planar surfaces end-tethered with poly(acrylic acid) polymers in electrolyte solutions containing calcium ions, using a molecular theory. We found that by adding divalent calcium ions to an aqueous solution of monovalent ions leads to a dramatic reduction in the size and range of effective interactions between the two polymer layers. This is caused by the formation of favorable calcium bridges, i.e., complexes of one calcium ion and two carboxylic acid monomers, that reduce the effective charge of the polymer layers and, at sufficient calcium ion concentrations, can cause the polymer layers to collapse. For calcium ion concentrations above approximately 1 mM, the repulsions between the opposing end-grafted surfaces disappear and attractions occur. These attractions are correlated with the occurrence of interlayer divalent calcium bridges and do not occur for poly(acrylic acid) layers in contact with reservoir solutions containing only monovalent ions. This result indicates the suitability of divalent calcium ions to control and change the interaction range and strength, which is a useful property that is desirable in the design of stimuli-responsive nanomaterials.