Repulsion Regime Research Articles

Effect of local Coulomb interaction on Majorana corner modes: Weak and strong correlation limits

Here we present an analysis of the evolution of Majorana corner modes realizing in a higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. The HOTSC spectral properties were considered in two regimes: when the intensities of many-body interactions are either weak or strong. The weak regime was studied using the mean-field approximation with self-consistent solutions carried out both in the uniform case and taking into account of the boundary of the finite square-shaped system. It is shown that in the uniform case the topologically nontrivial phase on the phase diagram is widened by the Coulomb repulsion. The boundary effect, resulting in an inhomogeneous spatial distribution of the correlators, leads to the appearance of the crossover from the symmetric spin-independent solution to the spin-dependent one characterized by a spontaneously broken symmetry. In the former the corner states have energies that are determined by the overlap of the excitation wave functions localized at the different corners. In the latter the corner excitation energy is defined by the Coulomb repulsion intensity with a quadratic law. The crossover is a finite size effect, i.e. the larger the system the lesser the critical value of the Coulomb repulsion. In the strong repulsion regime we derive the effective HOTSC Hamiltonian in the atomic representation and found a rich variety of interactions induced by virtual processes between the lower and upper Hubbard subbands. It is shown that Majorana corner modes still can be realized in the limit of the infinite repulsion. Although the boundaries of the topologically nontrivial phase are strongly renormalized by Hubbard corrections.

On the Stability of Particle–Particle Interaction during Gravitational Settling

The elevated energy demand and high dependency on fossil fuels have directed researchers’ attention to promoting and advancing hydraulic fracturing (HF) operations for a sustainable energy future. Even though previous studies have demonstrated that the proppant suspension and positioning in slickwater play a vital role during the shut-in stage of the HF operations, minimal experimental work has been conducted on the fundamental proppant–proppant interaction mechanisms, especially a complete mapping of the interactions. This study utilizes high-speed imaging to provide a 2D space- and time-resolved investigation of two-particle (proppant models: 2 mm Ø, 2.6 g·cm−3) interactions during gravitational settling in different initial spatial configurations and rheological properties. The mapping facilitates the identification of various interaction regimes and newly observed particle trajectories. Pure water results at a settling particle Reynolds number (Rep) ~ 470 show an unstable particle–particle interaction regime characterized by randomness while altering pure water to a 25% (v/v) water–glycerin mixture (Rep ~ 200) transitions an unstable interaction to a stable prominent repulsion regime where particles’ final separation distance can extend up to four times the initial distance. This indicates the existence of Rep at which the stability of the interactions is achieved. The quantified trajectories indicate that when particles are within minimal proximity, a direct relation between repulsion and Rep exists with varying repulsion characteristics. This was determined by observing unique bottle-shaped trajectories in the prominent repulsion regimes and further highlighted by investigating the rate of lateral separation distance and velocity characteristics. Additionally, a threshold distance in which the particles do not interact (or negligibly interact) and settle independently seems to exist at the normalized 2D lateral separation distance.

Mass-imbalance-induced structures of binary atomic mixtures in box potentials

We consider the ground states of binary atomic boson-boson and fermion-fermion mixtures confined in one-dimensional box potentials by simulating the systems using few-body models with delta-function interactions and many-body models with density-density interactions. For boson-boson mixtures, both models show signatures of phase separation in the strong repulsion regime and sandwiched structures emerge in the presence of mass imbalance. The structural difference between equal-mass and mass-imbalanced systems is due to the minimization of the interaction energy and the kinetic energies from the density distortion at the hard walls and at the phase-separation interface. The mass imbalance adjusts the kinetic energies and causes the lighter species to avoid the hard walls. For fermion-fermion mixtures, few-body simulations show a mass-imbalance induced structural changes in the strong repulsion regime, while many-body simulations show two-chunk phase separation due to the strong bulk kinetic energy. For equal-mass mixtures with strong inter-species repulsion, the few-body and many-body models predict different structures because the mean-field treatment in the many-body model approximates the contact interaction and smooths out the wavefunctions.

Separation of Floating Oil Drops Based on Drop-Liquid Substrate Interfacial Tension.

Though various strategies exist for the transport of oil drops suspended on a liquid substrate, selective manipulation of different kinds of drops based on their respective characteristics remains a challenge. In practice, it is possible to have multiple drops having different wetting states with the liquid substrate, whose separation is desired. In this work, we exploit curvature-induced capillary forces for the selective manipulation (transport as well as separation) of oil droplets based on their interfacial tension (IFT) with the underlying liquid substrate. To demonstrate this, we have selected two oils having different IFTs with the aqueous liquid substrate and tuned their curvature-induced capillary interaction (inward or outward from the source) by controlled addition of the surfactant. We experimentally realize three droplet manipulation regimes: repulsion, attraction, and separation regime. In the repulsion and attraction regimes, both the drops behave in a similar manner. Strikingly, in the separation regime, drops can be effectively separated based on their IFT; low IFT droplets are attracted toward the source, while high IFT droplets do the reverse.

Influence of the static field on a heavy body in a rotating drum with liquid.

The behaviour of a heavy cylindrical body in a rotating horizontal cylindrical cavity filled with viscous liquid is investigated experimentally. Several modes of the body behaviour depending on the rate of the cavity rotation, i.e., the ratio of the centrifugal force of inertia and the gravity, are detected. At a fast rotation rate, the body makes the solid-body rotation, remaining immobile relative to the cavity due to the action of the centrifugal force. In the absence of rotation, under the influence of gravity, the body occupies a position in the lower part of the cavity. At slow uniform rotation rate, the body is dragged by the cavity boundary and shifts to some angle relative to the initial position. With an increase in the rotation rate, the body is repulsed from the cavity boundary and occupies a suspended position, stationary in the laboratory frame, at a certain distance from it. In the suspension regime and the partial repulsion regime, which precedes it, the body performs auto-oscillations that resemble the precession. The flow structures near the suspended cylinder are studied using the PIV method.

A combined experimental and molecular simulation study of factors influencing interaction of quinoa proteins–carrageenan

The interaction between quinoa proteins isolate (QP isolate) and the negatively charged polysaccharide ι-Carragennan (Carr) as a function of pH was studied. Experimental measurements as turbidity, hydrophobic surface, ζ-potential, and hydrodynamic size were carried out. Associative interaction between QP and Carr was found in the pH range between 1 and 2.9. When both molecules are negatively charged (pH>5,5), a pure Coulombic repulsion regime is observed and the self-association of QP due to the Carr exclusion is proposed. In the intermediate pH range, the experimental data suggests that the charge regulation mechanism can overcome the electrostatic repulsion that may take place (and an attraction between QP and Carr can still be observed). Computational simulations by means of free energy derivatives using the Monte Carlo method were carried out to better understand the interaction mechanism between QP and Carr. QP was modeled as a single protein using one of the major proteins, Chenopodin (Ch), and Carr was modeled as a negatively charged polyelectrolyte (NCP) chain, both in the cell model framework. Simulation results showed attractive interactions in agreement with the experimental data.

Ground state properties of anti-ferromagnetic spinor Bose gases in one dimension

We investigate the ground state properties of anti-ferromagnetic spin-1 Bose gases in one dimensional harmonic potential from the weak repulsion regime to the strong repulsion regime. By diagonalizing the Hamiltonian in the Hilbert space composed of the lowest eigenstates of single particle and spin components, the ground state wavefunction and therefore the density distributions, magnetization distribution, one body density matrix, and momentum distribution for each components are obtained. It is shown that the spinor Bose gases of different magnetization exhibit the same total density profiles in the full interaction regime, which evolve from the single peak structure embodying the properties of Bose gases to the fermionized shell structure of spin-polarized fermions. But each components display different density profiles, and magnetic domains emerge in the strong interaction limit for $M=0.25$. In the strong interaction limit, one body density matrix and the momentum distributions exhibit the same behaviours as those of spin-polarized fermions. The fermionization of momentum distribution takes place, in contrast to the $\delta$-function-like distribution of single component Bose gases in the full interaction region.

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

The correlation function is an important quantity in the physics of ultracold quantum gases because it provides information about the quantum many-body wave function beyond the simple density profile. In this paper we first study the M-body local correlation functions, gM, of the one-dimensional (1D) strongly repulsive Bose gas within the Lieb–Liniger model using the analytical method proposed by Gangardt and Shlyapnikov (2003 Phys. Rev. Lett. 90 010401; 2003 New J. Phys. 5 79). In the strong repulsion regime the 1D Bose gas at low temperatures is equivalent to a gas of ideal particles obeying the non-mutual generalized exclusion statistics with a statistical parameter , i.e. the quasimomenta of N strongly interacting bosons map to the momenta of N free fermions via with . Here γ is the dimensionless interaction strength within the Lieb–Liniger model. We rigorously prove that such a statistical parameter α solely determines the sub-leading order contribution to the M-body local correlation function of the gas at strong but finite interaction strengths. We explicitly calculate the correlation functions gM in terms of γ and α at zero, low, and intermediate temperatures. For M = 2 and 3 our results reproduce the known expressions for g2 and g3 with sub-leading terms (see for instance (Vadim et al 2006 Phys. Rev. A 73 051604(R); Kormos et al 2009 Phys. Rev. Lett. 103 210404; Wang et al 2013 Phys. Rev. A 87 043634). We also express the leading order of the short distance non-local correlation functions of the strongly repulsive Bose gas in terms of the wave function of M bosons at zero collision energy and zero total momentum. Here is the boson annihilation operator. These general formulas of the higher-order local and non-local correlation functions of the 1D Bose gas provide new insights into the many-body physics.

Simulating the interactions of two freely settling spherical particles in Newtonian fluid using lattice-Boltzmann method

The interactions of two freely settling spherical particles in a three dimensional channel are investigated employing the lattice-Boltzmann method with discrete external boundary force (LBM-EBF). By changing the initial separation distance and relative angle between the two particles, a comprehensive analysis about the impact of various parameters on the dynamics of the particle motion and particle–particle interactions is made. The terminal Reynolds numbers based on the diameter of particle and the terminal vertical velocity is about O(100). Three different regimes are identified in the two particles settling system: repulsion, attraction and transition regime. Each regime depends on the initial separation distance and the relative angle of the two particles. The general trend is that the smaller the initial angle, the more likely interaction between them is repulsion. On the contrary, the larger the initial angle, the more likely interaction is attraction. Further, the translation and the rotation of the particles as well as the long-body particle pair behavior and some flow patterns are systematically investigated.

Variational Two-Particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-Adapted Lifting Conditions

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.

Dynamic properties of confined hydration layers

Prompted by the recent discovery that water and aqueous monovalent Na+ solutions remain fluid-like when confined to films of a few molecular layers between mica surfaces,[Raviv et al., Nature, 2001, 413, 51-54; and Raviv and Klein, Science, 2002, 297, 1540-1543] we now extend the previous study by comparing the shear- and normal-force properties of 0.1 M Na+, Cs+ and Ni2+ salt solutions which demonstrate a diverse range of behaviours under confinement. In the case of hydrated Na+ we extend the previous study to higher pressures, up to approximately 10 atmospheres, and record similar fluidity of the hydration layers at these elevated pressures. Aqueous Cs+ films under confinement between mica sheets have been found to be unable to support an applied load--that is to say they do not demonstrate any hydration repulsion regime--as a result of their lower hydration energy [see Goldberg et al., Phys. Chem. Chem. Phys., 2008, 10, 4939-4945] which contrasts with the properties of Na+. We show that 0.1 M Ni2+ solution remains close to its bulk viscosity down to nanometre thin films, but does not demonstrate a hydration repulsion. By comparing the properties of this range of cations, with differing valency and hydration, we aim to examine the conditions under which ions serve as effective lubricants and what we call the 'hydration lubrication' mechanism.

Interactions of flame balls

Flame ball interactions are numerically investigated in a reaction–diffusion system characterized by single-step Arrhenius kinetics and radiative heat losses. It is found that the interactions of two neighbouring flame balls are characterized by two distinct regimes – a repulsion regime and an attraction regime, depending upon the separation distance. The two regimes join at a critical separation distance, which corresponds to an unstable equilibrium state. For supercritical separation distances, the two flame balls repel and drift apart from each other; whereas for sub-critical separation distances, they move towards each other and eventually merge into a single stationary flame ball. In this connection, flame ball interactions are found to exhibit a qualitatively reverse character in comparison with the well-known van der Waals curve which characterizes intermolecular forces.

First-order coherent resonant tunneling through an interacting coupled-quantum-dot interferometer: Generic quantum rate equations and current noise

We carry out a detailed analysis of coherent resonant tunneling through two coupled quantum dots (CQDs) in a parallel arrangement in the weak-tunneling limit. We establish a set of quantum rate equations in terms of the eigenstate representation by means of a generic quantum Langevin equation approach, which is valid for arbitrary bias voltage, temperature, and interdot hopping strength. Based on linear-response theory, we further derive the current and frequency-independent shot noise formulas. Our results reveal that a previously used formula for evaluating Schottky-type noise of a ``classical'' single-electron transistor is a direct result of linear-response theory, and it remains applicable for small quantum devices with internal coupling. Our numerical calculations show some interesting transport features (i) for a series CQD: the appearance of a negative differential conductance due to the bias-voltage-induced shifting of bare levels or a finite interdot Coulomb repulsion, and (ii) for a parallel CQD in strong interdot Coulomb repulsion regime: finite-bias-induced Aharonov-Bohm oscillations of current, and magnetic-flux-controllable negative differential conductance and a huge Fano factor.

FINITE CHAINS WITH QUANTUM AFFINE SYMMETRIES

We consider an extension of the t-U Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XX Z model) in the presence of a Z field (2L states). The wave functions of the 3L-state system are obtained explicitly from those of the 2L-state system, and the degeneracies can be understood in terms of irreducible representations of [Formula: see text].

Self-consistent perturbation theory for random matrix ensembles: II

For pt I. see ibid, vol.23, p.1555 (1990). A method to evaluate perturbations of arbitrary spectra by one of the classical ensembles was presented in a previous paper. Its application to non-trivial problems is cumbersome and I shall show that by combining the previous results with singular perturbation theory, more complicated problems can be tackled. A scaling argument is also presented to obtain a general result that goes beyond the linear repulsion regime that we discussed previously. This result is of considerable interest as it allows us to obtain a good idea of the correlation function if we, in addition, know its long-range behaviour, which can be obtained by straightforward perturbation theory.

Random copolymers with long range interaction in the equilibrium state

Macromolecules with quenched random disorder along the chain and long range interaction between the monomers are studied. Averaging over the quenched disorder results in a collapse regime for the macromolecule. The mean-square radius depends on the polymer length L as a power law <R2≳∼L1/3 for large length, whereas for short length a repulsion regime <R2≳∼L2/3 was predicted. The thermodynamic equation of state for a diluted solution of these macromolecules is determined.

Phase separation and superconductivity

The thermodynamic stability of two widely investigated models for high Tc superconductivity, the Kondo-lattice and the extended three band Hubbard model, is analyzed in the strong local repulsion regime. Superconducting instabilities in these models are also found. For the first model superconductivity stabilizes the system against phase separation. For the second model the superconducting instabilities occur close to the phase separation region. In both models, therefore, phase separation and superconductivity appear to be related phenomena.

The structure of the interface in the solvent-mediated interaction of dipolar surfaces

Interaction of two dipolar surfaces separated by a polar medium is considered within the framework of nonlocal electrostatics. The dipolar-surface layers are modelled as regular lattices with fixed orientation of dipoles which are immersed into the solvent; solvent response is characterized by nonlocal dielectric function. The model is elaborated in order to reveal the role of the dipolar-layer discreteness in the electric field produced by one surface and the interaction between two surfaces (which gives rise to the so-called «hydration» or «structural» force acting between mineral surfaces and phospholipid bilayers). The discreteness effects are present only for commensurate lattices. Their special mutual arrangement then may lead to considerable reduction of structural forces,viz. the usual repulsion regime may change at short distances to attraction. Conditions are considered when repulsion is entirely replaced by attraction,i.e. the «hydration barrier» disappears. In appended note we discuss the role of solvation of surface dipolar groups. We propose an explanation of why two modes of decay (one with oscillative fine structure) may be present in the dependence of the force upon distance, if the surface dipolar groups are immersed deep enough in the solvent, and how the long-range oscillative mode disappears when the surface is but weakly solvated.