Stationary Density Profile Research Articles

Strain effects on electronic structure and optics of al-Doped monolayer GaS

This comprehensive study utilises rigorous first-principles calculations to meticulously investigate the influence of uniaxial tensile strain on the electronic configuration and optical behaviours of aluminium-doped gallium sulphide. The study highlights the modulation of electrical properties and optical responses in Al-doped monolayer GaS through the application of tensile strain. Notably, with increasing tensile strain, the bandgap value of the pristine GaS exhibits a pronounced decline, whereas the Al-doped variant maintains a more stable bandgap. A deeper exploration of the state density reveals the emergence of novel electronic states and energy levels in both the pristine and Al-doped monolayer GaS systems as tensile strain is applied. Crucially, the stabilising effect of the doped Al atoms minimises variations in the state density profiles of the Al-doped monolayer GaS systems, in contrast to their pristine counterparts. This result implies that fine control of the electrical structure and optical characteristics of Al-doped monolayer GaS may be achieved by the application of uniaxial tensile strain. The optoelectronic characteristics of GaS and its doped systems are explained in detail by these discoveries, which also offer a crucial theoretical foundation and direction for the use of these materials in optoelectronic devices.

A hydrodynamical description of Bose liquid with fractional exclusion statistics

Hydrodynamical systems are usually taken as chaotic systems with fast relaxations. It is counter intuitive for ‘ideal’ gas to have a hydrodynamical description. We find that a hydrodynamical model of one-dimensional |Φ|6 theory shares the same ground state density profile, density-wave excitation, as well as the similar dynamical and statistical properties with the Calogero–Sutherland model in thermodynamic limit when their interaction strengths matches each other. The interaction strength g 0 in |Φ|6 theory is then the index of fractional statistics. Although the model is interacting in Bose liquid sense, but it shows integrability with periodical coherent evolution. We also discussed the fractional statistics emerges from the |Φ|6 theory.

The bosonic skin effect: Boundary condensation in asymmetric transport

We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specifically, we show that as the current passing through this system increases, a transition occurs, which is signified by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal distribution and a Bose-condensed state with broken U(1)U(1)-symmetry. Furthermore, we show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes a direct connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic and plasmonic excitations.

Active Brownian particles can mimic the pattern of the substrate

ABSTRACT Active Brownian particles (ABPs) have been identified as a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by such work, we studied the dynamics and the steady state of ABP moving on a substrate with space-dependent activity. On the substrate, some regions are marked as high in activity, and other regions are such that particles behave as passive Brownian particles. The system is studied in two dimensions with step, sigmoid, Gaussian, and cone shape distribution of activity profile on the substrate. The whole interface of the activity profile is symmetrically divided into two regions. This led to the flow of particles from the active region to the passive region. The final steady state of particle density profile, polarization and flux very much follows the structure of the inhomogeneous activity, and the density in high activity region is lower, maximum at the interface and nearly constant with mean density in the passive region. Further, the steady state density profile for various shapes and designs on two-dimensional substrates is studied. Hence, the collection of ABPs on an inhomogeneous substrate can mimic the inhomogeneity of the substrate.

Local resetting with geometric confinement

‘Local resetting’ was recently introduced to describe stochastic resetting in interacting systems where particles independently try to reset to a common ‘origin’. Our understanding of such systems, where the resetting process is itself affected by interactions, is still very limited. One ubiquitous constraint that is often imposed on the dynamics of interacting particles is geometric confinement, e.g. restricting rigid spherical particles to a channel so narrow that overtaking becomes difficult. We here explore the interplay between local resetting and geometric confinement in a system consisting of two species of diffusive particles: ‘bath’ particles, and ‘tracers’ which undergo local resetting. Mean-field (MF) analysis and numerical simulations show that the resetting tracers, whose stationary density profile exhibits a typical ‘tent-like’ shape, imprint this shape onto the bath density profile. Upon varying the ratio of the degree of geometric confinement over particle diffusivity, the system is found to transition between two states. In one tracers expel bath particles away from the origin, while in the other they ensnare them instead. Between these two states, we find a special case where the MF approximation is exact.

Localization in Two-Dimensional Quasicrystalline Lattices.

We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.

Competition in a system of Brownian particles: Encouraging achievers.

We introduce and analytically and numerically study a simple model of interagent competition, where underachievement is strongly discouraged. We consider N≫1 particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it. We show that, in the limit of N→∞, the dynamics of the coarse-grained particle density field can be described by a nonlocal hydrodynamic theory which was encountered in a study of the spatial extent of epidemics in a critical regime. The hydrodynamic theory predicts relaxation of the system toward a stationary density profile of the "swarm" of particles, which exhibits a power-law decay at large distances. An interesting feature of this relaxation is a nonstationary "halo" around the stationary solution, which continues to expand in a self-similar manner. The expansion is ultimately arrested by finite-N effects at a distance of order sqrt[N] from the origin, which gives an estimate of the average radius of the swarm. The hydrodynamic theory does not capture the behavior of the particle farthest from the origin-the current leader. We suggest a simple scenario for typical fluctuations of the leader's distance from the origin and show that the mean distance continues to grow indefinitely as sqrt[t]. Finally, we extend the inter-agent competition from n=2 to an arbitrary number n of competing Brownian particles (n≪N). Our analytical predictions are supported by Monte Carlo simulations.

A repertoire of repulsive Keller–Segel models with logarithmic sensitivity: Derivation, traveling waves, and quasi‐stationary dynamics

In this paper, we show how the chemotactic model introduced in Alejo and López (2021), which accounts for a chemical production–degradation operator of Hamilton–Jacobi type involving first‐ and second‐order derivatives of the logarithm of the cell concentration, namely, with , can be formally reduced to a repulsive Keller–Segel model with logarithmic sensitivity whenever the chemotactic parameters are appropriately chosen and the cell concentration keeps strictly positive. In this way, some explicit solutions (namely, traveling waves and stationary cell density profiles) of the former system can be transferred to a number of variants of the the latter by means of an adequate change of variables.

Quantitative evaluation of plasma-damaged SiN/Si structures using bias-dependent admittance analysis

Plasma process-induced damage (PID) to SiN dielectric films was investigated by using an impedance (admittance)-based technique. Multi-layered equivalent circuits were introduced to assign the spatial and energy distribution of defects created in the SiN/Si system. We propose to use admittance as the principal parameter for damaged SiN/Si systems after Ar and He plasma exposures. The change in the border trap density was determined from the admittance in accumulation, whereas the interface state density and energy profile that was created was determined from the admittance in depletion. Plasma source-dependent damage-creation mechanisms are discussed. It was found that the extracted border trap density in the He plasma-damaged sample was larger than that in the Ar plasma-damaged sample under the same ion dosage. The proposed characterization scheme is useful for assessing PID to dielectric/Si systems.

Global Solutions to Multi-dimensional Topological Euler Alignment Systems

We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in [35]. While these systems exhibit flocking behavior emerging from purely local communication, bearing direct relevance to empirical field studies, global and even local well-posedness has proved to be a major challenge in multi-dimensional settings due to the presence of topological effects. In this paper we reveal two important classes of global smooth solutions—parallel shear flocks with incompressible velocity and stationary density profile, and nearly aligned flocks with close to constant velocity field but arbitrary density distribution. Existence of such classes is established via an efficient continuation criterion requiring control only on the Lipschitz norm of state quantities, which makes it accessible to the applications of fractional parabolic theory. The criterion presents a major improvement over the existing result of [28], and is proved with the use of quartic paraproduct estimates.

Rayleigh–Taylor instability of classical diffusive density profiles for miscible fluids in porous media: a linear stability analysis

A Rayleigh–Taylor instability typically develops when a denser layer overlies a less dense one in the gravity field. In that case, the initial base state density profile is a step function for which linear stability analysis results are well known. We investigate here analytically the linear stability analysis of other classical diffusive density profiles for porous media flows. We find that, for a species A initially distributed in the upper half of the domain with an initial concentration profile of \((-X)^m\) for \(0<m<1\) where X is the vertical coordinate, and absent from the bottom half of the domain, for large times the eigenfunctions grow like \(\exp \left( \omega _0 T^{(m+1)/2} + \omega _1 \ln (T) \right) \) where \(\omega _0\) and \(\omega _1\) are constants and T is time. Thus, the growth rate defined by \((1/A) (\mathrm{{d}}A/\mathrm{{d}}T)\) decays like \(c_1 T^{(m-1)/2} +c_2 T^{(m-2)/3}\) whilst the maximum growing wavenumber scales with \(T^{(m-2)/6}\). These results are compared to the growth rates obtained using numerical linear stability analysis. Our analytical predictions provide a set of generalised results that pave the way to the analysis of Rayleigh–Taylor instabilities of nontrivial density profiles.

Ion temperature anisotropy in the tokamak scrape-off layer

Understanding tokamak exhaust-power heat loads on divertor plates depends critically on having a realistic model of the scrape-off layer (SOL) plasma. The Braginskii fluid model is often solved to understand the SOL plasma behavior. This model is based on the collisional limit for transport along the magnetic field . The ions and electron gyrofrequencies are assumed to be much larger than the Coulomb collision frequencies, which are nonetheless, sufficiently large to yield common parallel and perpendicular temperatures for each species, i.e. the temperatures are assumed to be isotropic. In certain circumstances such as encountered for the tokamak H-mode, the ion temperature can be quite anisotropic. In this work, the anisotropy effects are implemented in the two-dimensional (2D) transport code UEDGE. Various geometries (1D slab, 2D slab and a toroidal tokamak geometry) are used to study the 2D structure of ion temperature anisotropy and its effects on plasma transport in detail. Results show that the effects of ion temperature anisotropy on the plasma parallel transport are substantial near the magnetic X-point, which leads to different steady state density profiles in the divertor regions. The extra mirror force introduced by ion temperature anisotropy can be one of the main forces contributing to the plasma flow in the SOL.

Proof of spherical flocking based on quantitative rearrangement inequalities

Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set. Here we show that this set is, in fact, a round ball. The essential mathematical structure needed in our proof is a strict rearrangement inequality with a quantitative error estimate, which we deduce from recent deep results of M. Christ.

Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate

We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches for any given dipole tilt angle. We also find that the tilt angle of the stationary state's body frame with respect to the rotation axis is a nontrivial function of the trapping geometry, rotation frequency, and dipole tilt angle. For rotation frequencies of at least an order of magnitude higher than the in-plane trapping frequency, the stationary state density profile is almost perfectly equivalent to the profile expected in a time-averaged dipolar potential that effectively vanishes when the dipoles are tilted along the ``magic angle'' 54.7 deg. However, by linearizing the fully time-dependent superfluid hydrodynamics about these stationary states, we find that they are dynamically unstable against the formation of collective modes, which we expect would result in turbulent decay.

Cooperative Dynamics in Bidirectional Transport on Flexible Lattice

Several theoretical models based on totally asymmetric simple exclusion process (TASEP) have been extensively utilized to study various non-equilibrium transport phenomena. Inspired by the the role of microtubule-transported vesicles in intracellular transport, we propose a generalized TASEP model where two distinct particles are directed to hop stochastically in opposite directions on a flexible lattice immersed in a three dimensional pool of diffusing particles. We investigate the interplay between lattice conformation and bidirectional transport by obtaining the stationary phase diagrams and density profiles within the framework of mean field theory. For the case when recycling strength is independent of density of particles, the topology of phase diagram alters quantitatively. However, if the lattice occupancy governs the global conformation of lattice, in addition to the pre-existing phases for bidirectional transport a new asymmetric shock-low density phase originates in the system. We identified that this phase is sensitive to finite size effect and vanishes in the thermodynamic limit.

Dependence of the impurity transport on the dominant turbulent regime in ELM-y H-mode discharges on the DIII-D tokamak

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft x-ray measurements, and vacuum ultraviolet spectroscopy provides a detailed uncertainty quantification of transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal a threefold drop in the impurity confinement time and order of magnitude increase in midradius impurity diffusion, when additional electron heating is applied. Furthermore, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend to electron and carbon density. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO [J. Candy and E. Belly, J. Comput. Phys. 324, 73 (2016)], significantly underpredicts the magnitude of the variation in Al transport. Diffusion increases three-times steeper with additional electron heat flux, and 10-times lower diffusion is observed in ion heated case than predicted by the modeling. The CGYRO model quantitatively matches the increase in the Al diffusion when approaching the linear threshold for the transition from the ion temperature gradient to trapped electron mode.

Phase transition in a 1D driven tracer model

The effect of particle overtaking on transport in a narrow channel is studied using a 1D model of a driven tracer in a quiescent bath. In contrast with the well-studied non-driven case, where the tracer’s long-time dynamics changes from sub-diffusive to diffusive whenever overtaking is allowed, the driven tracer is shown to exhibit a phase transition at a finite overtaking rate. The transition separates a phase in which the stationary bath density profile, as seen in the tracer’s frame, is extended, as in the non-overtaking case, to a phase with a localized bath density profile. In the extended phase the tracer velocity vanishes in the thermodynamic limit while it remains finite in the localized phase. The phase diagram of the model, as well as the tracer velocity and the bath density profile in both phases, are studied, demonstrating their distinct features.

FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates

We develop a FORTRAN code to compute fluctuations in atomic condensates (FACt) by solving the Bogoliubov–de Gennes (BdG) equations for two component Bose–Einstein condensate (TBEC) in quasi-two dimensions. The BdG equations are recast as matrix equations and solved self consistently. The code is suitable for handling quantum fluctuations as well as thermal fluctuations at temperatures below the critical point of Bose–Einstein condensation. The code is versatile, and the ground state density profile and low energy excitation modes obtained from the code can be easily adapted to compute different properties of TBECs — ground state energy, overlap integral, quasi particle amplitudes of BdG spectrum, dispersion relation and structure factor and other related experimental observables. Program summaryProgram Title: FACtProgram Files doi:http://dx.doi.org/10.17632/5h348ndydg.1Licensing provisions: MITProgramming language: FORTRAN 90External routines/libraries: ARPACKNature of problem: Compute the ground state density profile, ground state energy and chemical potential for individual species, evaluate the quasiparticle mode energies and corresponding amplitudes which can capture the transformation of the modes against the change of the parameters (intraspecies interaction, interspecies interaction, anisotropy parameter etc.) using Hartree–Fock–Bogoliubov theory with the Popov approximation. Calculate the overlap integral, dispersion relation and structure factor.Solution method: In the first step, the pair of coupled Gross–Pitaevskii equations (CGPEs) is solved using split time-step Fourier pseudospectral method to compute the condensate density. To solve the BdG equations, as a basic input the first Nb harmonic oscillator eigenstates are chosen as a basis to generate the BdG 011 matrix with dimension of 4(Nb+1)×4(Nb+1). Since the matrix size rapidly increases with Nb, Arpack routines are used to diagonalize the BdG matrix efficiently. To compute the fluctuation and non-condensate density, a set of the low energy quasiparticle amplitudes above a threshold value of the Bose factor are considered. The equations are then solved iteratively till the condensate, and non-condensate densities converge to predefined accuracies. To accelerate the convergence we use the method of successive under-relaxation (SUR).Additional comments including restrictions and unusual features: For a large system size, if the harmonic oscillator basis size is also taken to be large, the dimension of the BdG matrix becomes huge. It may take several days to compute the low energy modes at finite temperature and this package may be computationally expensive.After successful computation of this package, one should obtain the equilibrium density profiles for TBEC, low energy Bogoliubov modes and the corresponding quasiparticle amplitudes. In addition, one can calculate the dispersion relation, structure factor, overlap integral, correlation function, etc. using this package with minimal modifications. In the theory section of the manuscript, we have provided the expressions to compute the above quantities numerically.

Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects

We investigate the effects of disorder and lattice geometry against localisation phenomena in a weakly interacting ultracold bosonic gas confined in a 2D optical lattice. The behaviour of the quantum fluid is studied at the mean-field level performing computational experiments, as a function of disorder strength for lattices of sizes similar to current experiments. Quantification of localisation, away from the Bose glass phase, was obtained directly from the stationary density profiles through a robust statistical analysis of the condensate component, as a function of the disorder amplitude. Our results show a smooth transition, or crossover, to localisation induced by disorder in square and triangular lattices. In contrast, associated to its larger tunneling amplitude, honeycomb lattices show absence of localisation for the same range of disorder strengths and same lattice amplitude, while also exhibiting partial localisation for large disorder amplitudes. We also conclude that the coordination number z have a partial influence on how fast this smooth transition occurs as the system size increases. Signatures of disorder are also found in the ground state energy spectrum, where a continuous distribution emerges instead of a distribution of sharp peaks proper to the system in the absence of disorder.

Transport in Quantum Multi-barrier Systems as Random Walks on a Lattice

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method (Colangeli et al. in J Stat Mech Theor Exp 6:P06006, 2015). This quantum model is then associated with a stochastic process of independent random walks on a lattice, by properly relating the wave amplitudes with the hopping probabilities of the particles moving on the lattice and with the injection rates from external particle reservoirs. Analytical and numerical results prove that the stationary density profile of the particle system overlaps with the quantum mass density profile of the stationary Schrödinger equation, when the parameters of the two models are suitably matched. The equivalence between the quantum model and a stochastic particle system would mainly be fruitful in a disordered setup. Indeed, we also show, here, that this connection, analytically proven to hold for periodic barriers, holds even when the width of the barriers and the distance between barriers are randomly chosen.