Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Intrinsic Electron localization in manganites

We mention here an unusual disorder effect in manganites, namely the ubiquitous hopping behavior for electron transport observed in them over a wide range of doping. We argue that the implied Anderson localization is intrinsic to manganites, because of the existence of polarons in them which are spatially localized, generally at random sites (unless there is polaron ordering). We have developed a microscopic two fluid lb model for manganites, where l denotes lattice site localized l polarons, and b denotes band electrons. Using this, and the self-consistent theory of localization, we show that the occupied b states are Anderson localized in a large range of doping due to the scattering of b electrons from l polarons. Numerical simulations which further include the effect of long range Coulomb interactions support this, as well the existence of a novel polaronic Coulomb glass. A consequence is the inevitable hopping behaviour for electron transport observed in doped insulating manganites.

Transient analysis in Al-doped barium strontium titanate thin films grown by pulsed laser deposition

Thin films of (Ba0.5Sr0.5)TiO3 (BST) with different concentrations of Al doping were grown using a pulsed laser deposition technique. dc leakage properties were studied as a function of Al doping level and compared to that of undoped BST films. With an initial Al doping level of 0.1 at. % which substitutes Ti in the lattice site, the films showed a decrease in the leakage current, however, for 1 at. % Al doping level the leakage current was found to be relatively higher. Current time measurements at elevated temperatures on 1 at. % Al doped BST films revealed space-charge transient type characteristics. A complete analysis of the transient characteristics was carried out to identify the charge transport process through variation of applied electric field and ambient temperature. The result revealed a very low mobility process comparable to ionic motion, and was found responsible for the observed feature. Calculation from ionic diffusivity and charge transport revealed a conduction process associated with an activation energy of around 1 eV. The low mobility charge carriers were identified as oxygen vacancies in motion under the application of electric field. Thus a comprehensive understanding of the charge transport process in highly acceptor doped BST was developed and it was conclusive that the excess of oxygen vacancies created by intentional Al doping give rise to space-charge transient type characteristics. © 2001 American Institute of Physics.

Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

Quantum information processing in the wall of cytoskeletal microtubules

Microtubules (MT) are composed of 13 protofilaments, each of which is a series of two-state tubulin dimers. In the MT wall, these dimers can be pictured as "lattice" sites similar to crystal lattices. Based on the pseudo-spin model, two different location states of the mobile electron in each dimer are proposed. Accordingly, the MT wall is described as an anisotropic two-dimensional (2D) pseudo-spin system considering a periodic triangular "lattice". Because three different "spin-spin" interactions in each cell exist periodically in the whole MT wall, the system may be shown to be an array of three types of two-pseudo-spin-state dimers. For the above-mentioned condition, the processing of quantum information is presented by using the scheme developed by Lloyd.

The bipolar doping of ZnS via native defects and external dopants

By employing first-principle total-energy calculations, a systematic study of the dopability of ZnS to be both n- and p-types compared with that of ZnO is carried out. We find that all the attempted acceptor dopants, group V substituting on the S lattice site and group I and IB on the Zn sites in ZnS, have lower ionization energies than the corresponding ones in ZnO. This can be accounted for by the fact that ZnS has relative higher valence band maximum than ZnO. Native ZnS is weak p-type under S-rich condition, as the abundant acceptor V-Zn has rather large ionization energy. Self-compensations by the formation of interstitial donors in group I and IB-doped p-type ZnS can be avoided when sample is prepared under S-rich condition. In terms of ionization energies, Li-Zn and N-S are the preferred acceptors in ZnS. Native n- type doping of ZnS is limited by the spontaneous formation of intrinsic V-Zn(2-); high efficient n-type doping with dopants is harder to achieve than in ZnO because of the readiness of forming native compensating centers and higher ionization energy of donors in ZnS. (C) 2009 American Institute of Physics. [DOI 10.1063/1.3103585]

Donor defect in P-diffused bulk ZnO single crystal

A high concentration of shallow donor defect is formed in P-diffused ZnO single crystals. X-ray photoelectron spectroscopy analysis indicates that P atom occupy different lattice site at different diffusion temperature. Nature of the donor defect has been discussed.

Luminescence spectroscopy of ion implanted AlN bulk single crystal

High concentrations of Si and Zn were implanted into (0001) AlN bulk crystal grown by the self-seeded physical vapor transport (PVT) method. Cathode luminescence (CL) and photoluminescence (PL) spectroscopy were used to investigate the defects and properties of the implanted AlN. PL spectra of the implanted AlN are dominated by a broad near-band luminescence peak between 200 and 254 nm. After high temperature annealing, implantation induced lattice damages are recovered and the PL intensity increases significantly, suggesting that the implanted impurity Si and Zn occupy lattice site of Al. CL results imply that a 457 nm peak is Al vacancy related. Resistance of the AlN samples is still very high after annealing, indicating a low electrical activation efficiency of the impurity in AlN single crystal.

Simulated morphological landscape of polymer single crystals by phase-field model

The novel phase field model with the "polymer characteristic" was established based on a nonconserved spatiotemporal Ginzburg-Landau equation (TDGL model A). Especially, we relate the diffusion equation with the crystal growth faces of polymer single crystals. Namely, the diffusion equations are discretized according to the diffusion coefficient of every lattice site in various crystal growth faces and the shape of lattice is selected based on the real proportion of the unit cell dimensions.

Synthesis, crystal structure, and density of (W1-xAlx)C

A new solid solution system of Al in WC, with the stoichiometry of (W1-xAlx)C (x = 0.10, 0.25, 0.50, 0.75, 0.86), has been synthesized by a solid-state reaction between W1-xAlx alloys and carbon at around 1673 K in vacuum. Environment scanning electron microscope, energy- dispersive analysis of X-ray, X-ray photoelectron spectroscopy, and inductively coupled plasma analyses are used to certify the formation of the products. The mechanism of the solid-state reaction is also discussed. (W1-xAlx)C is identified to crystallize in the hexagonal space group P6m2 (No. 187) and belongs to the WC structure type. The atoms of W and Al occupy the same lattice site (la site) in the cell of (W1-xAlx)C. The cell parameters for each specimen in the phase of W-AI-C are quite close to that of WC, while their densities are far lower than that of WC.

The luminescence of Eu2+ in mixed phase system

The dependence of the structure of the hosts on the M ion radius in MMgAl10O17 (M = Be, Mg, Ca, Sr, Ba, Pb, Eu, Mn, Fe, Co, Ni, Zn, Cd, Sn) system was studied and the luminescence of Eu2+ the mixed phase system was discussed. When M ion radius is less than 0.10 nm, the system MMgAl10O17 constructs by the mixed phases consisting of manegtoplumbite and spinel, alpha-alumina or spinel and alpha-alumina. In the mixed phase of manegtoplumbite and spinel and alpha-alumina, Eu2+ ion preferentially occupies lattice site of the cations in manegtoplumbite well matched with the radius and charge of Eu2+. There exists only d-->f transition emission of Eu2+ and no characteristic emission of Eu3+ occurs in those hosts. In the mixed phase of spinel and alpha-alumina, Eu2+ can enter the lattice site of Mg2+ ion or Al3+ ion and the d-->f and f-->f transition of Eu2+ can been observed respectively. Meanwhile, since the radius and charge of matrix lattice ions substituted by Eu2+ do not match with those of Eu2+, the valence state of Eu2+ is unstable. Eu2+ is partly changed into Eu3+ and the emission of Eu3+ is obviously observed even under the condition of reduction atmosphere. If reaction temperature is more than 1 150 degrees C, Al2O3 forms alpha-Al2O3 structure, the f-->f transition of Eu2+ appears. If reaction temperature is less than 1 150 degrees C, a mixed phase of alpha-Al2O3 and gamma-Al2O3 is formed, the f-->f transition of Eu2+ disappears and a new band emission from d-->f transition of Eu2+ occurs.