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The double-well Bose Hubbard model with nearest-neighbor and cavitymediated long-range interactions
(2023)
We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte-Carlo simulations. We show that when the intra-well repulsion is as strong as the on-site repulsion a dimerized Mott insulator phase appears at the tip of the dimerized Density Wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
Chemotaxis, i.e. motion generated by chemical gradients, is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, auto-chemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of auto-chemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segels model in the continuous limit, for which we describe the rich phase behavior. We first rationalize a the chemically-mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.
We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. We find that, although an equation of state exists, a mechanical equilibrium does not apply to ABPs in activity landscapes. The pressure difference originates in the flux of polar order and the gradient of swim velocity across the interface between regions of different activity. In contrast to motility-induced phase separation of ABPs with a homogeneous swim velocity, a critical point does not exist for an active-passive patch system, which continuously splits into a dense and a dilute phase with increasing activity. However, if the global density is so high that not all particles can be packed onto the inactive patch, then MIPS-like behavior is restored and the pressure is balanced again.
Recently it was predicted, on the basis of a lattice gas model, that scalar active matter in a gravitational field would rise against gravity up a confining wall or inside a thin capillary - in spite of repulsive particle-wall interactions [Phys. Rev. Lett. 124, 048001 (2020)]. In this paper we confirm this prediction with sedimenting active Brownian particles (ABPs) in a box and elucidate the mechanism leading to the formation of a meniscus rising above the bulk of the sedimentation region. The height of the meniscus increases with the activity of the system, algebraically with the Péclet number. The formation of the meniscus is determined by a stationary circular particle current, a vortex, centered at the base of the meniscus, whose size and strength increases with the ABP activity. The origin of these vortices can be traced back to the confinement of the ABPs in a box: already the stationary state of ideal (non-interacting) ABPs without gravitation displays circular currents that arrange in a highly symmetric way in the eight octants of the box. Gravitation distorts this vortex configuration downward, leaving two major vortices at the two side walls, with a strong downward flow along the walls. Repulsive interactions between the ABPs change this situation only as soon as motility induced phase separation (MIPS) sets in and forms a dense, sedimented liquid region at the bottom, which pushes the center of the vortex upwards towards the liquid-gas interface. Self-propelled particles therefore represent an impressive realization of scalar active matter that forms stationary particle currents being able to perform visible work against gravity or any other external field, which we predict to be observable experimentally in active colloids under gravitation.
An important challenge in active matter lies in harnessing useful global work from entities that produce work locally, e.g., via self-propulsion. We investigate here the active matter version of a classical capillary rise effect, by considering a non-phase separated sediment of self-propelled Janus colloids in contact with a vertical wall. We provide experimental evidence of an unexpected and dynamic adsorption layer at the wall. Additionally, we develop a complementary numerical model that recapitulates the experimental observations. We show that an adhesive and aligning wall enhances the pre-existing polarity heterogeneity within the bulk, enabling polar active particles to climb up a wall against gravity, effectively powering a global flux. Such steady-state flux has no equivalent in a passive wetting layer.
The mean first passage time~(MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.
We investigate the phase transitions of the q-state Brownian Potts model in two dimensions (2d) comprising Potts spins that diffuse like Brownian particles and interact ferromagnetically with other spins within a fixed distance. With extensive Monte Carlo simulations we find a continuous phase transition from a paramagnetic to a ferromagnetic phase even for q>4. This is in sharp contrast to the existence of a discontinuous phase transition in the equilibrium q-state Potts model in 2d with q>4. We present detailed numerical evidence for a continuous phase transition and argue that diffusion generated dynamical positional disorder suppresses phase coexistence leading to a continuous transition.
Many biological active agents respond to gradients of environmental cues by redirecting their motion. Besides the well-studied prominent examples such as photo- and chemotaxis, there has been considerable recent interest in topotaxis, i.e.\ the ability to sense and follow topographic environmental cues. We numerically investigate the topotaxis of active agents moving in regular arrays of circular pillars. While a trivial topotaxis is achievable through a spatial gradient of obstacle density, here we show that imposing a gradient in the characteristics of agent-obstacle interaction can lead to an effective topotaxis in an environment with a spatially uniform density of obstacles. As a proof of concept, we demonstrate how a gradient in the angle of sliding around pillars -- as e.g.\ observed in bacterial dynamics near surfaces -- breaks the spatial symmetry and biases the direction of motion. We provide an explanation for this phenomenon based on effective reflection at the imaginary interface between pillars with different sliding angles. Our results are of technological importance for design of efficient taxis devices.
We study the active Potts model with either site occupancy restriction or on-site repulsion to explore jamming and kinetic arrest in a flocking model. The incorporation of such volume exclusion features leads to a surprisingly rich variety of self-organized spatial patterns. While bands and lanes of moving particles commonly occur without or under weak volume exclusion, strong volume exclusion along with low temperature, high activity, and large particle density facilitates jams due to motility-induced phase separation. Through several phase diagrams, we identify the phase boundaries separating the jammed and free-flowing phases and study the transition between these phases which provide us with both qualitative and quantitative predictions of how jamming might be delayed or dissolved. We further formulate and analyze a hydrodynamic theory for the restricted APM which predicts various features of the microscopic model.
Cytotoxic T lymphocytes (CTLs) are involved in development of diabetes. However, the impact of excessive glucose on CTL-mediated antigen-independent killing remains elusive. Here, we report that TNF-related apoptosis inducing ligand (TRAIL) is substantially up- regulated in CTLs in environments with high glucose (HG) both in vitro and in vivo. The PI3K- Akt-NFκB axis and non-mitochondrial reactive oxygen species are essential in HG-induced TRAIL upregulation in CTLs. TRAILhigh CTLs induce apoptosis of pancreatic beta cell line 1.4E7. Metformin and Vitamin D synergistically reduce HG-enhanced expression of TRAIL in CTLs and coherently protect 1.4E7 cells from TRAIL-mediated apoptosis. Notably, in patients with diabetes, correlation between Vitamin D concentrations in plasma and glucose levels is linked to HG-enhanced TRAIL expression on CTLs. Microarray data reveal that OXCT2, an important enzyme in ketone body catabolism, is a promising target in response to vitamin D. Our work not only reveals a novel mechanism of CTL involvement in progression of diabetes, but also establishes CTLs as a target for combined metformin and vitamin D therapy to protect pancreatic beta cells of diabetic patients.Competing Interest StatementThe authors have declared no competing interest.
