Quantum Phase Transitions in a Generalized Dicke Model.

We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.

Modelling of transport processes: Theory and simulations.

The transport processes, being a non-equilibrium system, have been a point of interest for physicists since many years revealing and explaining several unexpected effects. Such systems are often dealt with an archetypal model, known as totally asymmetric simple exclusion process, with two different types of boundary conditions: open and periodic. Moreover, these models are analyzed in two varieties of dynamics, random sequential and parallel updates, even at the micro level which play an important role in the global dynamics of the system. On contrary to the random sequential rule, the parallel updates introduce correlations in the system. Using theoretical and numerical methods in the framework based on mean-field approaches, the system properties are analyzed in both transient and steady state.•Both the updating rules are realized using Monte Carlo simulations.•In simplest form, mean-field approach ignores all the correlations and the results coincide with the random sequential update.•Correlations are induced in the system due to parallel update, therefore, a cluster mean-field theory is also discussed to handle them.

Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach.

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides.

Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample.

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

A General Theoretical Framework to Study the Influence of Electrical Fields on Mesenchymal Stem Cells.

Mesenchymal stem cell dynamics involve cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.

Cooperative effect of random and time-periodic coupling strength on synchronization transitions in one-way coupled neural system: mean field approach.

The cooperative effect of random coupling strength and time-periodic coupling strengh on synchronization transitions in one-way coupled neural system has been investigated by mean field approach. Results show that cooperative coupling strength (CCS) plays an active role for the enhancement of synchronization transitions. There exist an optimal frequency of CCS which makes the system display the best CCS-induced synchronization transitions, a critical frequency of CCS which can not further affect the CCS-induced synchronization transitions, and a critical amplitude of CCS which can not occur the CCS-induced synchronization transitions. Meanwhile, noise intensity plays a negative role for the CCS-induced synchronization transitions. Furthermore, it is found that the novel CCS amplitude-induced synchronization transitions and CCS frequency-induced synchronization transitions are found.

Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks.

We investigate the effects of delaying the time to recovery (delayed recovery) and of nonuniform transmission on the propagation of diseases on structured populations. Through a mean-field approximation and large-scale numerical simulations, we find that postponing the transition from the infectious to the recovered states can largely reduce the epidemic threshold, therefore promoting the outbreak of epidemics. On the other hand, if we consider nonuniform transmission among individuals, the epidemic threshold increases, thus inhibiting the spreading process. When both mechanisms are at work, the latter might prevail, hence resulting in an increase of the epidemic threshold with respect to the standard case, in which both ingredients are absent. Our findings are of interest for a better understanding of how diseases propagate on structured populations and to a further design of efficient immunization strategies.

An alternative approach to characterize the topology of complex networks and its application in epidemic spreading.

Based on the mean-field approach, epidemic spreading has been well studied. However, the mean-field approach cannot show the detailed contagion process, which is important in the control of epidemic. To fill this gap, we present a novel approach to study how the topological structure of complex network influences the concrete process of epidemic spreading. After transforming the network structure into hierarchical layers, we introduce a set of new parameters, i.e., the average fractions of degree for outgoing, ingoing, and remaining in the same layer, to describe the infection process. We find that this set of parameters are closely related to the degree distribution and the clustering coefficient but are more convenient than them in describing the process of epidemic spreading. Moreover, we find that the networks with exponential distribution have slower spreading speed than the networks with power-law degree distribution. Numerical simulations have confirmed the theoretical predictions.