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Journal of Physics A: Mathematical and Theoretical - latest papers

Latest articles for Journal of Physics A: Mathematical and Theoretical

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  • On the location and the strength of controllers to desynchronize coupled Kuramoto oscillators
    Synchronization is an ubiquitous phenomenon in systems composed of coupled oscillators. While it is often beneficial to the system under consideration, there are nevertheless relevant examples where one would like to reduce it, e.g. in brain dynamics. Indeed although synchronization is essential to the good functioning of brain dynamics, hyper-synchronization can induce problems such as epilepsy seizures. Motivated by this problem, we study a pinning control scheme able to decrease synchronization in a system of coupled Kuramoto oscillators, by focusing on the determination of the best selection strategy for the controllers, i.e. capable to guarantee a lower synchronization level. We show that hubs are generally the most advantageous nodes to control, especially when the degree distribution is heterogeneous. Nevertheless in cases of homogeneous degree distribution having a large distance between pinned nodes, in term of network shortest path length, appears to be also a key factor. We challenge the analytical findings on both synthetic and empirical networks, e.g. brain connectome. Our results are in line with previous works that studied pinning control with the opposite goal, i.e. increasing synchronization. These observations shed light on an interesting universality of good practice of node selection disregarding the actual goal of the control scheme.

  • Shannon entropy of an electron on a conical surface: Aharonov–Bohm effects
    In this work, we solve the Schrödinger equation of a particle restricted to move on a cone surface of finite height under the influence of an Aharonov–Bohm magnetic field. The energy eigenvalues and their respective wave functions are obtained analytically as a function of the radial distance from the apex and the apex angle. We compute the Shannon entropy in configuration and momentum space for the ground and the first excited states as a function of the slant height and the apex angle. In the absence of magnetic flux the states (n,m) and (n,−m) have identical Shannon entropies, but for non-zero fluxes the Shannon entropies of these states are different, their values depending on the state, the apex angle and the value of the magnetic flux.

  • Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales
    Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic applications, they often display interaction with their environment through energy or material exchange with a reservoir. This requires intricate mathematical considerations, especially in the case of material exchange since the varying number of particles/agents results in ‘on-the-fly’ modification of the system dimension. In this work, we first overview the probabilistic description of reaction-diffusion processes at the particle level, which readily handles varying number of particles. We then extend this model to consistently incorporate interactions with macroscopic material reservoirs. Based on the resulting expressions, we bridge the probabilistic description with macroscopic concentration-based descriptions for linear and nonlinear reaction-diffusion systems, as well as for an archetypal open reaction-diffusion system. Using these mathematical bridges across scales, we finally develop numerical schemes for open reaction-diffusion systems, which we implement in two illustrative examples. This work establishes a methodological workflow to bridge particle-based probabilistic descriptions with macroscopic concentration-based descriptions of reaction-diffusion in open settings, laying the foundations for a multiscale theoretical framework upon which to construct theory and simulation schemes that are consistent across scales.

  • Effective electromagnetic Lagrangians in the derivative expansion method
    We calculate the effective electromagnetic Lagrangian up to the lowest-order corrections in the derivatives for two fermionic systems of interest in condensed matter physics in the linearized approximation of the tight-binding Hamiltonian near the Fermi level in the Brillouin zone: (i) the description of the simplest Weyl semimetal and (ii) the massive electrodynamics, which can serve as a model for the interface between two topological insulators. We employ the derivative expansion method which directly provides local effective Lagrangians and allows selecting from the outset both the powers of the electromagnetic potential to be considered together with the number of relevant derivatives. We find new higher-order derivative corrections to Carroll-Field-Jackiw electrodynamics. In general, the new terms we find either have a similar structure or constitute a relativistic generalization of some recent phenomenological proposals found in the literature. In this way, they should be incorporated into these proposals for assessing the relative significance of all the terms included up to a given order.

  • Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups: 2. Systems with dilatation and shift symmetries
    3d quantum mechanical systems with position dependent masses (PDMs) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty seven such systems are specified and the completeness of the classification results is proved. In this way the next step to the complete classification of integrable PDM system is realized.