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Traffic congestion and safety continue to pose significant challenges in urban environments. In this paper, we introduce the Smart Speed Bump (SSBump), a novel traffic calming solution that leverages the Internet of Things (IoT) and innovative non-Newtonian fluid materials to enhance road safety, optimize emergency response times, and improve the overall driving experience. The SSBump uses IoT sensors to detect and communicate with emergency vehicles, reducing response times by temporarily deflating. These sensors also analyze traffic patterns and inform data-driven decisions. Additionally, the SSBump uses an Oobleck mixture that adapts its behavior based on the velocity of approaching vehicles, resulting in a safer and more comfortable experience for drivers. This study commences with an overview of the prevalent traffic congestion, followed by a discussion on various available options in this domain. Subsequently, the paper explores the advantages of smart speed bumps and their operational mechanisms. Finally, it presents a comprehensive analysis of the results, its challenges, and the prospects of the work. The findings of this research demonstrate the potential of the SSBump system to revolutionize traffic control, emergency response time, and the driving experience in smart cities, making it a game-changing innovation for advanced transportation systems., Comment: 7 pages, 5 figures

Skyrmions are topological magnetic textures that can arise in non-centrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with nanometer length scales has sparked interest in their quantum properties. Here, we simulate the ground states of two-dimensional spin-$1/2$ Heisenberg lattices with Dzyaloshinskii-Moriya interactions and discover a broad region in the zero-temperature phase diagram which hosts quantum skyrmion lattices. We argue that the quantum skyrmion lattice phase can be detected experimentally in the magnetization profile via local magnetic polarization measurements as well as in the spin structure factor measurable via neutron scattering experiments. Finally, we explore the resulting quantum skyrmion state, analyze its real-space polarization profile and show that it is a non-classical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion., Comment: 14 pages, 13 figures

Integer quantum Hall (IQH) states and quantum anomalous Hall (QAH) states show the same static (dc) response but distinct dynamical (ac) response. In particular, the ac anomalous Hall conductivity profile $\sigma_{yx}(\omega)$ is sensitive to the band shape of QAH states. For example, dispersive QAH bands shows resonance profile without a sign change at the band gap while the IQH states shows the sign change resonance at the cyclotron energy. We argue by flattening the dispersive QAH bands, $\sigma_{yx}(\omega)$ should recover to that of flat Landau bands in IQH, thus it is necessary to know the origin of the sign change. Taking a topological lattice model with tunable bandwidth, we found that the origin of the sign change is not the band gap but the Van Hove singularity energy of the QAH bands. In the limit of small bandwidth, the flat QAH bands recovers $\sigma_{yx}(\omega)$ of the IQH Landau bands. Because of the Hall response, these topological bands exhibit giant polarization rotation and ellipticity in the reflected waves (Kerr effect) and rotation in the order of fine structure constant in the transmitted waves (Faraday effect) with profile resembles $\sigma_{yx}(\omega)$. Our results serve as a simple guide to optical characterization for topological flat bands., Comment: 10 pages, 4 figures

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian which is parameterized by an angular parameter $\lambda$. We find strong $\lambda$ dependence in both Drude and interband optical absorption of these systems. The deviation of the $T^2$ coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular $\lambda=\pi/6$ point, we find that the "helicity" reversal optical transition matrix element is identically zero. But deviating from this point, the helicity reversal emerges as an absorption channel., Comment: 12 pages, 11 figures

In the binary-alloy with composition A$_x$B$_{1-x}$ of two atoms with ionic energy scales $\pm\Delta$, an apparent Ander- son insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard $U$ to the binary alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction $U$, the resulting AI phase will become metallic which in our formulation can be clearly attributed to the screening of disorder by Hubbard $U$. Upon further increase in $U$, again the AI phase emerges which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction of which the randomness takes advantage and localizes the quasi-particles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator (MI). We construct the phase diagram of this model in the plane of ($U,\Delta$) for various compositions $x$.

Topological index of a system specifies gross features of the system. However, in situations such as strong disorder where by level repulsion mechanism the spectral gap is closed, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined from appropriate use of transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices of the related Hamiltonians. As a case study, we study a generalized XY model (2XY model) plus a generalized Dziyaloshinskii-Moriya-like (DM) interaction that after fermionization breaks the time-reversal invariance and is parameterized by $\phi$. The {\em parent} Hamiltonian at $\phi=0$ which belongs to BDI class is indexed by integer winding number while the $\phi\ne 0$ {\em daughter} Hamiltonian which belongs to class D is specified by a $Z_2$ index $\nu=\pm 1$. We show that the localization length in addition to determining the $Z_2$ can count the number of Majorana zero modes left over at the boundary of the daughter Hamiltonian -- which are not protected by winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian., Comment: please compile with included .bbl file

We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is han- dled with strong-coupling perturbation theory which encodes the Mott transition physics into a rich dynamical structure of a local self-energy. The local nature of self-energy allows us to combine it with kernel polynomial method and transfer matrix methods. The locality of self-energy combined with the analytic nature of the strong- coupling perturbation theory enables us to study lattices with millions of sites. The transfer matrix method in the ribbon geometry is essentially free from finite size errors and allows us to perform a careful finite size scaling of the width of the ribbon. This finite size scaling enables us to rule out the possibility of metallic phase in between the Mott and Anderson insulating phases. We therefore find a direct transition between Anderson and Mott insulators when the disorder strength W is comparable to the Hubbard interaction U . For a fixed disorder W , we obtain an interaction dependent nonmonotonic behavior of the localization length which reflects interac- tion induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually at strong interactions U, the Mott localization takes over and the localization length becomes comparable to the lattice scale. This is reminiscent of the holographic determination of the Mott state where the system at IR recognizes its UV lattice scale., Comment: please compile with the .bbl file

We elucidate the reduction of the winding number (WN) caused by the onsite disorder in a higher WN next nearest neighbor XY model. When disorder becomes strong enough, Majorana edge modes become critically extended, beyond which they collapse into Anderson localized (AL) states in the bulk, resulting in a topological Anderson insulating state (TAI). We identify a resilience threshold $W_t$ for every pair of Majorana fermions (MFs). In response to increasing disorder every pair of MFs collapse into AL bulk at their resilience threshold. For very strong disorder, all Majorana fermions collapse and a topologically trivial state is obtained. We show that the threshold values are deeply related to the localization length of Majorana fermions, which can be efficiently calculated by an appropriate modification of the transfer matrix method. At the topological transition point, localization length of the zero modes diverges and the system becomes scale invariant. The number of peaks in the localization length as the function of disorder strength determines the number of zero modes in the clean state before disorder is introduced. This finding elevates the transfer matrix method to the level of a tool for determination of the topological index of both clean and disordered systems., Comment: please compile with included .bbl file

Dirac electrons in clean graphene can mediate the interactions between two localized magnetic moments. The functional form of the RKKY interaction in pristine graphene is specified by two main features: (i) an atomic scale oscillatory part determined by a wave vector $\vec Q$ connecting the two valleys. Furthermore with doping another longer range oscillation appears which arise from the existence of an extended Fermi surface characterized by a single momentum scale $k_F$. (ii) $R^{\alpha}$ decay in large distances where the exponent $\alpha=-3$ is a distinct feature of undoped Dirac sea (with a linear dispersion relation) in two dimensions. In this work, we investigate the effect of a few percent vacancies on the above properties. Depending on the doping level, if the chemical potential lies on the linear part of the density of states, the exponent $\alpha$ remains close to -3. Otherwise $\alpha$ reduces towards more negative values which means that the combined effect of vacancies and the randomness in their positions makes it harder for the carriers of the medium to mediate the magnetic interaction. Addition of a few percent of vacancies diminishes the atomic scale oscillations of the RKKY interaction signaling the destruction of two-valley structure of the parent graphene material. Surprisingly by allowing the chemical potential to vary, we find that the longer-range oscillations expected to arise from the existence of a $k_F$ scale in the vacant graphene are absent. This may indicate possible non-Fermi liquid behavior by "alloying" graphene with vacancies. The complete absence of oscillations in heavily vacant graphene can be considered an advantage for applications as a uniform sign of the exchange interaction is desirable for magnetic ordering.