Browsing by Author "Yahyavi, Mohammad"

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Open Access
Generalized Aubry-Andre-Harper model with modulated hopping and p-wave pairing
(American Physical Society, 2019) Yahyavi, Mohammad; Hetenyi, Balazs; Tanatar, Bilal
We study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.
Open Access
Numerical study on a polymer-shelled microbubble submerged in soft tissue
(IOP Publishing, 2020) Ghalichi, F.; Behnia, S.; Mottaghi, F.; Yahyavi, Mohammad
Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of the encapsulated microbubbles under the action of an ultrasound field are complex and high nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. The dynamics of a polymer-shelled agent are studied through applying the method of chaos physics whereas the effects of the outer medium compressibility and the shell were considered. The stability of the ultrasound contrast agent is examined by plotting the bifurcation diagrams, Lyapunov exponent, and time series over a wide range of variations of influential parameters. The findings of the study indicate that by tuning the shear modulus of surrounding medium and shell viscosity, the radial oscillations of microbubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic pulse are increased mainly due to the period doubling phenomenon. Furthermore, influences of various parameters which present a comprehensive view of the radial oscillations of the microbubble are quantitatively discussed with clear descriptions of the stable and unstable regions of the microbubble oscillations for typical therapeutic ultrasound pulses.
Open Access
Scaling and renormalization in the modern theory of polarization: application to disordered systems
(American Physical Society, 2021-12-15) Hetényi, Balázs; Parlak, Selçuk; Yahyavi, Mohammad
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension, the renormalized disorder strength tends to infinity, indicating the entire absence of extended states. Zero (infinite) disorder is a repulsive (attractive) fixed point. In two and three dimensions, at small system sizes, two additional fixed points appear, both at finite disorder: Wa(Wr) is attractive (repulsive) such that Wa
Open Access
Study of encapsulated microbubble cluster based on association schemes perspective
(Elsevier, 2018) Behnia, S.; Yahyavi, Mohammad; Habibpourbisafar, R.; Mottaghi, F.
Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of a cluster of encapsulated microbubbles under the action of an ultrasound field are complex and highly nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. In this paper, based on Qin-Ferrara’s model (Qin and Ferrara, 2010), the complete synchronization and cluster formation in targeted microbubbles network are studied. Also, association schemes as a novel approach are suggested for finding a relationship between coupled microbubbles elements which are immersed in blood or surrounding soft tissue. A significant advantage of this method is that the stability of the synchronized state (or symmetric eigenmode of mutual bubble oscillation) with respect to another state (another eigenmode) can now predict. More interestingly, we find a significant relationship between an isolated and multiple microbubbles. The results show that the problem of studying the dynamics of encapsulated microbubble cluster at synchronization state is dependent on the dynamical characteristics of isolated cases, shell thickness, density. Also, the distance between microbubbles has an important role in their synchronous modes.
Open Access
Topological aspects of charge transport in quantum many-body systems
(2019-01) Yahyavi, Mohammad
Motivated by the recent proposals and developments of topological insulators and topological superconductors for their potential applications in electronic devices and quantum computing, we have theoretically studied topological properties of quantum many-body systems. First, we calculate the gauge-invariant cumulants (and moments) associated with the Zak phase. The first cumulant corresponds to the Berry phase itself, the others turn out to be the associated spread, skew, kurtosis, etc. The cumulants are shown to be gauge invariant. We reconstruct the underlying probability distribution of the polarization by maximizing the information entropy and applying the moments as constraints in the Rice-Mele model and in the interacting, spinless Su-Schrieffer-Heeger model. When the Wannier functions are localized within one-unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We follow the probability distribution of the polarization in cycles around the topologically nontrivial point of these models. Secondly, we have constructed a topological one-dimensional analog of the Haldane and Kane-Mele models in two dimensions, with hexagonal lattices. Our Haldane one-dimensional analog model belongs to the C and CI symmetry classes, depending on the parameters, but, due to re ection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We also construct a topological one-dimensional ladder model following the steps which lead to the Kane-Mele model in two dimensions. We couple two Haldane-type ladder models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of re ection symmetries. Thirdly, we consider the edge at the interface of a simple tight-binding model and a band insulator. We find that crossings in the band structure (one dimensional Dirac points) appear when an interface is present in the system. We calculate the hopping energy resolved along lines of bonds parallel to the interface as a function of distance from the interface. Similarly, we introduce a transport coe cient (Drude weight) for charge currents running parallel to the interface. We find that charge mobility (both the kinetic energy and the Drude weight) is significantly enhanced in the surface of the tight-binding part of the model near the interface. Finally, we study a variant of the generalized Aubry-Andre-Harper model with the effect of introducing next nearest-neighbor p-wave superconducting pairing with incommensurate and commensurate cosine modulations. We extend generalized Aubry-Andr e-Harper model with p-wave superconducting to topologically equivalent and nontrivial "anancestor" two-dimensional p-wave superconducting model. It is found that in incommensurate (commensurate) modulation, by varying next nearest-neighbor p-wave pairing order parameter, the system can switch between extended states and localized states (fully gapped phase and a gapless phase).
Open Access
Topological insulation in a ladder model with particle-hole and reflection symmetries
(Institute of Physics Publishing, 2018) Hetényi, Balazs; Yahyavi, Mohammad
A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the C and CI symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of reflection symmetries.
Open Access
Variational study of the interacting, spinless Su-Schrieffer-Heeger model
(Institute of Physics Publishing, 2018) Yahyavi, Mohammad; Saleem, ‪Luqman; Hetényi, Balazs
We study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution 'walks across' smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.
Open Access
Watermarking based on discrete wavelet transform and q-deformed chaotic map
(Elsevier Ltd, 2017) Behnia, Sohrab; Yahyavi, Mohammad; Habibpourbisafar, Reza
Hierarchy of one-dimensional ergodic chaotic maps with Tsallis type of q-deformation are studied. We find that in the chaotic region, these maps with q-deformation are ergodic as the Birkhoff ergodic theorem predicts. q-deformed maps are defined as ratios of polynomials of degree N. Hence, by using the Stieltjes transform approach (STA), invariant measure is proposed. In addition, considering Sinai-Ruelle-Bowen (SRB) measure, Kolmogorov-Sinai (KS) entropy for q-deformed maps is calculated analytically. The new q-deformed scheme have ability to keep previous significant properties such as ergodicity, sensitivity to initial condition. By adding q-parameter to the hierarchy in order increase the randomness and one-way computation, we present a new scheme for watermarking. The introduced algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security. To illustrate the effectiveness of the proposed scheme, some security analyses are presented. By considering the obtained results, it can be concluded that, this scheme have a high potential to be adopted for watermarking. It can be concluded that, the proposed novel watermarking scheme for image authentication can be applied for practical applications. © 2017 Elsevier Ltd