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We examined a one-dimensional quantum Heisenberg model that includes trimer-like correlated disordered exchange couplings and a non-uniform magnetic field. We conducted numerical experiments to study the transfer of magnons between the two ends of the chain. Using numerical methods, we calculated the time evolution of a localized magnon state at the left end of the chain. We evaluated the quality of the transfer from the left end to the right using standard tools such as fidelity and concurrence. Our calculations demonstrate the existence of magnon transfer with good fidelity for some specific energies ( E > 0 ) in the absence of a magnetic field. We also investigated the impact of the random magnetic field on our findings. [ABSTRACT FROM AUTHOR]

The transmission of a qubit in a tight-binding channel with exponentially decaying hopping terms and diagonal disorder is investigated. The end sites act as sender and receiver and are perturbatively coupled to the channel. This is done to suppress interference of the channel modes during the time evolution of the state. We explore the performance of the transfer fidelity against the disorder strength and hopping range within the channel. The scaling behavior of the participation number as a function of the hopping range is also discussed. Channels featuring long-range interactions display distinct robustness against disorder and high-quality quantum state transfer is attainable even for disorder levels of the order of the largest hopping amplitude. [ABSTRACT FROM AUTHOR]

We investigate a quantum-state transfer protocol through a quasi-1D spin-1/2 channel defined on a hexagonal layer featuring hopping disorder. In the absence of disorder, the quantum channel displays two flat bands hosting compact localized states. That is signalled by the appearance of singularities in the density of states. We show that an arbitrary qubit state can be transmitted with high fidelity between the two ends even in the presence of noise as long as they are not in resonance with energy levels surrounding the flat band. This higher sensitivity against disorder is due to the residual single-cell compact localized states accompanied by a degeneracy lifting. [ABSTRACT FROM AUTHOR]

We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated by using a sinusoidal function whose phase varies as a power-law, $\phi \propto n^{\nu}$, where n labels the positions along the media. By considering a discrete one-dimensional version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity. [ABSTRACT FROM AUTHOR]

We study the nature of the vibrational modes in a two-dimensional harmonic lattice with long-range correlated random masses, with power-law spectral density S(k)∼1/kα. We obtain numerically the scale invariance of the fluctuations of the relative participation number and the local density of states. We find signatures of extended vibrational modes when α>αc and αc depends on the magnitude of disorder. In order to confirm this claim, we also study the time evolution of an initially localized perturbation of the lattice. We show that the second moment of the spatial distribution of the energy displays a ballistic regime when α>αc, in agreement with the occurrence of extended vibrational modes. [ABSTRACT FROM AUTHOR]

In this work, a one-dimensional quantum Heisenberg ferromagnet with aperiodic exchange couplings is considered. To produce an aperiodic distribution of exchange couplings, it is used a sinusoidal function whose phase φ varies as a power-law, φ∝nν, where n labels the positions along the chain. By using exact diagonalization, the spin-wave participation number and the local density of states are computed. The numerical calculations indicate that for 0 < ν < 1, this ferromagnetic system displays a phase of extended spin waves in the low-energy region. For ν > 1 all spin waves are localized except for the zero energy mode. By integrating the time-dependent Schrödinger equation, the temporal evolution of the mean-square displacement of the wave-packet was followed. Associated with the emergence of extended spin waves, it was observed that the wave-packet mean-square displacement displays a ballistic spread. [ABSTRACT FROM AUTHOR]

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet. [ABSTRACT FROM AUTHOR]