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Register a new userBloch-like oscillations in a one-dimensional lattice with long-range correlated disorder
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We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) sim 1/k^{alpha}$ with $alpha > 0$. Moura and Lyra [Phys. Rev. Lett. {bf 81}, 3735 (1998)] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided $alpha > 2$. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.
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We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and extended one-electron states separated by two mobility edges. We show that the electric field promotes sustained Bloch oscillations of an initial Gaussian wave packet whose amplitude reflects the band width of extended states. The frequency of these oscillations exhibit unique features, such as a sensitivity to the initial wave packet position and a multimode structure for weak fields, originating from the characteristics of the underlying aperiodic potential.
The standard two-dimensional Ising spin glass does not exhibit an ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as $(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground state and domain wall excitations. Our results indicate that the inclusion of bond correlations does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro/antiferromagnetic domains into the system. The length scale of ferro/antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, $a to a_c = 0$. Thus, our results suggest that the system becomes a ferro/antiferromagnet only in the limit $a to 0$.
We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel Polynomial Method, which has an $mathcal{O}(N)$ computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, $proptoleft|kright|^{-alpha}$, we show that the spectral function is not self-averaging for $alphageq1$.
A microwave setup for mode-resolved transport measurement in quasi-one-dimensional (quasi-1D) structures is presented. We will demonstrate a technique for direct measurement of the Greens function of the system. With its help we will investigate quasi-1D structures with various types of disorder. We will focus on stratified structures, i.e., structures that are homogeneous perpendicular to the direction of wave propagation. In this case the interaction between different channels is absent, so wave propagation occurs individually in each open channel. We will apply analytical results developed in the theory of one-dimensional (1D) disordered models in order to explain main features of the quasi-1D transport. The main focus will be selective transport due to long-range correlations in the disorder. In our setup, we can intentionally introduce correlations by changing the positions of periodically spaced brass bars of finite thickness. Because of the equivalence of the stationary Schrodinger equation and the Helmholtz equation, the result can be directly applied to selective electron transport in nanowires, nanostripes, and superlattices.
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $ u= 2/a + O((2-a)^3)$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent $eta_2=1/2-(2-a)/4+O((2-a)^2)$.
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