Binary Bose-Einstein condensates in a disordered time-dependent potential

We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.

Theory of bulk photovoltaic effect in Anderson insulator

The localization of wavefunction by disorder makes a conductive material an insulator with vanishing conductivity at zero temperature. A similar outcome is expected for the photocurrent in semiconductor p-n junctions because the photoexcited carriers cannot drift through the device. In contrast, we here show numerically that the bulk photovoltaic effect—the photovoltaic effect in noncentrosymmetric bulk materials—occurs in a noncentrosymmetric, disordered, one-dimensional insulator where all eigenstates are localized. We find this photocurrent remains, even when the energy scale of random potential is larger than the bandwidth. On the other hand, the photocurrent decays exponentially when the excitation is local, i.e., when only a part of the device is illuminated. The photocurrent also vanishes if the relaxation occurs only by contact with the electrodes. Our result implies that the ratio of the photovoltaic current and the direct current by the variable-range hopping increases with decreasing temperature. These results suggest a route to design high-efficiency solar cells and photodetectors.

Flooding dynamics of diffusive dispersion in a random potential

We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time T(x) to reach position x, arising from different realisations of the random potential. Specifically, we contrast the median $${\bar{T}}(x)$$ T ¯ ( x ) , which is an informative description of the typical course of the motion, with the expectation value $$\langle T(x)\rangle $$ ⟨ T ( x ) ⟩ , which is dominated by rare events where there is an exceptionally high barrier to diffusion. We show that at relatively short times the median $${\bar{T}}(x)$$ T ¯ ( x ) is explained by a ‘flooding’ model, where T(x) is predominantly determined by the highest barriers which are encountered before reaching position x. These highest barriers are quantified using methods of extreme value statistics.

Wave Propagation and Localization in a Complex Random Potential with Power-law Correlations: A Numerical Study

In this paper, we investigate numerically wave propagation and localization in a complex random potential with power-law correlations. Using a discrete stationary Schrӧdinger equation with the simultaneous presence of the spatial correlation and the non-Hermiticity of the random potential in the diagonal on-site terms of the Hamiltonian, we calculate the disorder-averaged logarithmic transmittance and the localization length. From the numerical analysis, we find that the presence of power-law correlation in the imaginary part of the on-site disordered potential gives rise to the localization enhancement as compared with the case of absence of correlation. Depending on the disorder's strength, we show that there exist different behaviors of the dependence of the localization on the correlation strength.