Long-time memory effects in a localizable central spin problem

We study the properties of the Nakajima-Zwanzig memory kernel for a qubit immersed in a many-body localized (i.e. disordered and interacting) bath. We argue that the memory kernel decays as a power law in both the localized and ergodic regimes, and show how this can be leveraged to extract t → ∞ populations for the qubit from finite time (Jt ≤ 10^2) data in the thermalizing phase. This allows us to quantify how the long-time values of the populations approach the expected thermalized state as the bath approaches the thermodynamic limit. This approach should provide a good complement to state-of-the-art numerical methods, for which the long-time dynamics with large baths are impossible to simulate in this phase. Additionally, our numerics on finite baths reveal the possibility for unbounded exponential growth in the memory kernel, a phenomenon rooted in the appearance of exceptional points in the projected Liouvillian governing the reduced dynamics. In small systems amenable to exact numerics, we find that these pathologies may have some correlation with delocalization.

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.

Comparing apples and oranges in priming of attention shifts?

Attentional priming involves speeded selection of task-relevant visual search items when search stimuli remain constant from one search to the next. There is a tendency in the literature to interpret diverse priming effects as reflecting activity modulations of the same mechanisms. Priming effects in various different paradigms (from lower-level to higher-level features) have been used interchangeably to study the nature of priming, even when tasks differ vastly in difficulty and neural mechanisms involved. Another view is that priming is a characteristic of all perceptual mechanisms, that operate at different processing levels. Here, this issue was addressed by contrasting time courses and relative sizes of priming effects for repetition of a lower-level and higher-level feature (color vs. facial expression). Attentional priming was tested in two odd-one-out search tasks, one involving discrimination, the other present/absent judgment. Firstly, the sizes of the normalized priming effects were very different for color and expression and secondly, color priming effects lasted for much longer than expression priming, as measured with memory kernel analyses, suggesting that the mechanics behind the effects differ. These two forms of priming should therefore only be compared with great caution. Generally, the results suggest that priming occurs at many levels of processing and can take many forms. This view is highly consistent with research on the neural mechanisms of priming. Priming of attention shifts should be thought of as a general principle of perceptual processing.

Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation

In this work, an explicit solution of the initial-boundary value problem for a multidimensional time-fractional differential equation is constructed. The possibility of obtaining this equation from an integro-differential wave equation with a Mittag–Leffler–type memory kernel is shown. An explicit solution to the problem under consideration is obtained using the Laplace and Fourier transforms, the properties of the Fox H-functions and the convolution theorem.