Roberto N. Muñoz | Searcharxiv

arXiv2024

Capturing long-range memory structures with tree-geometry process tensors

We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network with tree-like geometry whose component tensors are (1) causality-preserving maps (superprocesses) and (2) locality-preserving temporal change of scale transformations. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects, and can accommodate genuinely quantum power-law correlations in time. Importantly, this class allows efficient computation of multi-time correlation functions. To showcase the potential utility of this model-agnostic class for numerical simulation of physical models, we show how it can efficiently approximate the strong memory dynamics of the paradigmatic spin-boson model, in terms of arbitrary multitime features. In contrast to an equivalently costly matrix product operator (MPO) representation, the ansatz produces a fiducial characterization of the relevant physics. Finally, leveraging 2D tensor network renormalization group methods, we detail an algorithm for deriving a process tree from an underlying Hamiltonian, via the Feynmann-Vernon influence functional. Our work lays the foundation for the development of more efficient numerical techniques in the field of strongly interacting open quantum systems, as well as the theoretical development of a temporal renormalization group scheme.

quant-ph↗

arXiv2020

General anesthesia reduces complexity and temporal asymmetry of the informational structures derived from neural recordings in Drosophila

We apply techniques from the field of computational mechanics to evaluate the statistical complexity of neural recording data from fruit flies. First, we connect statistical complexity to the flies' level of conscious arousal, which is manipulated by general anesthesia (isoflurane). We show that the complexity of even single channel time series data decreases under anesthesia. The observed difference in complexity between the two states of conscious arousal increases as higher orders of temporal correlations are taken into account. We then go on to show that, in addition to reducing complexity, anesthesia also modulates the informational structure between the forward- and reverse-time neural signals. Specifically, using three distinct notions of temporal asymmetry we show that anesthesia reduces temporal asymmetry on information-theoretic and information-geometric grounds. In contrast to prior work, our results show that: (1) Complexity differences can emerge at very short timescales and across broad regions of the fly brain, thus heralding the macroscopic state of anesthesia in a previously unforeseen manner, and (2) that general anesthesia also modulates the temporal asymmetry of neural signals. Together, our results demonstrate that anesthetized brains become both less structured and more reversible.

q-bio.NC↗