Antoni Jankiewicz | Searcharxiv

arXiv2026

Dynamical quantum phase transitions in a hybrid quantum dot system with superconducting and ferromagnetic leads

We theoretically explore the non-equilibrium dynamics of a single quantum dot system coupled to both ferromagnetic and superconducting electrodes. To investigate its time evolution, we utilize the time-dependent numerical renormalization group technique, which captures the system's response to abrupt parameter changes in a fully non-perturbative manner. Our analysis focuses on dynamics following a sudden modification in the couplings to the leads or a shift of the orbital level. In particular, we calculate the time evolution of the induced local superconducting pairing correlations and magnetization. In this context, the relevant energy spectra are examined. Moreover, we study the behavior of the Loschmidt echo and the return function to shed light on the signatures of dynamical quantum phase transitions. The determined dependencies reveal non-trivial competition between relevant correlations, involving superconducting pairing and ferromagnetic-contacted induced exchange field, and deepen our understanding of nanoscale hybrid systems' dynamical behavior.

cond-mat.mes-hall↗

arXiv2023

Universal representation by Boltzmann machines with Regularised Axons

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.

cond-mat.stat-mech↗