A bstract We study the operator growth in open quantum systems with dephasing dissipation
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …

A bstract Continuing the previous initiatives [1, 2], we pursue the exploration of operator
growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort …

The steady states of dynamical processes can exhibit stable nontrivial phases, which can
also serve as fault-tolerant classical or quantum memories. For Markovian quantum …

The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-
body systems and plays a significant role in the Haldane gap phenomena and topological …

The dynamics of quantum systems unfolds within a subspace of the state space or operator
space, known as the Krylov space. This review presents the use of Krylov subspace …

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, N fermions
with aq-body interaction of infinite range, coupled to a Markovian environment. Close to the …

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of
certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate …

Understanding the dynamics of bound state formation is one of the fundamental questions in
confining quantum field theories such as Quantum Chromodynamics (QCD). One …

The eigenstate thermalization hypothesis (ETH) represents a cornerstone in the theoretical
understanding of the emergence of thermal behavior in closed quantum systems. The ETH …

These Lecture Notes discuss the recent theoretical advances in the understanding of open
quantum many-body physics in platforms where both dissipative and coherent processes …