Related papers: Opening Krylov space to access all-time dynamics v…
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this…
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 (classical) dynamics, these steady states are extremal eigenvectors…
We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a…
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…
Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the…
We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (the closure of) the Krylov subspace associated to such…
Open system dynamics in a classical setting is microscopically governed by the structure of the thermal environment which influences the dynamics of the probe particle (free or in an external potential). Nonlinear baths have recently been…
Dirac-Frenkel variational method with Davydov D2 trial wavefunction is extended by introducing a thermalization algorithm and applied to simulate dynamics of a general open quantum system. The algorithm allows to control temperature…
We demonstrate a surprising connection between pure steady state entanglement and relaxation timescales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems $A$ and $B$ interact locally with a common…
In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous…
Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for…
The recently developed formalism of Markovian master equations for quantum open systems with external periodic driving is applied to the theory of dynamical decoupling by periodic control. This new approach provides a more detailed…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal…
Controllable Markov chains describe the dynamics of sequential decision making tasks and are the central component in optimal control and reinforcement learning. In this work, we give the general form of an optimal policy for learning…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…