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Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…
For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system…
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden…
Simple, controllable models play an important role to learn how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class…
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or…
Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical…
Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory…
In the last years, the application of machine learning methods has become increasingly relevant in different fields of physics. One of the most significant subjects in the theory of open quantum systems is the study of the characterization…
We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e.,…
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which…
Experiments often probe observables that correspond to low-dimensional projections of highdimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that…
We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…
Recent success in developing increasingly general purpose agents based on sequence models has led to increased focus on the problem of deploying computationally limited agents within the vastly more complex real-world. A key challenge…
Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond…
Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee…
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices, to qubit decoherence in quantum technologies, and even protein…