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Understanding the non-equilibrium dynamics of quantum many-body systems remains one of the grand challenges of modern physics. In particular, increasing attention has been devoted to the emergence of non-equilibrium universality classes…
The dynamics of a Bose-Einstein condensate is studied theoretically in a combined periodic plus harmonic external potential. Different dynamical regimes of stable and unstable collective dipole and Bloch oscillations are analysed in terms…
We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After…
Going beyond the currently investigated regimes in experiments on quantum transport of ultracold atoms in disordered potentials, we predict a crossover between regular and quantum-chaotic dynamics when varying the strength of disorder. Our…
The quantum dynamics of open many-body systems poses a challenge for computational approaches. Here we develop a stochastic scheme based on the positive P phase-space representation to study the nonequilibrium dynamics of coupled spin-boson…
The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…
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 can be tuned and controlled to a high degree. We start by…
Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into…
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations…
Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation timescales even in the absence of static disorder. Here, we report on the observation of such constrained dynamics arising…
We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential. Because the two-body interaction admits a bound state, the many-body model is best described by a Hamiltonian that…
Controlled quantum systems such as ultracold atoms can provide powerful platforms to study non-equilibrium dynamics of closed many-body quantum systems, especially since a complete theoretical description is generally challenging. In this…
We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with…
A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian…
A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium…
Ultracold atomic gases have revolutionized the study of non-equilibrium dynamics in quantum many-body systems. Many counterintuitive non-equilibrium effects have been observed, such as suppressed thermalization in a one-dimensional (1D)…
We explore the dynamics of hard-core lattice bosons in the presence of strong non-local particle loss. The evolution occurs on two distinct time-scales, first a rapid strongly correlated decay into a highly degenerate Zeno state subspace,…
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and…
The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We…