The study of thermalization and chaos in driven quantum many-body systems has emerged as a critical area of research due to its profound implications for quantum statistical mechanics, information theory, and condensed matter physics. Unlike classical systems, isolated quantum systems do not always thermalize in accordance with conventional statistical mechanics, giving rise to phenomena such as many-body localization (MBL) and prethermalization, which have significant applications in quantum information processing and quantum computing. The characterization of quantum chaos, often through out-of-time-ordered correlators (OTOCs), provides key insights into information scrambling and entanglement growth, with deep connections to black hole physics and the AdS/CFT correspondence. Moreover, periodically driven (Floquet) systems exhibit novel nonequilibrium phases, including time crystals, challenging traditional thermodynamic paradigms. Recent experimental progress in ultracold atoms, trapped ions, and superconducting qubits has enabled direct exploration of these theoretical concepts, positioning this field at the forefront of modern quantum science and technology.
The study of linear and nonlinear transport in quantum magnets is a rapidly advancing field with significant implications for condensed matter physics, spintronics, and quantum materials. In quantum magnetic systems, transport properties are governed by intricate interactions between spin, charge, and lattice degrees of freedom, leading to exotic behaviors beyond conventional electronic transport. Linear response theory describes transport in the regime of small perturbations, capturing fundamental properties such as spin and thermal conductivities, while nonlinear transport arises under strong driving fields, revealing emergent phenomena such as magnon drag, spin Seebeck effects, and nonlinear Hall effects. Additionally, quantum geometry, including Berry curvature and quantum metric effects, plays a crucial role in shaping transport properties, particularly in topological and strongly correlated magnetic systems. Nontrivial topological and quantum many-body effects further enrich transport dynamics, with implications for the study of frustrated magnets, quantum spin liquids, and topological magnons. Advances in experimental techniques, including neutron scattering, spin caloritronics, and ultrafast optical probes, have enabled direct observation of these transport phenomena, paving the way for next-generation quantum technologies based on spin and heat currents rather than conventional charge transport.