Several new numerical techniques for tackling the problem of quantum many-body non-equilibrium dynamics have been developed in the past few years, both in the field of physics and chemistry. Although sometimes being conceptually very simillar, awareness of new methods is often restricted to their disciplines of origin. The goal of this workshop is to bring the physics and chemistry communities together to unlock synergies in numerical method development. In particular, we identified the following three numerical concepts that will be discussed at this workshop:

• Techniques for far-from-equilibrium quantum dynamics in many body systems (MPS/tensor networks): Recently developed algorithms with matrix product states (MPS) [1] rely e.g. on time-evolving block decimation (TEBD) [2], time-evolving variational principles (TDVP) [3], or matrix product evolution operators (MPOs) [4], and they have led to simulations of coherent “quantum quench dynamics” on unprecedented time-scales in 1D geometries. Such methods have unlocked the door to studying fundamental far-from-equilibrium physics, such as: quantum thermalization, many-body localization, information spreading (scrambling / Lieb-Robinson bounds / entanglement growth), or driven dissipative phase-transitions. The workshop will discuss current open fundamental questions in far-from-equilibrium quantum physics and how ideas from chemistry may help to lift current numerical limitations (e.g. current restrictions to 1D and pseudo-1D, i.e. tree, geometries).

• Techniques for non-adiabatic quantum dynamics from theoretical chemistry:  The need for understanding precise molecular dynamics in chemical reactions and photodynamics has led to impressive advances with quantum mechanical and semi-classical techniques [5]. This workshop will discuss (multilayer) multiconfiguration time dependent Hartree [(ML-) MCTDH] methods [6, 7], and how ML-MCTDH can be combined and formulated in terms of a tensor-network language. How can synergies lead to new algorithms in both communities? Can very recent developments in ML-MCTDH for density matrix evolution be recast and accelerated as Matrix Product Operator forms? ML-MCTDH methods have also been used with linear vibronic (harmonic) Hamiltonians to find relaxed reference geometries for DFT simulations [8]. Could tensor network methods also be used in these schemes? Furthermore we will focus on QM/MM simulations [9; 10], and how these semi-classical methods could capture quantum (nuclear) effects and lead to enhanced algorithms for physics problems.
• Open system dynamics for transport, advanced spectroscopies, data visualization and interfaces with electronic structure theory: Tensor network methods have also been a crucial new tool for studying open system dynamics and, increasingly, quantum thermodynamics across fields. Formalisms range from path integrals [11, 12], MPS/MPO methods [13; 14 ;15], and numerically exact simulations of real-time dynamics and multi-time response functions can now be performed on model systems with 100-1000s of bosonic and fermionic modes [16; 17]. However, these methods are often restricted to linear system-environment couplings, and applications to realistic ab initio models of molecules are extremely challenging [1]. Methods such as ML-MCTDH appear to be more flexible, in terms of microscopic models. Why? Are tensor methods less general, but more optimized for certain problems? Finally, could the data produced by 'physics' methods - based on purely diabatic states and Fock state represenations - be visualized in the typical chemistry picture of wavepackets moving on (adiabatic) potential energy surfaces (PES) [18]?