Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. For instance, using real-space Monte Carlo to sample polymer systems becomes impractical for increasing size, rigidity, and density of the chains. In response to these challenges, we introduce and apply a formalism to recast polymer sampling as a quadratic unconstrained binary optimization (QUBO) problem [1]. Thanks to this mapping, dense systems of stiff polymers on a lattice can be efficiently sampled with classical QUBO solvers, resulting in more favourable performance scaling compared to real-space Monte Carlo [2]. Tackling the same problems with the D-Wave quantum annealer leads to further performance improvements [2]. As an application, we discuss the use of the quantum-inspired encoding on a hitherto untackled problem, namely the linking probability of equilibrated melts of ring polymers, for which we unveil counterintuitive topological effects. References [1] C.Micheletti, P. Hauke and P. Faccioli, "Polymer physics by quantum computing", Phys. Rev. Lett. 127, 080501 (2021) [2] F. Slongo, P. Hauke, P. Faccioli and C. Micheletti "Quantum-inspired encoding enhances stochastic sampling of soft matter systems", Sci. Adv. 9, art. no adi0204 (2023)
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TBA

In driven non-linear systems, various kinds of bifurcations can be observed on their route to chaos. From the evolution of Floquet multipliers one can extract information which serves as a precursor for phase transitions and dynamical instabilities. This method is applied in classical non-linear physics, for example, to obtain early warning signals. Utilising our impressive control over an atom-cavity platform, we are able to prepare our system in various dynamical regimes and study the bifurcation experimentally in a quantum gas to obtain insights that could potentially be applied to more complex systems. We prepare a Bose-Einstein condensate inside the centre of a cavity and pumping it perpendicular to the cavity axis with a standing wave light field. Upon crossing a critical pump strength, we observe a pitchfork phase transition from a normal to a steady state self-organized phase [1]. Employing an open three- level Dicke model, this transition can be understood as a transition between two fixpoints, indicating a pitchfork bifurcation. If the pump strength is increased further, the system undergoes a Hopf bifurcation. This causes limit cycles, which have time crystalline properties, to emerge [2]. In this regime, our model no longer shows fixpoints but stable attractive periodic orbits [3]. For strong pumping, we observe a second bifurcation, in our case a Neimark-Sacker bifurcation. Its main characteristics is an oscillation with two incommensurate frequencies, this may indicate the formation of a continuous time quasicrystal [4]. Finally, in the regime of very strong pumping, we observe chaotic dynamics with many contributing frequencies. References: [1] J. Klinder, et al., PNAS 112, 11 (2015) [2] P. Kongkhambut, et al., Science 307 (2022) [3] J. Skulte, et al., arXiv:2401.05332 (2023) [4] P. Kongkhambut, et al., manuscript in preparation

Electrochemistry is a discipline promising to advance material science towards more environmentally friendly and sustainable technologies for energy solutions. Electrochemical systems are usually composed of interacting complex molecules, making understanding collective effects limited for macroscopic experiments. Computer simulations offer a way to obtain insights in silico. In particular, molecular dynamics simulations, with detailed interatomic potentials, allow us to rationalize experimental results by exploring the dynamics of physical systems through virtual experiments. In the first part of this thesis, I systematically review molecular dynamics simulation methods providing the foundation for preparing our physical system in silico. I introduce the basic principles of an all-atom molecular simulation within the framework of statistical physics and discuss in detail the treatment of electrostatic interactions and the importance of dielectric boundary conditions. In the second part of this thesis, I present our molecular dynamics study of a liquid system composed of water and acetonitrile molecules and their response to an external electric field. This mixture exhibits unique properties, including a distinctive electrical conductivity detection in the absence of an electrolyte in novel electrolysis flow cells. However, the underlying physical mechanism behind this phenomenon remains unknown. As a first step to understanding this mechanism, this work focuses on the bulk system structure and how a macroscopic external electric field influences its properties.