“I learned very early the difference between knowing the name of something and knowing something.” Richard Feynman
Undergraduate Thesis
Parallelization of a Discrete Element Method (DEM) algorithm using the Graphical Processing Unit (GPU)
This paper presents a GPU-based parallel implementation of a Discrete Element Method (DEM) algorithm. The technique is applied in the simulation of free-falling particles in a rectangular bed. The effects on computation time for different number of particles are compared for the cases of performing the calculations using the GPU and the CPU (Central Processing Unit). It is found that the GPU provides a subsequent speed-up as compared to the CPU as the number of particles is increased.
Master Thesis
Non-equilibrium dynamics of quantum systems and Matrix Product States
This report was the culmination of my 4 months internship at the LPTM at CY Cergy Paris University. My work involved a great deal of analytical work and simulation. The main aim of this internship was to study the non-equilibrium dynamic of quantum spin chains using state of the art numerical method. For this purpose, a particular class of variational quantum states, the so-called matrix product states, were used to describe the time evolution of a quantum many-body systems and study the emergence of macroscopic behaviours. The values of the transport coefficients obtained numerically using matrix product states were compared with the analytical results obtained using the framework of generalised hydrodynamics. We managed to approach the prediction to some degree, however we did not manage to go to the large time regime where generalised hydrodynamics holds. In the last chapter, we discuss an alternative method that could potentially be employed in order to reach the hydrodynamic regime.
Doctoral Thesis
Exploring quantum dynamics: from hydrodynamics to measurement induced phase transition
This thesis summarizes research work done over 3 years at the LPTM at CY Cergy Paris University where I studied the dynamics of quantum many-body systems, with a focus on emergent hydrodynamic behaviours. This thesis introduces key concepts in quantum integrable systems and generalized hydrodynamics, along with Matrix Product States (MPS) for simulating 1D quantum dynamics. In Chapter 2, a model based on generalized hydrodynamics is developed to describe the relaxation of spin helices, accurately predicting long-term behavior and revealing anomalous diffusion. Chapter 3 examines phenomena in the easy-axis regime, identifying unique equilibrium states and different dynamical behaviours depending on the initial state, including super-diffusive and diffusive scaling. Chapter 4 investigates quantum spin chains under continuous monitoring, using the Time-Dependent Variational Principle (TDVP) to approximate quantum evolution. The analysis reveals a phase transition in error rates and a distinct charge-sharpening transition, independent of entanglement, when U(1) symmetry is present. The thesis concludes by summarizing these findings and suggesting directions for future research.
Publications
- https://arxiv.org/abs/2211.03 (Phys. Rev. B 108, 075135)
- https://arxiv.org/abs/2303.08832 (Phys. Rev. Research 6, 023083)
- https://arxiv.org/abs/2307.05379 (Phys. Rev. Lett. 132, 130401)
- https://arxiv.org/abs/2402.13160 (Phys. Rev. Research 6, 033220)
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Guillaume Cecile 