Quantum simulation of atomic nulei
Atomic nuclei constitute strongly correlated quantum many-body systems governed by the strong interaction of QCD. The nuclear shell model, which diagonalizes the Hamiltonian in a basis whose dimension grows exponentially with the number of nucleons, represents a well-established approach for describing their structure. However, this combinatorial explosion confines classical high-performance computing to a restricted fraction of the nuclear chart.
Quantum computers offer a promising alternative through their natural ability to manipulate exponentially large Hilbert spaces. Although we remain in the NISQ era with its noisy qubits, they could revolutionize shell model applications.
This thesis aims to develop a comprehensive approach for quantum simulation of complex nuclear systems. A crucial first milestone involves creating a software interface that integrates nuclear structure data (nucleonic orbitals, nuclear interactions) with quantum computing platforms, thereby facilitating future applications in nuclear physics.
The project explores two classes of algorithms: variational and non-variational approaches. For the former, the expressivity of quantum ansätze will be systematically analyzed, particularly in the context of symmetry breaking and restoration. Variational Quantum Eigensolvers (VQE), especially promising for Hamiltonian-based systems, will be implemented with emphasis on the ADAPT-VQE technique tailored to the nuclear many-body problem.
A major challenge lies in accessing excited states, which are as crucial as the ground state in nuclear structure, while VQE primarily focuses on the latter. The thesis will therefore develop quantum algorithms dedicated to excited states, testing various methods: Hilbert space expansion (Quantum Krylov), response function techniques (quantum equations of motion), and phase estimation-based methods. The ultimate objective is to identify the most suitable approaches in terms of scalability and noise resilience for applications with realistic nuclear Hamiltonians.
Machine Learning-Accelerated Electron Density Calculations
Density Functional Theory (DFT) in the Kohn-Sham formalism is one of the most widespread methods for simulating microscopic properties in solid-state physics and chemistry. Its main advantage lies in its ability to strike a favorable balance between accuracy and computational cost. The continuous evolution of increasingly efficient numerical techniques has constantly broadened the scope of its applicability.
Among these techniques that can be associated with DFT, machine learning is being used more and more. Today, a very common application consists in producing potentials capable of predicting interactions between atoms using supervised learning models, relying on properties computed by DFT.
The objective of the project proposed as part of this thesis is to use machine learning techniques at a deeper level, notably to predict the electronic density in crystals or molecules. Compared to predicting properties such as forces between atoms, calculating the electronic density presents certain challenges: the electronic density is high-dimensional since it must be calculated throughout all space; its characteristics vary strongly from one material to another (metals, insulators, charge transfer, etc.). Ultimately, this can represent a significant computational cost. There are several options to reduce the dimensionality of the electronic density, such as computing projections or using localization functions.
The final goal of this project is to be able to predict, with the highest possible accuracy, the electronic density, in order to use it as a prediction or as a starting point for calculations of electron-specific properties (magnetism, band structure, for example).
In a first stage, the candidate will be able to implement methods recently proposed in the literature; in a second part of the thesis, it will then be necessary to propose new ideas. Finally, the implemented method will be used to accelerate the prediction of properties of large systems involving charge transfers, such as defect migration in crystals.
The nonresonant streaming instability in turbulent plasmas
The magnetic turbulence prevalent in many astrophysical systems, such as the solar wind and supernova remnants, plays a crucial role in accelerating high-energy particles, particularly within collisionless shock waves. By trapping particles near the shock front, this turbulence facilitates their energy gain through repeated crossings between the upstream and downstream regions – a process known as Fermi acceleration, believed to be the origin of cosmic rays.
It happens that the turbulence surrounding supernova remnants is likely generated by the cosmic rays themselves via plasma instabilities as they stream ahead of the shock. In the specific case of a shock wave propagating parallel to the ambient magnetic field, the dominant instability is thought to be the non-resonant streaming instability, or Bell's instability, which acts to amplify the preexisting turbulence.
The objective of this PhD is to build a comprehensive analytical model of this instability within a turbulent plasma, and to validate its predictions against advanced numerical simulations.
Electronic effects dans les cascades de collisions dans le GaN
In radiation environments like space and nuclear plants, microelectronic devices are subject to intense flux of particles degrading the devices by damaging the materials they are made of. Particles collide with atoms of the semi-conducting materials, ejecting them for their lattice site. Those displaced atoms also collide and set in motion a new generation of atoms, and so on, leading to a cascade of collisions which creates defects in the material. Moreover, primary or secondary particles (created following interaction with a neutron for example) also specifically interact with electrons of the target material, and lose kinetic energy in doing so by promoting electrons to higher energy bands. This aspect is called electronic stopping. Simulations of collision cascades must therefore describe both nuclei-nuclei collisions and electronic stopping effects.
The preferred method for collision cascades simulations at the atomic scale is Molecular Dynamics (MD). However, electronic effects are not included in this method as electrons are not taken into account explicitly. To circumvent this issue, additional modules have to be employed on top of MD to model electronic effects in a collision cascade. The state-of-the-art regarding electronic stopping simulation of a projectile in a target material is the real time - time dependent density functional theory (RT-TDDFT). The purpose of this thesis is to combine MD and RT-TDDFT to perform collision cascades simulations in GaN and study the influence of electronic effects. In addition to skills common to all thesis, the candidate will develop very specific skills in different atomic scale simulation methods, solid state physics, particle-matter interactions, linux environment and programming.
Measurement of the speed of sound in H2 and He, key components of gas giant interiors.
The goal of this thesis is to study hydrogen-helium mixtures in the fluid phase under high pressure and high temperature using Raman and Brillouin spectroscopy. The experiments will be conducted in a diamond anvil cell with laser heating, allowing exploration of a wide range of pressure and temperature conditions representative of the interiors of gas giant planets (1-300 GPa, 300-4000 K). Raman spectroscopy will be used to probe possible chemical changes occurring under extreme conditions, while Brillouin spectroscopy will provide access to the adiabatic sound velocity and the equations of state of these fluid mixtures. These data will be particularly useful for improving the modeling of Jupiter and Saturn’s interiors.
Multiscale modeling of the magnetic response of heterogeneous material
The spectral dependence of the permeability of magnetic materials, whether in composite or dense materials, remains a complex issue due to the different scales of the phenomena involved. Approximate analytical models are often used to describe the frequency response of magnetic materials, particularly to improve their performance in areas such as power electronics. Recent results have shown that micro-magnetism codes can now predict the response of a system of coupled nanoparticles or a particle representing the volume of the materials in question. This thesis aims to use these tools to improve existing analytical models. An inclusion immersed in an effective field will be the paradigm from which the domain structure and the spectral response of the particle will be calculated using a micro-magnetism code. The materials studied include spherical particles or those with a high aspect ratio (magnetic oxides, ferromagnetic petals) at varying concentrations, ranging from dilute media to dense materials. This work will identify pathways to optimize the microstructure of materials for better performance in applications such as power electronics and microwave components. To this end, CEA provides a scientific computing environment with access to HPC resources, as well as facilities for sample preparation and static and dynamic magnetic characterization. At the end of this work, the candidate will have gained a solid understanding of the microstructure-property relationships described by a numerical approach applied to magnetic materials. More generally, this approach is expanding in the field of materials to improve their properties in various fields, under the designation "materials by design".
Description of collective phenomena in atomic nuclei beyond Time-Dependent Density Functional
Context :
Predicting the organization and dynamics of neutrons and protons within atomic nuclei is a significant
scientific challenge, crucial for designing future nuclear technologies and addressing fundamental questions
such as the origin of heavy atoms in our universe. In this context, CEA, DAM, DIF develops theoretical
approaches to simulate the dynamics of the elementary constituents of atomic nuclei. The equations of
motion, derived within the framework of quantum mechanics, are solved on our supercomputers. The 2010s
saw the rise of the time-dependent density functional theory (TDDFT) approach for tackling this problem.
While TDDFT has provided groundbreaking insights into phenomena such as giant resonances observed in
atomic nuclei and nuclear fission, this approximation has intrinsic limitations.
Objectives :
This PhD project aims to develop and explore a novel theoretical approach to describe the collective motion
of protons and neutrons within the atomic nucleus. The goal is to generalize the TDDFT framework to
improve the prediction of certain nuclear reaction properties, such as the energy distribution among the
fragments resulting from nuclear fission. Building on initial work in this direction, the PhD candidate will
derive the equations of motion for this new approach and implement them as an optimized C++ library
designed to leverage the computational power of CEA's supercomputers. The final objective will be to assess
how this new framework enhances predictions of phenomena such as the damping of giant resonances in
atomic nuclei and the formation of fragments during nuclear fission.
Assimilation of heterogeneous data in simulations of atmospheric dispersion of radionuclides at regional scale
Modeling and simulation provide essential knowledge on the aerial dispersion of gases and particles and the resulting environmental marking. This applies in particular to the releases that were generated by atmospheric nuclear tests carried out in the past by France in Polynesia. While regional-scale meteorological and dispersion calculations are reasonably reliable, their results have a degree of uncertainty and present discrepancies with heterogeneous measurements of activities or dose rates in the air, on the ground and in biological compartments. The thesis will aim to develop inversion methods, based on data assimilation, in order to reduce errors and uncertainties in simulations of regional dispersion of radionuclides. The application will concern certain nuclear tests in the atmosphere. However, the methods developed during the thesis, such as Monte Carlo sampling by Markov chains, will have a more general field of implementation. After a literature review on nuclear testing and data assimilation methods, original inverse modeling algorithms will be programmed, tested, and applied to the simulation of the dispersion of aerial releases from tests. This will allow us to estimate the anticipated important role of measurement assimilation in improving simulations.
Etude du comportement d'un composite CMC en température par essais in situ en tomographie X
The proposed topic concerns the study of the mechanical behavior of an oxide/oxide ceramic matrix composite material at temperature (up to 1000°C). The originality of the subject lies in the use of in situ X-ray tomography to access, on the one hand, the macroscopic deformation of the tested specimens and, on the other hand, the microscopic damage mechanisms that characterize this type of so-called "damageable" material.
This technique was developed at room temperature during a previous thesis: the aim here is to apply it at higher temperature and to more complex stresses (e.g., traction-torsion). The aim will also be to propose developments to the existing volumetric image correlation analysis protocol.