AX-GADGET: a new code for cosmological simulations of Fuzzy Dark Matter and Axion models

We present a new module of the parallel N-Body code P-GADGET3 for cosmological simulations of light bosonic non-thermal dark matter, often referred as Fuzzy Dark Matter (FDM). The dynamics of the FDM features a highly non-linear Quantum Potential (QP) that suppresses the growth of structures at small scales. Most of the previous attempts of FDM simulations either evolved suppressed initial conditions, completely neglecting the dynamical effects of QP throughout cosmic evolution, or resorted to numerically challenging full-wave solvers. The code provides an interesting alternative, following the FDM evolution without impairing the overall performance. This is done by computing the QP acceleration through the Smoothed Particle Hydrodynamics (SPH) routines, with improved schemes to ensure precise and stable derivatives. As an extension of the P-GADGET3 code, it inherits all the additional physics modules implemented up to date, opening a wide range of possibilities to constrain FDM models and explore its degeneracies with other physical phenomena. Simulations are compared with analytical predictions and results of other codes, validating the QP as a crucial player in structure formation at small scales.Comment: 18 page

On Nori's Fundamental Group Scheme

We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).Comment: 29 page

Investigation on sound propagation for the measurement of diffusion in microporous solids.

The basic definitions of micropore diffusivities and the experimental techniques applied for their measurement are reviewed. Through a historical perspective, the techniques are briefly described, with an emphasis on the measured property, the theoretical and practical limitations. As a result the need for a novel experimental technique has been identified. The extension of the frequency response (FR) method to frequencies in the audible sound range is proposed. A detailed mathematical model is presented to describe the propagation of sound between two parallel adsorbing plates. The main body of the thesis is the description and derivation of a model that relates an acoustic quantity (i.e. propagation constant) to adsorption parameters (i.e. diffusivity and equilibrium constant) in microporous solids. The theoretical analysis describes the ranges of physical parameters where the complete model reduces to simplified versions: classical absorption isothermal limit equilibrium control temperature control. Based on the theoretical study a prototype apparatus has been designed and constructed. The system allows for flexibility in the loading of adsorbent material, geometrical properties and gas used. Preliminary experimental results are reported and interpreted based upon the theory of acoustics described above

Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility

We study quantum interference effects due to electron motion on a three-dimensional cubic lattice in a continuously-tunable magnetic field of arbitrary orientation and magnitude. These effects arise from the interference between magnetic phase factors associated with different electron closed paths. The sums of these phase factors, called lattice path-integrals, are ``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type argument. Our lattice path integral calculation enables us to obtain various important physical quantities through several different methods. The spirit of our approach follows Feynman's programme: to derive physical quantities in terms of ``sums over paths". From these lattice path-integrals we compute analytically, for several lengths of the electron path, the half-filled Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic lattice. Our results are valid for any strength of the applied magnetic field in any direction. We also study in detail two experimentally important quantities: the magnetic moment and orbital susceptibility at half-filling, as well as the zero-field susceptibility as a function of the Fermi energy.Comment: 14 pages, RevTe

The dynamical Casimir effect in superconducting microwave circuits

We theoretically investigate the dynamical Casimir effect in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose to implement a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum interference devices (SQUIDs) that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyze the properties of the dynamical Casimir effect in these two setups by calculating the generated photon-flux density, output-field correlation functions, and the quadrature squeezing spectra. We show that these properties of the output field exhibit signatures unique to the radiation due to the dynamical Casimir effect, and could therefore be used for distinguishing the dynamical Casimir effect from other types of radiation in these circuits. We also discuss the similarities and differences between the dynamical Casimir effect, in the resonator setup, and downconversion of pump photons in parametric oscillators.Comment: 18 pages, 14 figure