Related papers: Generalized Second-Order Thomas-Fermi Method for S…
We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space.…
We extensively develop an algorithm of implementing the Hartree-Fock-Bogolyubov calculations, in which the Gaussian expansion method is employed. This algorithm is advantageous in describing the energy-dependent exponential and oscillatory…
The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$\Delta$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the…
We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
This thesis considers out-of-equilibrium dynamics of strongly interacting non-relativistic Fermi gases in several two and three dimensional geometries. The tools of second-order hydrodynamics and gauge-gravity duality will be utilized to…
On the basis of the Kadanoff-Baym (KB) varient of the time dependent Green's function method a new ansatz for the approximation of a spectral function is offered. The ansatz possesses all the advantages of quasiparticle (QP) and extended…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
We investigate the "twist" mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is…
In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited…
A diffusion process is usually assumed for the phase of the order parameter of a Bose system of finite size. The theoretical basis is limited to the so called Bogoliubov approximation. We show that a suitable generalization of the…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…
We generalize normal mode expansion of Green's tensor $\bar{\bar{G}}(\bf{r},\bf{r}')$ to lossy resonators in open systems, resolving a longstanding open challenge. We obtain a simple yet robust formulation, whereby radiation of energy to…
We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
The one-band Hubbard model at half-filling on a truncated tetrahedron (C$_{12}$), and on the C$_{60}$ molecule is studied. Within the Hartree-Fock approximation, we find a magnetic-like instability of the `Fermi sea' towards a spin-ordered…
The applicability of the Hartree-Fock and random phase approximations to models of strongly correlated electrons is discussed. The 2D Hubbard model is analyzed. An antiferromagnetic phase (at half filling) and Fermi liquid behavior (at low…
We present systematic ab initio calculations of the charge carrier correlations between adjacent layers of two-dimensional materials in the presence of both charged impurity and strain disorder potentials using the examples of monolayer and…