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Semidefinite programs can be constructed to provide a non-perturbative view of the zero-temperature behavior of quantum systems. This paper examines the properties of these semidefinite programs when applied to lattice-regulated field…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
Since its first appearance in 1971, Gutzwiller's trace formula has been extended to systems with continuous symmetries, in which not all periodic orbits are isolated. In order to avoid the divergences occurring in connection with symmetry…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
A semiclassical Thomas-Fermi method, including a Weizs\"acker gradient term, is implemented to describe ground states of two dimensional nanostructures of arbitrary shape. Time dependent density oscillations are addressed in the same spirit…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing…
Using the concept of open systems where the classical geometry is treated as the system and the quantum matter field as the environment, we derive a fluctuation-dissipation theorem for semiclassical cosmology. This theorem which exists…
In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat…
An effective quasiparticle description of the thermodynamics of deconfined matter, compatible with both finite-temperature lattice data and the perturbative limit, is generalized to finite chemical potential. Within this approach, the…
In the standard model, stabilization of a classically unstable cosmic string may occur through the quantum fluctuations of a heavy fermion doublet. We review numerical results from a semiclassical expansion in a reduced version of the…