Related papers: The quantitative semi-classical limit of a large F…
We consider the three-dimensional semi-relativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we…
We study the time dependent Schr\"odinger equation for large spinless fermions with the semiclassical scale $\hbar = N^{-1/3}$ in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schr\"odinger…
We study the regularity properties of fermionic equilibrium states at finite positive temperature and show that they satisfy certain semiclassical bounds. As a corollary, we identify explicitly a class of positive temperature states…
We consider the Wigner equation corresponding to a nonlinear Schroedinger evolution of the Hartree type in the semiclassical limit $\hbar\to 0$. Under appropriate assumptions on the initial data and the interaction potential, we show that…
The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of…
We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous…
A quasiclassical correspondent for the fermion degrees of freedom is obtained by using a time-dependent variational principle with Grassmann coherent states as trial functions. In the real parametrization provided by the canonical…
I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished:…
In this paper we calculate properties of the three-dimensional system of N species of fermions at zero temperature and finite chemical potential, with the four-fermionic interaction of the Thirring type. We observe that this model fits…
We consider the semiclassical limit from the Hartree to the Vlasov equation with general singular interaction potential including the Coulomb and gravitational interactions, and we prove explicit bounds in the strong topologies of Schatten…
We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at the zero temperature. The results can be expressed in terms of linear combinations of the elliptic…
We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function…
We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relativistic dispersion law and interacting through a singular…
We develop a field theory for a partially filled Landau level based on composite fermions with a finite vortex core, whose mean-field states are exactly those described by well-tested trial wave functions. Despite non-orthogonality of free…
We obtain a central limit theorem for bulk counting statistics of free fermions in smooth domains of $\mathbb{R}^n$ with an explicit description of the covariance structure. This amounts to a study of the asymptotics of norms of commutators…
We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the…
We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between Landau levels set to the same order as that of potential…
We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. In particular, we consider a lattice with a linear, as well as a continuum system with a…