Related papers: From the Hartree to the Vlasov dynamics: condition…
In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent…
We study the relativistic Hartree approach with the exact treatment of the vacuum polarization in the Walecka sigma-omega model. The contribution from the vacuum polarization of nucleon-antinucleon field to the source term of the meson…
Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the Disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential…
We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by adding an attractive external potential decaying at…
The time-dependent Hartree-Fock equations are derived from the N-particle Schr\"odinger equation with mean-field scaling in the infinite particle limit, for initial data that are like Slater determinants. Only the case of bounded…
The time-dependent Hartree-Fock approach may be derived from a variational principle and a Slater Determinant wavefunction Ansatz. It gives a good description of nuclear processes in which one-body collisions dominate and has been applied…
In this paper, we consider the scattering theory of the radial solution to focusing energy-subcritical Hartree equation with inverse-square potential in the energy space $H^{1}(\mathbb{R}^d)$ using the method from \cite{Dodson2016}. The…
Relativistic superfluidity at arbitrary temperature, chemical potential and (uniform) superflow is discussed within a self-consistent field-theoretical approach. Our starting point is a complex scalar field with a $\varphi^4$ interaction,…
We consider the long time asymptotics of (not necessarily small) odd solutions to the nonlinear Schr\"odinger equation with semi-linear and nonlocal Hartree nonlinearities, in one dimension of space. We assume data in the energy space…
We extend the derivation of the time-dependent Hartree-Fock equation recently obtained in [2] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the…
In this paper we consider a semiclassical version of the wave equations with singular H\"{o}lder time-dependent propagation speeds on the lattice $\hbar\mathbb{Z}^{n}$. We allow the propagation speed to vanish leading to the weakly…
Motivated by the recent progress in cooling and trapping polar molecules, we present a simplified version of the rigorous contact pseudopotential for anisotropically-interacting polarized particles [A. Derevianko, Phys. Rev. A 67, 033607…
We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
Assuming the dynamical convergence $P_t^\varepsilon\to\bar P_t$ for singular limits of time-homogeneous Markov diffusion semigroups, we develop a semigroup-level framework that upgrades this convergence into four levels of thermodynamic…
The Langevin dynamics of a system exhibiting a Fluctuation Induced First Order Phase Transition is solved within the self consistent Hartree Approximation. Competition between interactions at short and long length scales gives rise to…
We derive the restricted optical-conductivity sum rule for a model with circulating orbital currents. It is shown that an unusual coupling of the vector potential to the interaction term of the model Hamiltonian results in a non-standard…
The dynamic properties of normalized ground states for the Hartree equation with a harmonic potential are addressed. The existence of normalized ground state for any prescribed mass is confirmed according to mass-energy constrained…
We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we deduce the equation of motions, the action…
The Liouville equation with non-constant magnetic field is obtained as a limit in the Planck constant \hbar of the Heisenberg equation with the same magnetic field. The convergence is with respect to an appropriate semi-classical pseudo…