arXiv subjects

Itaru Sasaki

Publications and source records attributed to Itaru Sasaki.

21 records · Page 2Linked to original sources

arXiv2010

On the ionization energy of the semi-relativistic Pauli-Fierz model for a single particle

A semi-relativistic Pauli-Fierz model is defined by the sum of the free Hamiltonian $H_{\rm f}$ of a Boson Fock space, an nuclear potential $V$ and a relativistic kinetic energy: $$ H=\sqrt{[σ\cdot(\mathbf{p}+e\mathbf{A})]^2+M^2} - M + V + H_{\rm f}. $$ Let $-e_0<0$ be the ground state energy of a semi-relativistic Schrödinger operator $$ H_{\rm p}=\sqrt{\mathbf{p}^2+M^2} - M + V. $$ It is shown that the ionization energy $E^{\rm ion}$ of $H$ satisfies $$E^{\rm ion}\geq e_0>0$$ for all values of both of the coupling constant $e\in\mathbb{R}$ and the rest mass $M\geq 0$. In particular our result includes the case of M=0.

math-ph↗

arXiv2008

Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium

We discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under negligence of the particle pair interactions. We derive the kinetic scaling limit for the momentum distribution function with a translation invariant initial state and prove that it is determined by a linear Boltzmann equation. Moreover, we prove that if the initial state is quasifree, then the time evolved state, averaged over the randomness, has a quasifree kinetic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field are stationary solutions of the linear Boltzmann equation; this includes the limit of zero temperature.

math-ph↗

arXiv2006

Enhanced binding for N-particle system interacting with a scalar bose field I

An enhanced binding of an $N$-particle system interacting through a scalar bose field is investigated, where $N\geq 2$. It is not assumed that this system has a ground state for a zero coupling. It is shown, however, that there exists a ground state for a sufficiently large values of coupling constants. When the coupling constant is sufficiently large, $N$ particles are bound to each other by the scalar bose field, and are trapped by external potentials. Basic ideas of the proofs in this paper are applications of a weak coupling limit and a modified HVZ theorem.

math-ph↗