1,082 research outputs found
Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics
Starting from a formal Hamiltonian as found in the physics literature --
omitting photons -- we define a renormalized Hamiltonian through charge and
mass renormalization. We show that the restriction to the one-electron subspace
is well-defined. Our construction is non-perturbative and does not use a
cut-off. The Hamiltonian is relevant for the description of the Lamb shift in
muonic atoms.Comment: Reformulation of main theorem, minor changes in the proo
The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian
We consider a large neutral atom of atomic number , modeled by a
pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably
rescaled one-particle ground state density on the Thomas--Fermi length scale
. Using an observation by Fefferman and Seco (1989), we find that the
density on this scale converges to the minimizer of the Thomas--Fermi
functional of hydrogen as when is fixed to a value not
exceeding . This shows that the electron density on the Thomas--Fermi
length scale does not exhibit any relativistic effects
The Ground State Energy of Heavy Atoms According to Brown and Ravenhall: Absence of Relativistic Effects in Leading Order
It is shown that the ground state energy of heavy atoms is, to leading order,
given by the non-relativistic Thomas-Fermi energy. The proof is based on the
relativistic Hamiltonian of Brown and Ravenhall which is derived from quantum
electrodynamics yielding energy levels correctly up to order Ry
Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots
We study interacting massless Dirac fermions confined in a
two-dimensional quantum dot. Physical realizations of this problem include a
graphene monolayer and the surface state of a strong topological insulator. We
consider both a magnetic confinement and an infinite mass confinement. The
ground state energy is computed as a function of the effective interaction
parameter from the Hartree-Fock approximation and, alternatively, by
employing the M\"uller exchange functional. For N=2, we compare those
approximations to exact diagonalization results. The Hartree-Fock energies are
highly accurate for the most relevant interaction range \alpha\alt 2, but the
M\"uller functional leads to an unphysical instability when \alpha\agt 0.756.
Up to 20 particles were studied using Hartree-Fock calculations. Wigner
molecule formation was observed for strong but realistic interactions,
accompanied by a rich peak structure in the addition energy spectrum.Comment: 8 pages, 8 figure
The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction
We consider relativistic many-particle operators which - according to Brown
and Ravenhall - describe the electronic states of heavy atoms. Their ground
state energy is investigated in the limit of large nuclear charge and velocity
of light. We show that the leading quasi-classical behavior given by the
Thomas-Fermi theory is raised by a subleading correction, the Scott correction.
Our result is valid for the maximal range of coupling constants, including the
critical one. As a technical tool, a Sobolev-Gagliardo-Nirenberg-type
inequality is established for the critical atomic Brown-Ravenhall operator.
Moreover, we prove sharp upper and lower bound on the eigenvalues of the
hydrogenic Brown-Ravenhall operator up to and including the critical coupling
constant.Comment: 42 page
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