281 research outputs found
Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field
In this paper the Hamiltonian for the system of semi-relativistic particles
interacting with a scalar bose field is investigated. A scaled total
Hamiltonian of the system is defined and its scaling limit is considered. Then
the semi-relativistic Schrodinger operator with an effective potential is
derived
Kramers degeneracy theorem in nonrelativistic QED
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is
proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed
total momentum is also investigated.Comment: LaTex, 11 page
Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration
Starting from the N-particle Nelson Hamiltonian defined by imposing an
ultraviolet cutoff, we perform ultraviolet renormalization by showing that in
the zero cutoff limit a self-adjoint operator exists after a logarithmically
divergent term is subtracted from the original Hamiltonian. We obtain this term
as the diagonal part of a pair interaction appearing in the density of a Gibbs
measure derived from the Feynman-Kac representation of the Hamiltonian. Also,
we show existence of a weak coupling limit of the renormalized Hamiltonian and
derive an effective Yukawa interaction potential between the particles.Comment: 28 pages, revision of section 2 and typos correcte
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a
spin-1/2 electron in the standard model of non-relativistic QED. We study the
Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum.
For small enough values of the fine-structure constant, we prove that the
ground state is unique. This result reflects the hyperfine structure of the
hydrogen atom ground state.Comment: 22 pages, 3 figure
Ultra-Weak Time Operators of Schrodinger Operators
In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schr¨odinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f : R ! R such that f(HV ) has an ultra-weak time operator is found
Field evolution of the magnetic structures in ErTiO through the critical point
We have measured neutron diffraction patterns in a single crystal sample of
the pyrochlore compound ErTiO in the antiferromagnetic phase
(T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the
[110] direction. We determine all the characteristics of the magnetic structure
throughout the quantum critical point at =2\,T. As a main result, all Er
moments align along the field at and their values reach a minimum. Using
a four-sublattice self-consistent calculation, we show that the evolution of
the magnetic structure and the value of the critical field are rather well
reproduced using the same anisotropic exchange tensor as that accounting for
the local paramagnetic susceptibility. In contrast, an isotropic exchange
tensor does not match the moment variations through the critical point. The
model also accounts semi-quantitatively for other experimental data previously
measured, such as the field dependence of the heat capacity, energy of the
dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure
- …