50 research outputs found
Asymptotic completeness in dissipative scattering theory
We consider an abstract pseudo-Hamiltonian for the nuclear optical model,
given by a dissipative operator of the form , where is self-adjoint and is a bounded operator. We study the wave
operators associated to and . We prove that they are asymptotically
complete if and only if does not have spectral singularities on the real
axis. For Schr\"odinger operators, the spectral singularities correspond to
real resonances.Comment: 48 page
Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED
We consider an atom interacting with the quantized electromagnetic field in
the standard model of non-relativistic QED. The nucleus is supposed to be
fixed. We prove smoothness of the resolvent and local decay of the photon
dynamics for quantum states in a spectral interval I just above the ground
state energy. Our results are uniform with respect to I. Their proofs are based
on abstract Mourre's theory, a Mourre inequality established in [FGS1],
Hardy-type estimates in Fock space, and a low-energy dyadic decomposition.Comment: 31 page
Analyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field
We study a neutral atom with a non-vanishing electric dipole moment coupled
to the quantized electromagnetic field. For a sufficiently small dipole moment
and small momentum, the one-particle (self-) energy of an atom is proven to be
a real-analytic function of its momentum. The main ingredient of our proof is a
suitable form of the Feshbach-Schur spectral renormalization group.Comment: Small typos and inconsistencies corrected. Accepted for publication
in J. Funct. Ana
Spectral Analysis of a Model for Quantum Friction
An otherwise free classical particle moving through an extended spatially
homogeneous medium with which it may exchange energy and momentum will undergo
a frictional drag force in the direction opposite to its velocity with a
magnitude which is typically proportional to a power of its speed. We study
here the quantum equivalent of a classical Hamiltonian model for this friction
phenomenon that was proposed in [11]. More precisely, we study the spectral
properties of the quantum Hamiltonian and compare the quantum and classical
situations. Under suitable conditions on the infrared behaviour of the model,
we prove that the Hamiltonian at fixed total momentum has no ground state
except when the total momentum vanishes, and that its spectrum is otherwise
absolutely continuous.Comment: 40 page
Quasi-classical Ground States. I. Linearly Coupled Pauli-Fierz Hamiltonians
We consider a spinless, non-relativistic particle bound by an external
potential and linearly coupled to a quantized radiation field. The energy
of product states of the form , where
is a normalized state for the particle and is a coherent state in Fock
space for the field, gives the energy of a Klein-Gordon--Schr\''odinger system.
We minimize the functional on its natural energy space. We
prove the existence and uniqueness of a ground state under general conditions
on the coupling function. In particular, neither an ultraviolet cutoff nor an
infrared cutoff is imposed. Our results establish the convergence in the
ultraviolet limit of both the ground state and ground state energy of the
Klein-Gordon--Schr\''odinger energy functional, and provide the second-order
asymptotic expansion of the ground state energy at small coupling
L'ion hydrogénoïde piégé en électrodynamique quantique non relativiste
International audienceNous considérons un noyau et un électron non relativistes interagissant avec un champ électromagnétique quantifié. Nous ne supposons pas le noyau fixe, mais nous supposons que le système est confiné par son centre de masse. Ce modèle est utilisé en physique théorique pour décrire l'effet Lamb–Dicke et l'effet Mössbauer. Nous définissons l'hamiltonien associé au système en introduisant une troncature ultraviolette, puis nous prouvons l'existence d'un état fondamental non dégénéré. Ce résultat est obtenu sans condition sur les constantes de couplage