28 research outputs found
Scale Dependence of the Retarded van der Waals Potential
We study the ground state energy for a system of two hydrogen atoms coupled
to the quantized Maxwell field in the limit together with the
relative distance between the atoms increasing as , . In particular we determine explicitly the crossover function from the
van der Waals potential to the retarded van der Waals
potential, which takes place at scale .Comment: 19 page
Pauli-Fierz model with Kato-class potentials and exponential decays
Generalized Pauli-Fierz Hamiltonian with Kato-class potential \KPF in
nonrelativistic quantum electrodynamics is defined and studied by a path
measure. \KPF is defined as the self-adjoint generator of a strongly
continuous one-parameter symmetric semigroup and it is shown that its bound
states spatially exponentially decay pointwise and the ground state is unique.Comment: We deleted Lemma 3.1 in vol.
Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
We consider a class of translation invariant models of non-relativistic QED
with net charge. Under certain natural assumptions we prove that ground states
do not exist in the Fock space
Ground States in the Spin Boson Model
We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
Infrared problem for the Nelson model on static space-times
We consider the Nelson model with variable coefficients and investigate the
problem of existence of a ground state and the removal of the ultraviolet
cutoff. Nelson models with variable coefficients arise when one replaces in the
usual Nelson model the flat Minkowski metric by a static metric, allowing also
the boson mass to depend on position. A physical example is obtained by
quantizing the Klein-Gordon equation on a static space-time coupled with a
non-relativistic particle. We investigate the existence of a ground state of
the Hamiltonian in the presence of the infrared problem, i.e. assuming that the
boson mass tends to 0 at infinity
Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations
For classical lattice systems with finite (Ising) spins, we show that the
implementation of momentum-space renormalization at the level of Hamiltonians
runs into the same type of difficulties as found for real-space
transformations: Renormalized Hamiltonians are ill-defined in certain regions
of the phase diagram.Comment: 14 pages, late
Rapid Internalization of the Oncogenic K+ Channel KV10.1
KV10.1 is a mammalian brain voltage-gated potassium channel whose ectopic expression outside of the brain has been proven relevant for tumor biology. Promotion of cancer cell proliferation by KV10.1 depends largely on ion flow, but some oncogenic properties remain in the absence of ion permeation. Additionally, KV10.1 surface populations are small compared to large intracellular pools. Control of protein turnover within cells is key to both cellular plasticity and homeostasis, and therefore we set out to analyze how endocytic trafficking participates in controlling KV10.1 intracellular distribution and life cycle. To follow plasma membrane KV10.1 selectively, we generated a modified channel of displaying an extracellular affinity tag for surface labeling by α-bungarotoxin. This modification only minimally affected KV10.1 electrophysiological properties. Using a combination of microscopy and biochemistry techniques, we show that KV10.1 is constitutively internalized involving at least two distinct pathways of endocytosis and mainly sorted to lysosomes. This occurs at a relatively fast rate. Simultaneously, recycling seems to contribute to maintain basal KV10.1 surface levels. Brief KV10.1 surface half-life and rapid lysosomal targeting is a relevant factor to be taken into account for potential drug delivery and targeting strategies directed against KV10.1 on tumor cells