8,158 research outputs found
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
Uniqueness of the ground state in the Feshbach renormalization analysis
In the operator theoretic renormalization analysis introduced by Bach,
Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page
Optical conductivity for a dimer in the Dynamic Hubbard model
The Dynamic Hubbard Model represents the physics of a multi-band Hubbard
model by using a pseudo-spin degree of freedom to dynamically modify the
on-site Coulomb interaction. Here we use a dimer system to obtain analytical
results for this model. The spectral function and the optical conductivity are
calculated analytically for any number of electrons, and the distribution of
optical spectral weight is analyzed in great detail. The impact of polaron-like
effects due to overlaps between pseudo-spin states on the optical spectral
weight distribution is derived analytically. Our conclusions support results
obtained previously with different models and techniques: holes are less mobile
than electrons.Comment: 11 pages, 4 figure
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
Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
The acoustic fields and streaming in a confined fluid depend strongly on the
acoustic boundary layer forming near the wall. The width of this layer is
typically much smaller than the bulk length scale set by the geometry or the
acoustic wavelength, which makes direct numerical simulations challenging.
Based on this separation in length scales, we extend the classical theory of
pressure acoustics by deriving a boundary condition for the acoustic pressure
that takes boundary-layer effects fully into account. Using the same
length-scale separation for the steady second-order streaming, and combining it
with time-averaged short-range products of first-order fields, we replace the
usual limiting-velocity theory with an analytical slip-velocity condition on
the long-range streaming field at the wall. The derived boundary conditions are
valid for oscillating cavities of arbitrary shape and wall motion as long as
the wall curvature and displacement amplitude are both sufficiently small.
Finally, we validate our theory by comparison with direct numerical simulation
in two examples of two-dimensional water-filled cavities: The well-studied
rectangular cavity with prescribed wall actuation, and the more generic
elliptical cavity embedded in an externally actuated rectangular elastic glass
block.Comment: 18 pages, 5 figures, pdfLatex, RevTe
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
- …