43 research outputs found
Strong-coupling perturbation theory for the two-dimensional Bose-Hubbard model in a magnetic field
The Bose-Hubbard model in an external magnetic field is investigated with
strong-coupling perturbation theory. The lowest-order secular equation leads to
the problem of a charged particle moving on a lattice in the presence of a
magnetic field, which was first treated by Hofstadter. We present phase
diagrams for the two-dimensional square and triangular lattices, showing a
change in shape of the phase lobes away from the well-known power-law behavior
in zero magnetic field. Some qualitative agreement with experimental work on
Josephson-junction arrays is found for the insulating phase behavior at small
fields.Comment: 7 pages, 5 figures include
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Hyperbolic phase and squeeze-parameter estimation
We define a new representation, the hyperbolic phase representation, which enables optimal estimation of a squeeze parameter in the sense of quantum estimation theory. We compare the signal-to-noise ratio for such measurements, with conventional measurement based on photon counting and homodyne detection. The signal-to-noise ratio for hyperbolic phase measurements is shown to increase quadratically with the squeezing parameter for fixed input power
Higher spin quaternion waves in the Klein-Gordon theory
Electromagnetic interactions are discussed in the context of the Klein-Gordon
fermion equation. The Mott scattering amplitude is derived in leading order
perturbation theory and the result of the Dirac theory is reproduced except for
an overall factor of sixteen. The discrepancy is not resolved as the study
points into another direction. The vertex structures involved in the scattering
calculations indicate the relevance of a modified Klein-Gordon equation, which
takes into account the number of polarization states of the considered quantum
field. In this equation the d'Alembertian is acting on quaternion-like plane
waves, which can be generalized to representations of arbitrary spin. The
method provides the same relation between mass and spin that has been found
previously by Majorana, Gelfand, and Yaglom in infinite spin theories
New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production
Since the work of Sauter, and Heisenberg, Euler and K\"ockel, it has been
understood that vacuum polarization effects in quantum electrodynamics (QED)
predict remarkable new phenomena such as light-light scattering and pair
production from vacuum. However, these fundamental effects are difficult to
probe experimentally because they are very weak, and they are difficult to
analyze theoretically because they are highly nonlinear and/or nonperturbative.
The Extreme Light Infrastructure (ELI) project offers the possibility of a new
window into this largely unexplored world. I review these ideas, along with
some new results, explaining why quantum field theorists are so interested in
this rapidly developing field of laser science. I concentrate on the
theoretical tools that have been developed to analyze nonperturbative vacuum
pair production.Comment: 20 pages, 9 figures; Key Lecture at the ELI Workshop and School on
"Fundamental Physics with Ultra-High Fields", 29 Sept - 2 Oct. 2008,
Frauenworth Monastery, Germany; v2: refs updated, English translations of
reviews of Nikishov and Ritu