220 research outputs found
Special K\"ahler-Ricci potentials on compact K\"ahler manifolds
A special K\"ahler-Ricci potential on a K\"ahler manifold is any nonconstant
function such that is a Killing vector field
and, at every point with , all nonzero tangent vectors orthogonal
to and are eigenvectors of both and
the Ricci tensor. For instance, this is always the case if is a
nonconstant function on a K\"ahler manifold of complex
dimension and the metric , defined wherever , is Einstein. (When such exists, may be called {\it
almost-everywhere conformally Einstein}.) We provide a complete classification
of compact K\"ahler manifolds with special K\"ahler-Ricci potentials and use it
to prove a structure theorem for compact K\"ahler manifolds of any complex
dimension which are almost-everywhere conformally Einstein.Comment: 45 pages, AMSTeX, submitted to Journal f\"ur die reine und angewandte
Mathemati
Bright and dark excitons in an atom--pair filled optical lattice within a cavity
We study electronic excitations of a degenerate gas of atoms trapped in pairs
in an optical lattice. Local dipole-dipole interactions produce a long lived
antisymmetric and a short lived symmetric superposition of individual atomic
excitations as the lowest internal on-site excitations. Due to the much larger
dipole moment the symmetric states couple efficiently to neighbouring lattice
sites and can be well represented by Frenkel excitons, while the antisymmetric
dark states stay localized. Within a cavity only symmetric states couple to
cavity photons inducing long range interactions to form polaritons. We
calculate their dispersion curves as well as cavity transmission and reflection
spectra to observe them. For a lattice with aspherical sites bright and dark
states get mixed and their relative excitation energies depend on photon
polarizations. The system should allow to study new types of solid state
phenomena in atom filled optical lattices
Microscopic physics of quantum self-organisation of optical lattices in cavities
We study quantum particles at zero temperature in an optical lattice coupled
to a resonant cavity mode. The cavity field substantially modifies the particle
dynamics in the lattice, and for strong particle-field coupling leads to a
quantum phase with only every second site occupied. We study the growth of this
new order out of a homogeneous initial distribution for few particles as the
microscopic physics underlying a quantum phase transition. Simulations reveal
that the growth dynamics crucially depends on the initial quantum many-body
state of the particles and can be monitored via the cavity fluorescence.
Studying the relaxation time of the ordering reveals inhibited tunnelling,
which indicates that the effective mass of the particles is increased by the
interaction with the cavity field. However, the relaxation becomes very quick
for large coupling.Comment: 14 pages 6 figure
Quantum stability of self-organized atomic insulator-like states in optical resonators
We investigate a paradigm example of cavity quantum electrodynamics with many
body systems: an ultracold atomic gas inside a pumped optical resonator. In
particular, we study the stability of atomic insulator-like states, confined by
the mechanical potential emerging from the cavity field spatial mode structure.
As in open space, when the optical potential is sufficiently deep, the atomic
gas is in the Mott-like state. Inside the cavity, however, the potential
depends on the atomic distribution, which determines the refractive index of
the medium, thus altering the intracavity field amplitude. We derive the
effective Bose-Hubbard model describing the physics of the system in one
dimension and study the crossover between the superfluid -- Mott insulator
quantum states. We determine the regions of parameters where the atomic
insulator states are stable, and predict the existence of overlapping stability
regions corresponding to competing insulator-like states. Bistable behavior,
controlled by the pump intensity, is encountered in the vicinity of the shifted
cavity resonance.Comment: 13 pages, 6 figures. Replaced with revised version. Accepted for
publication in New J. Phys., special issue "Quantum correlations in tailord
matter
Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity QED
Studies of ultracold atoms in optical lattices link various disciplines,
providing a playground where fundamental quantum many-body concepts, formulated
in condensed-matter physics, can be tested in much better controllable atomic
systems, e.g., strongly correlated phases, quantum information processing.
Standard methods to measure quantum properties of Bose-Einstein condensates
(BECs) are based on matter-wave interference between atoms released from traps
which destroys the system. Here we propose a nondestructive method based on
optical measurements, and prove that atomic statistics can be mapped on
transmission spectra of a high-Q cavity. This can be extremely useful for
studying phase transitions between Mott insulator and superfluid states, since
various phases show qualitatively distinct light scattering. Joining the
paradigms of cavity quantum electrodynamics (QED) and ultracold gases will
enable conceptually new investigations of both light and matter at ultimate
quantum levels, which only recently became experimentally possible. Here we
predict effects accessible in such novel setups.Comment: 6 pages, 3 figure
Dynamical Coupling between a Bose-Einstein Condensate and a Cavity Optical Lattice
A Bose-Einstein condensate is dispersively coupled to a single mode of an
ultra-high finesse optical cavity. The system is governed by strong
interactions between the atomic motion and the light field even at the level of
single quanta. While coherently pumping the cavity mode the condensate is
subject to the cavity optical lattice potential whose depth depends nonlinearly
on the atomic density distribution. We observe bistability already below the
single photon level and strong back-action dynamics which tunes the system
periodically out of resonance.Comment: 5 pages, 4 figure
A bargaining procedure leading to the serial rule in games with veto players
This paper studies an allocation procedure for coalitional games with veto players. The procedure is similar to the one presented by Arin and Feltkamp (J Math Econ 43:855-870, 2007), which is based on Dagan et al. (Games Econ Behav 18:55-72, 1997). A distinguished player makes a proposal that the remaining players must accept or reject, and conflict is solved bilaterally between the rejector and the proposer. We allow the proposer to make sequential proposals over several periods. If responders are myopic maximizers (i.e. consider each period in isolation), the only equilibrium outcome is the serial rule of Arin and Feltkamp (Eur J Oper Res 216:208-213, 2012) regardless of the order of moves. If all players are fully rational, the serial rule still arises as the unique subgame perfect equilibrium outcome if the order of moves is such that stronger players respond to the proposal after weaker ones
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