817 research outputs found
Finite Volume Chiral Partition Functions and the Replica Method
In the framework of chiral perturbation theory we demonstrate the equivalence
of the supersymmetric and the replica methods in the symmetry breaking classes
of Dyson indices \beta=1 and \beta=4. Schwinger-Dyson equations are used to
derive a universal differential equation for the finite volume partition
function in sectors of fixed topological charge, \nu. All dependence on the
symmetry breaking class enters through the Dyson index \beta. We utilize this
differential equation to obtain Virasoro constraints in the small mass
expansion for all \beta and in the large mass expansion for \beta=2 with
arbitrary \nu. Using quenched chiral perturbation theory we calculate the first
finite volume correction to the chiral condensate demonstrating how, for all
\betathere exists a region in which the two expansion schemes of quenched
finite volume chiral perturbation theory overlap.Comment: RevTeX, 18 pages. Some typos corrected and a note added in the
introduction to section III. To appear in Phys. Rev.
Interaction of Wave-Driven Particles with Slit Structures
Can a classical system as walking oil droplets on a vibrating surface
simulate the single and double slit Quantum Mechanics experiment? A systematic
investigation reveals that the answer is no, but that the classical system
exhibits rich and fascinating structures.Comment: Submitted to Phys. Rev. E, 22 pages, 26 postscript figure
Efimov trimers under strong confinement
The dimensionality of a system can fundamentally impact the behaviour of
interacting quantum particles. Classic examples range from the fractional
quantum Hall effect to high temperature superconductivity. As a general rule,
one expects confinement to favour the binding of particles. However,
attractively interacting bosons apparently defy this expectation: while three
identical bosons in three dimensions can support an infinite tower of Efimov
trimers, only two universal trimers exist in the two dimensional case. We
reveal how these two limits are connected by investigating the problem of three
identical bosons confined by a harmonic potential along one direction. We show
that the confinement breaks the discrete Efimov scaling symmetry and destroys
the weakest bound trimers. However, the deepest bound Efimov trimer persists
under strong confinement and hybridizes with the quasi-two-dimensional trimers,
yielding a superposition of trimer configurations that effectively involves
tunnelling through a short-range repulsive barrier. Our results suggest a way
to use strong confinement to engineer more stable Efimov-like trimers, which
have so far proved elusive.Comment: 8 pages, 4 figures. Typos corrected, published versio
Microscopic description of exciton-polaritons in microcavities
We investigate the microscopic description of exciton-polaritons that
involves electrons, holes and photons within a two-dimensional microcavity. We
show that in order to recover the simplified exciton-photon model that is
typically used to describe polaritons, one must correctly define the
exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare
microscopic parameters. For the case of unscreened Coulomb interactions, we
find that the exciton-photon detuning is strongly shifted from its bare value
in a manner akin to renormalization in quantum electrodynamics. Within the
renormalized theory, we exactly solve the problem of a single exciton-polariton
for the first time and obtain the full spectral response of the microcavity. In
particular, we find that the electron-hole wave function of the polariton can
be significantly modified by the very strong Rabi couplings achieved in current
experiments. Our microscopic approach furthermore allows us to properly
determine the effective interaction between identical polaritons, which goes
beyond previous theoretical work. Our findings are thus important for
understanding and characterizing exciton-polariton systems across the whole
range of polariton densities.Comment: 14 pages, 5 figure
Three-body problem in a two-dimensional Fermi gas
We investigate the three-body properties of two identical "up" fermions and
one distinguishable "down" atom interacting in a strongly confined
two-dimensional geometry. We compute exactly the atom-dimer scattering
properties and the three-body recombination rate as a function of collision
energy and mass ratio m_up/m_down. We find that the recombination rate for
fermions is strongly energy dependent, with significant contributions from
higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer
scattering below threshold is completely described by the scattering length.
Furthermore, we examine the "up-up-down" bound states (trimers) appearing at
large m_up/m_down and find that the energy spectrum for the deepest bound
trimers resembles that of a hydrogen atom confined to two dimensions.Comment: 6 pages, 6 figure
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