484 research outputs found

### Poor man's derivation of the Bethe-Ansatz equations for the Dicke model

We present an elementary derivation of the exact solution (Bethe-Ansatz
equations) of the Dicke model, using only commutation relations and an informed
Ansatz for the structure of its eigenstates.Comment: 2 page

### Expansion of a mesoscopic Fermi system from a harmonic trap

We study quantum dynamics of an atomic Fermi system with a finite number of
particles, N, after it is released from a harmonic trapping potential. We
consider two different initial states: The Fermi sea state and the paired state
described by the projection of the grand-canonical BCS wave function to the
subspace with a fixed number of particles. In the former case, we derive exact
and simple analytic expressions for the dynamics of particle density and
density-density correlation functions, taking into account the level
quantization and possible anisotropy of the trap. In the latter case of a
paired state, we obtain analytic expressions for the density and its
correlators in the leading order with respect to the ratio of the trap
frequency and the superconducting gap (the ratio assumed small). We discuss
several dynamic features, such as time evolution of the peak due to pair
correlations, which may be used to distinguish between the Fermi sea and the
paired state.Comment: 4 pages, 1 color figure; v2.: A reference adde

### Low temperature dephasing saturation from elastic magnetic spin disorder and interactions

We treat the question of the low temperature behavior of the dephasing rate
of the electrons in the presence of elastic spin disorder scattering and
interactions. In the frame of a self-consistent diagrammatic treatment, we
obtain saturation of the dephasing rate in the limit of low temperature for
magnetic scattering, in agreement with the non-interacting case. The magnitude
of the dephasing rate is set by the strength of the magnetic scattering rate.
We discuss the agreement of our results with relevant experiments.Comment: This paper supersedes cond-mat/021022

### Comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations"

Recently, A. Jerez, P. Vitushinsky and M. Lavagna [Phys. Rev. Lett. 95,
127203 (2005)] claimed that the transmission phase through a quantum fot, as
measured via the Aharonov-Bohm interferometer, differs from the phase which
determines the corresponding conductance. Here we show that this claim is wrong
for the single level Anderson model, which is usually used to describe the
quantum dot. So far, there exists no derivation of this claim from any explicit
theoretical model.Comment: To appear as a Comment in PR

### Derivation of exact flow equations from the self-consistent parquet relations

We exploit the parquet formalism to derive exact flow equations for the
two-particle-reducible four-point vertices, the self-energy, and typical
response functions, circumventing the reliance on higher-point vertices. This
includes a concise, algebraic derivation of the multiloop flow equations, which
have previously been obtained by diagrammatic considerations. Integrating the
multiloop flow for a given input of the totally irreducible vertex is
equivalent to solving the parquet equations with that input. Hence, one can
tune systems from solvable limits to complicated situations by variation of
one-particle parameters, staying at the fully self-consistent solution of the
parquet equations throughout the flow. Furthermore, we use the resulting
differential form of the Schwinger-Dyson equation for the self-energy to
demonstrate one-particle conservation of the parquet approximation and to
construct a conserving two-particle vertex via functional differentiation of
the parquet self-energy. Our analysis gives a unified picture of the various
many-body relations and exact renormalization group equations

### Mesoscopic Spin-Boson Models of Trapped Ions

Trapped ions arranged in Coulomb crystals provide us with the elements to
study the physics of a single spin coupled to a boson bath. In this work we
show that optical forces allow us to realize a variety of spin-boson models,
depending on the crystal geometry and the laser configuration. We study in
detail the Ohmic case, which can be implemented by illuminating a single ion
with a travelling wave. The mesoscopic character of the phonon bath in trapped
ions induces new effects like the appearance of quantum revivals in the spin
evolution.Comment: 4.4 pages, 5 figure

### Dynamical conductance in the two-channel Kondo regime of a double dot system

We study finite-frequency transport properties of the double-dot system
recently constructed to observe the two-channel Kondo effect [R. M. Potok et
al., Nature 446, 167 (2007)]. We derive an analytical expression for the
frequency-dependent linear conductance of this device in the Kondo regime. We
show how the features characteristic of the 2-channel Kondo quantum critical
point emerge in this quantity, which we compute using the results of conformal
field theory as well as numerical renormalization group methods. We determine
the universal cross-over functions describing non-Fermi liquid vs. Fermi liquid
cross-overs and also investigate the effects of a finite magnetic field.Comment: 11 pages in PRB forma

### Absorption and Emission in quantum dots: Fermi surface effects of Anderson excitons

Recent experiments measuring the emission of exciton recombination in a
self-organized single quantum dot (QD) have revealed that novel effects occur
when the wetting layer surrounding the QD becomes filled with electrons,
because the resulting Fermi sea can hybridize with the local electron levels on
the dot. Motivated by these experiments, we study an extended Anderson model,
which describes a local conduction band level coupled to a Fermi sea, but also
includes a local valence band level. We are interested, in particular, on how
many-body correlations resulting from the presence of the Fermi sea affect the
absorption and emission spectra. Using Wilson's numerical renormalization group
method, we calculate the zero-temperature absorption (emission) spectrum of a
QD which starts from (ends up in) a strongly correlated Kondo ground state. We
predict two features: Firstly, we find that the spectrum shows a power law
divergence close to the threshold, with an exponent that can be understood by
analogy to the well-known X-ray edge absorption problem. Secondly, the
threshold energy $\omega_0$ - below which no photon is absorbed (above which no
photon is emitted) - shows a marked, monotonic shift as a function of the
exciton binding energy $U_{\rm exc}$Comment: 10 pages, 9 figure

### Spatial correlations of trapped 1d bosons in an optical lattice

We investigate a quasi-one dimensional system of trapped cold bosonic atoms
in an optical lattice by using the density matrix renormalization group to
study the Bose-Hubbard model at T=0 for experimentally realistic numbers of
lattice sites. It is shown that a properly rescaled one-particle density matrix
characterizes superfluid versus insulating states just as in the homogeneous
system. For typical parabolic traps we also confirm the widely used local
density approach for describing correlations in the limit of weak interaction.
Finally, we note that the superfluid to Mott-insulating transition is seen most
directly in the half width of the interference peak

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