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