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

A many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.Comment: v3: fixed pdf problem; v2: added exact formula (Eq. 42) for Green's function and discussion of equilibrium density matrix (new Fig. 2); 10 figures, 21 pages, see quant-ph/0305098 for brief version of some of these result

Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior

We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time \tPh(T) from diffusive or ergodic 1D (\tPh^{-1} \propto T^{2/3}, T^{1}) to $0D$ behavior (\tPh^{-1} \propto T^{2}) as $T$ drops below the Thouless energy \ETh. We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the $0D$ regime on equal footing as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for 3D systems, has so far eluded experimental observation. We will show that for T \ll \ETh, $0D$ dephasing governs not only the $T$-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry holds promise of finally observing the crossover to $0D$ experimentally.Comment: in "Perspectives of Mesoscopic Physics - Dedicated to Yoseph Imry's 70th Birthday", edited by Amnon Aharony and Ora Entin-Wohlman (World Scientific, 2010), chap. 20, p. 371-396, ISBN-13 978-981-4299-43-

Thermal noise and dephasing due to electron interactions in non-trivial geometries

We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.Comment: 9 pages, 6 figures (version submitted to PRB

Mesoscopic to universal crossover of transmission phase of multi-level quantum dots

Transmission phase \alpha measurements of many-electron quantum dots (small mean level spacing \delta) revealed universal phase lapses by \pi between consecutive resonances. In contrast, for dots with only a few electrons (large \delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of \alpha for small \delta follows from Fano-type antiresonances of the renormalized single-particle levels.Comment: 4 pages, version accepted for publication in PR

Universal dephasing in a chiral 1D interacting fermion system

We consider dephasing by interactions in a one-dimensional chiral fermion system (e.g. a Quantum Hall edge state). For finite-range interactions, we calculate the spatial decay of the Green's function at fixed energy, which sets the contrast in a Mach-Zehnder interferometer. Using a physically transparent semiclassical ansatz, we find a power-law decay of the coherence at high energies and zero temperature (T=0), with a universal asymptotic exponent of 1, independent of the interaction strength. We obtain the dephasing rate at T>0 and the fluctuation spectrum acting on an electron.Comment: 5 pages, 3 figures; minor changes, version as published

Fixed-N Superconductivity: The Crossover from the Bulk to the Few-Electron Limit

We present a truly canonical theory of superconductivity in ultrasmall metallic grains by variationally optimizing fixed-N projected BCS wave-functions, which yields the first full description of the entire crossover from the bulk BCS regime (mean level spacing $d \ll$ bulk gap $\tilde\Delta$) to the ``fluctuation-dominated'' few-electron regime ($d\gg\tilde\Delta$). A wave-function analysis shows in detail how the BCS limit is recovered for $d\ll \tilde \Delta$, and how for $d \gg \tilde \Delta$ pairing correlations become delocalized in energy space. An earlier grand-canonical prediction for an observable parity effect in the spectral gaps is found to survive the fixed-N projection.Comment: 4 pages, 3 figures, RevTeX, V2: minor charges to mach final printed versio

Arrays of Cooper Pair Boxes Coupled to a Superconducting Reservoir: `Superradiance' and `Revival.'

We consider an array of Cooper Pair Boxes, each of which is coupled to a superconducting reservoir by a capacitive tunnel junction. We discuss two effects that probe not just the quantum nature of the islands, but also of the superconducting reservoir coupled to them. These are analogues to the well-known quantum optical effects `superradiance,' and `revival.' When revival is extended to multiple systems, we find that `entanglement revival' can also be observed. In order to study the above effects, we utilise a highly simplified model for these systems in which all the single-electron energy eigenvalues are set to be the same (the strong coupling limit), as are the charging energies of the Cooper Pair Boxes, allowing the whole system to be represented by two large coupled quantum spins. Although this simplification is drastic, the model retains the main features necessary to capture the phenomena of interest. Given the progress in superconducting box experiments over recent years, it is possible that experiments to investigate both of these interesting quantum coherent phenomena could be performed in the forseeable future.Comment: 23 pages, 5 figures Clarifications made as recommended by refere