Scattering phases in quantum dots: an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.Comment: 18 pages, 9 figures. to appear in Physical Review

Towards an Explanation of the Mesoscopic Double-Slit Experiment: a new model for charging of a Quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.Comment: 4 pages, 2 figures, Journal versio

Quantum universal detectors

We address the problem of estimating the expectation value of an arbitrary operator O via a universal measuring apparatus that is independent of O, and for which the expectation values for different operators are obtained by changing only the data-processing. The ``universal detector'' performs a joint measurement on the system and on a suitably prepared ancilla. We characterize such universal detectors, and show how they can be obtained either via Bell measurements or via local measurements and classical communication between system and ancilla.Comment: 4 pages, no figure

Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy

We construct a Laplacian-level meta-generalized gradient approximation (meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy density $\tau$ of an electronic ground state of density $n$. This meta-GGA is designed to recover the fourth-order gradient expansion $\tau^{GE4}$ in the appropiate slowly-varying limit and the von Weizs\"{a}cker expression $\tau^{W}=|\nabla n|^2/(8n)$ in the rapidly-varying limit. It is constrained to satisfy the rigorous lower bound $\tau^{W}(\mathbf{r})\leq\tau(\mathbf{r})$. Our meta-GGA is typically a strong improvement over the gradient expansion of $\tau$ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas, Hooke's atom, one-electron Gaussian density, quasi-two dimensional electron gas, and nonuniformly-scaled hydrogen atom. We also construct a Laplacian-level meta-GGA for exchange and correlation by employing our approximate $\tau$ in the Tao, Perdew, Staroverov and Scuseria (TPSS) meta-GGA density functional. The Laplacian-level TPSS gives almost the same exchange-correlation enhancement factors and energies as the full TPSS, suggesting that $\tau$ and $\nabla^2 n$ carry about the same information beyond that carried by $n$ and $\nabla n$. Our kinetic energy density integrates to an orbital-free kinetic energy functional that is about as accurate as the fourth-order gradient expansion for many real densities (with noticeable improvement in molecular atomization energies), but considerably more accurate for rapidly-varying ones.Comment: 9 pages, 16 figure

The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.Comment: 8 pages, LaTex, one postscript figur

Correlations in the cotunneling regime of a quantum dot

Off-resonance conductance through weakly coupled quantum dots ("valley conductance") is governed by cotunneling processes in which a large number of dot states participate. Virtually the same states participate in the transport at consecutive valleys, which leads to significant valley-valley conductance correlations. These correlations are calculated within the constant interaction model. Comparison with experiment shows that these correlations are less robust in reality. Among the possible reasons for this is the breakdown of the constant interaction model, accompanied by "scrambling" of the dot as the particle number is varied.Comment: 10 pages, 4 eps-figures; reference adde

Aharonov-Bohm Interferometry with Interacting Quantum Dots: Spin Configurations, Asymmetric Interference Patterns, Bias-Voltage-Induced Aharonov-Bohm Oscillations, and Symmetries of Transport Coefficients

We study electron transport through multiply-connected mesoscopic geometries containing interacting quantum dots. Our formulation covers both equilibrium and non-equilibrium physics. We discuss the relation of coherent transport channels through the quantum dot to flux-sensitive Aharonov-Bohm oscillations in the total conductance of the device. Contributions to transport in first and second order in the intrinsic line width of the dot levels are addressed in detail. We predict an interaction-induced asymmetry in the amplitude of the interference signal around resonance peaks as a consequence of incoherence associated with spin-flip processes. This asymmetry can be used to probe the total spin of the quantum dot. Such a probe requires less stringent experimental conditions than the Kondo effect, which provides the same information. We show that first-order contributions can be partially or even fully coherent. This contrasts with the sequential-tunneling picture, which describes first-order transport as a sequence of incoherent tunneling processes. We predict bias-voltage induced Aharonov-Bohm oscillations of physical quantities which are independent of flux in the linear-response regime. Going beyond the Onsager relations we analyze the relations between the space symmetry group of the setup and the flux-dependent non-linear conductance.Comment: 22 pages, 11 figure

The ‘Galilean Style in Science’ and the Inconsistency of Linguistic Theorising

Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics? First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second step, a case study is carried out which exemplifies that the principle of epistemological tolerance may be interpreted as the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics and that the integration of different data types requires a novel methodology which, for the time being, is not available

The ‘Galilean Style in Science’ and the Inconsistency of Linguistic Theorising

Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics? First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second step, a case study is carried out which exemplifies that the principle of epistemological tolerance may be interpreted as the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics and that the integration of different data types requires a novel methodology which, for the time being, is not available