Theory of charge sensing in quantum-dot structures

Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization-group methods. Charge sensing is characterized by repeated cycling of the occupation of current-carrying states due to the capacitive coupling to trap states. In agreement with recent experiments, it results in characteristic asymmetric Coulomb-blockade peaks as well as sawtooth and domelike structures. Temperature introduces asymmetric smearing of these features and correlations in the conductance provide a fingerprint of charge sensing.     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].     

Grothendieck's theorem on non-abelian and local-global principles

A theorem of Grothendieck asserts that over a perfect field of cohomological dimension one, all non-abelian -cohomology sets of algebraic groups are trivial. The purpose of this paper is to establish a formally real generalization of this theorem. The generalization - to the context of perfect fields of virtual cohomological dimension one - takes the form of a local-global principle for the -sets with respect to the orderings of the field. This principle asserts in particular that an element in is neutral precisely when it is neutral in the real closure with respect to every ordering in a dense subset of the real spectrum of . Our techniques provide a new proof of Grothendieck's original theorem. An application to homogeneous spaces over is also given.

     

Progress in metric-affine gauge theories of gravity with local scale invariance

Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective low-energy theory.Based on a plenary talk given by one of us (EWM) at the 53rd annual meeting of the Deutsche Physikalische Gesellschaft in Bonn on March 14, 1989.Supported by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.Supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, project He 528/12-1.Supported in part by DOE Grant DE-FG05-85-ER40200.     

The absolute order of a permutation representation of a Coxeter group

A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.     

Ultrafast proton transfer of three novel quinone cyanine photoacids

Steady-state and time-resolved emission techniques were used to study the photoprotolytic properties of three recently synthesized strong quinone cyanine photoacids (QCy7 and its sulfonated derivatives). The rate coefficient of the excited-state proton transfer (ESPT), k(PT), of the three dyes is roughly 1.5 × 10(12) s(-1), a high value that is comparable to the solvation dynamics rate of large polar organic molecules in H(2)O and D(2)O. It is twice as fast as the proton transfer rate between two adjacent water molecules in liquid water. We found that, as expected, two of the sulfonated photoacids geminately recombines with the proton at an elevated rate. The accelerated geminate recombination process of the sulfonated derivatives is different from a simple diffusion process of protons. The ESPT rate coefficient of these molecules is the highest recorded thus far.     

Ultrafast excited-state intermolecular proton transfer of cyanine fluorochrome dyes

Steady-state and time-resolved emission spectroscopy techniques were employed to study the excited-state proton transfer (ESPT) to water and D(2)O from QCy7, a recently synthesized near-infrared (NIR)-emissive dye with a fluorescence band maximum at 700 nm. We found that the ESPT rate constant, k(PT), of QCy7 excited from its protonated form, ROH, is ~1.5 × 10(12) s(-1). This is the highest ever reported value in the literature thus far, and it is comparable to the reciprocal of the longest solvation dynamics time component in water, τ(S) = 0.8 ps. We found a kinetic isotope effect (KIE) on the ESPT rate of ~1.7. This value is lower than that of weaker photoacids, which usually have KIE value of ~3, but comparable to the KIE on proton diffusion in water of ~1.45, for which the average time of proton transfer between adjacent water molecules is similar to that of QCy7.     

A quantum dot close to Stoner instability: The role of the Berry phase

The physics of a quantum dot with electron–electron interactions is well captured by the so called “Universal Hamiltonian” if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close to the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].     

On recurrence and transience of self-interacting random walks

Let µ₁,...,µ _k be d-dimensional probabilitymeasures in ? ^d with mean 0. At each time we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.