Variational approach to transport in quantum dots

We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a Gutzwiller's variational space, and applied to the study of the simple single-orbital Anderson impurity model at half filling, finding a good qualitative accord with the observed behavior in quantum dots for the expected regime of values of the bias. Beyond the purely theoretical interest in the formal definition of a variational principle in a nonequilibrium problem, the particular methods proposed have the important advantage to be simple and flexible enough to deal with more complicated systems and variational spaces.Comment: 15 pages, 4 figure

The Out-of-Equilibrium Time-Dependent Gutzwiller Approximation

We review the recently proposed extension of the Gutzwiller approximation, M. Schiro' and M. Fabrizio, Phys. Rev. Lett. 105, 076401 (2010), designed to describe the out-of-equilibrium time-evolution of a Gutzwiller-type variational wave function for correlated electrons. The method, which is strictly variational in the limit of infinite lattice-coordination, is quite general and flexible, and it is applicable to generic non-equilibrium conditions, even far beyond the linear response regime. As an application, we discuss the quench dynamics of a single-band Hubbard model at half-filling, where the method predicts a dynamical phase transition above a critical quench that resembles the sharp crossover observed by time-dependent dynamical mean field theory. We next show that one can actually define in some cases a multi-configurational wave function combination of a whole set of mutually orthogonal Gutzwiller wave functions. The Hamiltonian projected in that subspace can be exactly evaluated and is equivalent to a model of auxiliary spins coupled to non-interacting electrons, closely related to the slave-spin theories for correlated electron models. The Gutzwiller approximation turns out to be nothing but the mean-field approximation applied to that spin-fermion model, which displays, for any number of bands and integer fillings, a spontaneous $Z_2$ symmetry breaking that can be identified as the Mott insulator-to-metal transition.Comment: 25 pages. Proceedings of the Hvar 2011 Workshop on 'New materials for thermoelectric applications: theory and experiment

Time-Dependent and Steady-State Gutzwiller approach for nonequilibrium transport in nanostructures

We extend the time-dependent Gutzwiller variational approach, recently introduced by Schir\`o and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at half-filling, modeling a quantum dot coupled to two leads. In these first exploratory calculations the Gutzwiller projector is limited to act only on the impurity. The strengths and the limitations of this approximation are assessed via comparison with state of the art continuous time quantum Monte Carlo results. Finally, we discuss how the method can be systematically improved by extending the region of action of the Gutzwiller projector.Comment: 13 pages, 6 figure

High frequency poroelastic waves in hydrogels

In this work a continuum model for high frequency poroelastic longitudinal waves in hydrogels is presented. A viscoelastic force describing the interaction between the polymer network and the bounded water present in such materials is introduced. The model is tested by means of ultrasound wave speed and attenuation measurements in polyvinylalcohol hydrogel samples. The theory and experiments show that ultrasound attenuation decreases linearly with the increase of the water volume fraction "{\beta}" of the hydrogel. The introduction of the viscoelastic force between the bounded water and the polymer network leads to a bi-phasic theory showing an ultrasonic fast wave attenuation that can vary as a function of the frequency with a non-integer exponent in agreement with the experimental data in literature. When {\beta} tends to 1 (100% of interstitial water) due to the presence of bounded water in the hydrogel, the ultrasound phase velocity acquires higher value than that of pure water. The ultrasound speed gap at {\beta} = 1 is confirmed by the experimental results that show that it increases in less cross-linked gel samples that own a higher concentration of bounded water

Heart and brain: Change in cardiac entropy is related to lateralised visual inspection in horses

Cerebral lateralisation is the tendency for an individual to preferentially use one side of their brain and is apparent in the biased use of paired sensory organs. Horses vary in eye use when viewing a novel stimulus which may be due to different physiological reactions. To understand the interplay between physiology and lateralisation, we presented a novel object (an inflated balloon) to 20 horses while electrocardiogram traces were collected. We measured the amount of time each horse looked at the balloon with each eye. We calculated ‘sample entropy’ as a measure of non-linear heart rate variability both prior to and during the stimulus presentation. A smaller drop in sample entropy values between the habituation phase and the sample presentation indicates the maintenance of a more complex signal associated with a relaxed physiological state. Horses that spent longer viewing the balloon with their left eye had a greater reduction in sample entropy, while time spend looking with the right eye was unrelated to the change in sample entropy. Therefore, the horses that exhibited a greater reduction in sample entropy tended to use their right hemisphere more, which may take precedence in emotional reactions. These results may help to explain the variation in lateralisation observed among horses

Fermi-Surface Reconstruction in the Periodic Anderson Model

We study ground state properties of periodic Anderson model in a two-dimensional square lattice with variational Monte Carlo method. It is shown that there are two different types of quantum phase transition: a conventional antiferromagnetic transition and a Fermi-surface reconstruction which accompanies a change of topology of the Fermi surface. The former is induced by a simple back-folding of the Fermi surface while the latter is induced by localization of $f$ electrons. The mechanism of these transitions and the relation to the recent experiments on Fermi surface are discussed in detail.Comment: 8 pages, 7 figures, submitted to Journal of the Physical Society of Japa