Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.

Dynamical typicality of quantum expectation values

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schroedinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Our approach is based on the Hilbert space average method. We support the analytical investigations with numerics obtained by exact diagonalization of the full time-dependent Schroedinger equation for some pertinent, abstract Hamiltonian model. Furthermore, we discuss the implications on the applicability of projection operator methods with respect to initial states, as well as on irreversibility in general.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Spatial Resolution with Time-and-Polarization-Resolved Acoustic Microscopy

Spatial resolution is an important factor in ultrasonic materials characterization. Scanning acoustic microscopy [1–2] has proved to be a useful tool for materials evaluation with micrometer-scale spatial resolution. Point-focus-beam (PFB) acoustic microscopy has high spatial resolution and is often used to produce images as well as to probe material inhomogeneity. However, a disadvantage of the PFB technique lies in its insensitivity to material anisotropy. In contrast, line-focus-beam (LFB) acoustic microscopy can provide a directional ultrasonic velocity measurement and is employed for characterization of anisotropic materials [3–5]. But the LFB technique, with its unidirectional spatial resolution, is generally incapable of producing images, and is therefore disadvantageous for probing inhomogeneous materials. In response to this need, a variety of lens designs [6–9] in acoustic microscopy have been proposed for measuring materials, which are both inhomogeneous and anisotropic

Magnetization reversal driven by spin-injection : a mesoscopic spin-transfer effect

A mesoscopic description of spin-transfer effect is proposed, based on the spin-injection mechanism occurring at the junction with a ferromagnet. The effect of spin-injection is to modify locally, in the ferromagnetic configuration space, the density of magnetic moments. The corresponding gradient leads to a current-dependent diffusion process of the magnetization. In order to describe this effect, the dynamics of the magnetization of a ferromagnetic single domain is reconsidered in the framework of the thermokinetic theory of mesoscopic systems. Assuming an Onsager cross-coefficient that couples the currents, it is shown that spin-dependent electric transport leads to a correction of the Landau-Lifshitz-Gilbert equation of the ferromagnetic order parameter with supplementary diffusion terms. The consequence of spin-injection in terms of activation process of the ferromagnet is deduced, and the expressions of the effective energy barrier and of the critical current are derived. Magnetic fluctuations are calculated: the correction to the fluctuations is similar to that predicted for the activation. These predictions are consistent with the measurements of spin-transfer obtained in the activation regime and for ferromagnetic resonance under spin-injection.Comment: 20 pages, 2 figure

Covariance and Fisher information in quantum mechanics

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasis that Fisher informations are obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.Comment: LATE

Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas

For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self energy is derived in terms of the interaction strength. Employing a generalization of the projector technique a compact representation of the general terms of the expansion results. The general aspects of the approach are discussed with special emphasis on the effects characteristic for quantum systems. The expansion is systematic and leads directly to contributions beyond mean-field of all thermodynamic quantities. These features are explicitly demonstrated and illustrated for two non-trivial systems, the infinite range quantum spin glass and the weakly interacting Bose gas. The Onsager terms of both systems are calculated, which represent the first beyond mean-field contributions. For the spin glass new TAP-like equations are presented and discussed in the paramagnetic region. The investigation of the Bose gas leads to a beyond mean-field thermodynamic description. At the Bose-Einstein condensation temperature complete agreement is found with the results presented recently by alternative techniques.Comment: 17 pages, 0 figures; revised version accepted by Phys Rev

Relating chaos to deterministic diffusion of a molecule adsorbed on a surface

Chaotic internal degrees of freedom of a molecule can act as noise and affect the diffusion of the molecule on a substrate. A separation of time scales between the fast internal dynamics and the slow motion of the centre of mass on the substrate makes it possible to directly link chaos to diffusion. We discuss the conditions under which this is possible, and show that in simple atomistic models with pair-wise harmonic potentials, strong chaos can arise through the geometry. Using molecular-dynamics simulations, we demonstrate that a realistic model of benzene is indeed chaotic, and that the internal chaos affects the diffusion on a graphite substrate

Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate approach based on the T-matrix (TM). Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences (nondiagonal elements of the density matrix) between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary (zero-frequency) limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.Comment: 29 pages, 12 figures; revised published versio

An Examination of Public Opinion in Austria Towards Inclusion. Development of the “Attidutes Towards Inclusion Scale”- ATIS

The ‘Attitudes Towards Integration Scale’ (ATIS) assesses the attitude of the general public towards the school integration of children with disabilities. The scale was empirically created in a pilot study (n=351) and later used to survey 2158 people. The data from both surveys are analysed in the present paper; the results show that the scale exhibits acceptable internal consistency (Cronbach’s α=.83) and that the factorial structure of the scale can be considered as largely confirmed. Overall, the surveyed persons reported a positive attitude towards the school integration of children with disabilities. However, the form of the disability of the integrated child and the level of education as well as the participants’ familiarity with the topic of integration of persons with disabilities, age and gender played a role in their assessment. In addition, the results show that pupils in general have a more negative attitude than students and employed persons. Sequence effects could also be shown. Inclusive education is seen as more positive when respondents are first asked to evaluate how a child with a disability gets on in an integrated class and have to evaluate later how a child with the same disability gets on in a special school setting of an integrated class

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.