Weak Coherent State Path Integrals

Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.Comment: 21 pages, no figures, accepted by J. Math. Phy

Theory and Algorithms

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated. View Full-Tex

Variational approach to rare event simulation using least-squares regression

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e. zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman-Kac representation of the associated dynamic programming equations, and we discuss numerical aspects for high-dimensional problems along with simple toy examples.Comment: 28 pages, 7 figure

Thermal expansion of the magnetically ordering intermetallics RTMg (R = Eu, Gd and T = Ag, Au)

We report measurements of the thermal expansion for two Eu$^{+2}$- and two Gd$^{+3}$-based intermetallics which exhibit ferro- or antiferromagnetic phase transitions. These materials show sharp positive (EuAgMg and GdAuMg) and negative (EuAuMg and GdAgMg) peaks in the temperature dependence of the thermal expansion coefficient $\alpha$ which become smeared and/or displaced in an external magnetic field. Together with specific heat data we determine the initial pressure dependences of the transition temperatures at ambient pressure using the Ehrenfest or Clausius-Clapeyron relation. We find large pressure dependences indicating strong spin-phonon coupling, in particular for GdAgMg and EuAuMg where a quantum phase transition might be reached at moderate pressures of a few GPa.Comment: 6 pages, 3 figure

Mott-Hubbard exciton in the optical conductivity of YTiO3 and SmTiO3

In the Mott-Hubbard insulators YTiO3 and SmTiO3 we study optical excitations from the lower to the upper Hubbard band, d^1d^1 -> d^0d^2. The multi-peak structure observed in the optical conductivity reflects the multiplet structure of the upper Hubbard band in a multi-orbital system. Absorption bands at 2.55 and 4.15 eV in the ferromagnet YTiO3 correspond to final states with a triplet d^2 configuration, whereas a peak at 3.7 eV in the antiferromagnet SmTiO3 is attributed to a singlet d^2 final state. A strongly temperature-dependent peak at 1.95 eV in YTiO3 and 1.8 eV in SmTiO3 is interpreted in terms of a Hubbard exciton, i.e., a charge-neutral (quasi-)bound state of a hole in the lower Hubbard band and a double occupancy in the upper one. The binding to such a Hubbard exciton may arise both due to Coulomb attraction between nearest-neighbor sites and due to a lowering of the kinetic energy in a system with magnetic and/or orbital correlations. Furthermore, we observe anomalies of the spectral weight in the vicinity of the magnetic ordering transitions, both in YTiO3 and SmTiO3. In the G-type antiferromagnet SmTiO3, the sign of the change of the spectral weight at T_N depends on the polarization. This demonstrates that the temperature dependence of the spectral weight is not dominated by the spin-spin correlations, but rather reflects small changes of the orbital occupation.Comment: Strongly extended version; new data of SmTiO3 included; detailed discussion of temperature dependence include

Top-Down Modulation of the Auditory Steady-State Response in a Task-Switch Paradigm

Auditory selective attention is an important mechanism for top-down selection of the vast amount of auditory information our perceptual system is exposed to. In the present study, the impact of attention on auditory steady-state responses is investigated. This issue is still a matter of debate and recent findings point to a complex pattern of attentional effects on the auditory steady state response (aSSR). The present study aimed at shedding light on the involvement of ipsilateral and contralateral activations to the attended sound taking into account hemispheric differences and a possible dependency on modulation frequency. In aid of this, a dichotic listening experiment was designed using amplitude-modulated tones that were presented to the left and right ear simultaneously. Participants had to detect target tones in a cued ear while their brain activity was assessed using MEG. Thereby, a modulation of the aSSR by attention could be revealed, interestingly restricted to the left hemisphere and 20 Hz responses: contralateral activations were enhanced while ipsilateral activations turned out to be reduced. Thus, our findings support and extend recent findings, showing that auditory attention can influence the aSSR, but only under specific circumstances and in a complex pattern regarding the different effects for ipsilateral and contralateral activations

Alpha Rhythms in Audition: Cognitive and Clinical Perspectives

Like the visual and the sensorimotor systems, the auditory system exhibits pronounced alpha-like resting oscillatory activity. Due to the relatively small spatial extent of auditory cortical areas, this rhythmic activity is less obvious and frequently masked by non-auditory alpha-generators when recording non-invasively using magnetoencephalography (MEG) or electroencephalography (EEG). Following stimulation with sounds, marked desynchronizations can be observed between 6 and 12 Hz, which can be localized to the auditory cortex. However knowledge about the functional relevance of the auditory alpha rhythm has remained scarce so far. Results from the visual and sensorimotor system have fuelled the hypothesis of alpha activity reflecting a state of functional inhibition. The current article pursues several intentions: (1) Firstly we review and present own evidence (MEG, EEG, sEEG) for the existence of an auditory alpha-like rhythm independent of visual or motor generators, something that is occasionally met with skepticism. (2) In a second part we will discuss tinnitus and how this audiological symptom may relate to reduced background alpha. The clinical part will give an introduction into a method which aims to modulate neurophysiological activity hypothesized to underlie this distressing disorder. Using neurofeedback, one is able to directly target relevant oscillatory activity. Preliminary data point to a high potential of this approach for treating tinnitus. (3) Finally, in a cognitive neuroscientific part we will show that auditory alpha is modulated by anticipation/expectations with and without auditory stimulation. We will also introduce ideas and initial evidence that alpha oscillations are involved in the most complex capability of the auditory system, namely speech perception. The evidence presented in this article corroborates findings from other modalities, indicating that alpha-like activity functionally has an universal inhibitory role across sensory modalities

Determinants of Plate Leftovers in one German Catering Company

Since the majority of food waste in high-income countries occurs at the consumption stage and given the clear trend towards out-of-home food consumption, it is important to understand the factors that lead to food waste in the hospitality sector. The present study uses a behavioral structural equation model to test the drivers of consumers’ leftover behavior in an out-of-home setting. Based on the Theory of Planned Behavior, we additionally consider “personal norms” and the situational “taste perception” of food as determinants. Our results in a company canteen demonstrate that personal norms and attitudes greatly determine consumers’ intention to prevent leftovers, whereas subjective norms and perceived behavioral control appear less relevant. Stated leftover behavior depends on both behavioral intention and the situational taste perception of food. We show that in order to understand individual food leftover behavior in an out-of-home setting, determinants from behavioral theories should be complemented by situational variables.ISSN:2071-105

The Sure-Thing Principle

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance