Foerster resonance energy transfer rate and local density of optical states are uncorrelated in any dielectric nanophotonic medium

Motivated by the ongoing debate about nanophotonic control of Foerster resonance energy transfer (FRET), notably by the local density of optical states (LDOS), we study an analytic model system wherein a pair of ideal dipole emitters - donor and acceptor - exhibit energy transfer in the vicinity of an ideal mirror. The FRET rate is controlled by the mirror up to distances comparable to the donor-acceptor distance, that is, the few-nanometer range. For vanishing distance, we find a complete inhibition or a four-fold enhancement, depending on dipole orientation. For mirror distances on the wavelength scale, where the well-known `Drexhage' modification of the spontaneous-emission rate occurs, the FRET rate is constant. Hence there is no correlation between the Foerster (or total) energy transfer rate and the LDOS. At any distance to the mirror, the total energy transfer between a closely-spaced donor and acceptor is dominated by Foerster transfer, i.e., by the static dipole-dipole interaction that yields the characteristic inverse-sixth-power donor-acceptor distance dependence in homogeneous media. Generalizing to arbitrary inhomogeneous media with weak dispersion and weak absorption in the frequency overlap range of donor and acceptor, we derive two main theoretical results. Firstly, the spatially dependent Foerster energy transfer rate does not depend on frequency, hence not on the LDOS. Secondly the FRET rate is expressed as a frequency integral of the imaginary part of the Green function. This leads to an approximate FRET rate in terms of the LDOS integrated over a huge bandwidth from zero frequency to about 10 times the donor emission frequency, corresponding to the vacuum-ultraviolet. Even then, the broadband LDOS hardly contributes to the energy transfer rates. We discuss practical consequences including quantum information processing.Comment: 17 pages, 9 figure

Spotless? Perceived Cleanliness in Service Environments

This dissertation presents research on customers’ perceptions of cleanliness in service environments. The research contributes to the gap in the literature on cleanliness examined from a customer perspective, and adds to the understanding of environmental cues that influence perceived cleanliness. Part one of the dissertation includes the operationalisation of the concept of perceived cleanliness and the development of an instrument to measure perceived cleanliness. Results showed that perceived cleanliness consists of three dimensions: cleaned, fresh, and uncluttered. Next, the Cleanliness Perceptions Scale (CP-scale) was developed and validated in different service environments, resulting in a 12 item questionnaire that can be used to measure perceived cleanliness in service environments. Part two includes the experimental research on the effects of different environmental cues on perceived cleanliness. It furthermore explores to what extent the effects of these environmental cues on perceived cleanliness can be explained by the concept of priming. The experiments demonstrated that particular environmental cues influence perceived cleanliness: the visible presence of cleaning staff, light colour, light scent, and uncluttered architecture positively influence customers’ perceptions of cleanliness in service environments. Also, empirical support was found for priming as one of the mechanisms involved in the effects. Part three reflects on the implications of the dissertation for theory and practice. The research provides knowledge that is relevant for the fields of facility management, service marketing, social psychology, and environmental psychology. The dissertation improves the understanding of the concept of perceived cleanliness by enabling scholars and practitioners to measure the concept and the effects of particular environmental cues in service environments

Multilinear transference of Fourier and Schur multipliers acting on non-commutative LpL_p-spaces

Let $G$ be a locally compact unimodular group, and let $\phi$ be some function of $n$ variables on $G$. To such a $\phi$, one can associate a multilinear Fourier multiplier, which acts on some $n$-fold product of the non-commutative $L_p$-spaces of the group von Neumann algebra. One may also define an associated Schur multiplier, which acts on an $n$-fold product of Schatten classes $S_p(L_2(G))$. We generalize well-known transference results from the linear case to the multilinear case. In particular, we show that the so-called `multiplicatively bounded $(p_1,\ldots,p_n)$-norm' of a multilinear Schur multiplier is bounded above by the corresponding multiplicatively bounded norm of the Fourier multiplier, with equality whenever the group is amenable. Further, we prove that the bilinear Hilbert transform is not bounded as a vector valued map $L_{p_1}(\mathbb{R}, S_{p_1}) \times L_{p_2}(\mathbb{R}, S_{p_2}) \rightarrow L_{1}(\mathbb{R}, S_{1})$, whenever $p_1$ and $p_2$ are such that $\frac{1}{p_1} + \frac{1}{p_2} = 1$. A similar result holds for certain Calder\'on-Zygmund type operators. This is in contrast to the non-vector valued Euclidean case.Comment: v3 incorporates reviewer comments and suggestions. To appear in the Canadian Journal of Mathematic

Relative Haagerup property for arbitrary von Neumann algebras

We introduce the relative Haagerup approximation property for a unital, expected inclusion of arbitrary von Neumann algebras and show that if the smaller algebra is finite then the notion only depends on the inclusion itself, and not on the choice of the conditional expectation. Several variations of the definition are shown to be equivalent in this case, and in particular the approximating maps can be chosen to be unital and preserving the reference state. The concept is then applied to amalgamated free products of von Neumann algebras and used to deduce that the standard Haagerup property for a von Neumann algebra is stable under taking free products with amalgamation over finite-dimensional subalgebras. The general results are illustrated by examples coming from q-deformed Hecke-von Neumann algebras and von Neumann algebras of quantum orthogonal groups.Comment: 48 pages; v2 corrects a few minor point