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Photosynthetic organisms rely on a network of light-harvesting protein-pigment complexes to efficiently absorb sunlight and transfer excitation energy to reaction center proteins for charge separation. In photosynthetic purple bacteria, these complexes are embedded in the cell membrane, where lipid composition affects their clustering and inter-complex energy transfer. However, the lipid bilayer's impact on intra-complex excitation dynamics is less understood. Recent experiments compared photo-excitation dynamics in detergent-isolated light harvesting complex 2 (LH2) to LH2 embedded in membrane discs mimicking the biological environment, revealing differences in spectra and intra-complex energy transfer rates. We use available quantum chemical and spectroscopy data to develop a complementary theoretical study on the excitonic structure and intra-complex energy transfer kinetics of the LH2 from photosynthetic purple bacteria Rhodoblastus acidophilus in two conditions: LH2 in a membrane environment and detergent-isolated LH2. Dark excitonic states crucial for B800-B850 energy transfer within LH2 are found to be more delocalised in the membrane model. Using non-perturbative and generalised F\"orster calculations, it is shown that the increased quantum delocalisation leads to a B800 to B850 transfer rate 30% faster than in the detergent-isolated complex, consistent with experimental results. We identify the main energy transfer pathways in each environment and show how differences in the B800 to B850 transfer rate stem from changes in LH2's electronic properties when embedded in the membrane. By considering quasi-static variations of electronic excitation energies in LH2, we show that the broadening of the B800 to B850 transfer rate distribution is affected by lipid composition. We argue that the variation in broadening could indicate a speed-accuracy trade-off, common in biological systems., Comment: 25 pages, 10 figures

We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution of disorder realizations of the original heterogeneous quantum ensemble. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation. Alternatively, by exploiting the reverse map, one can obtain lattice dynamics by averaging over realisations of disorder. The potential of this equivalence is showcased with examples of the map in both directions: obtaining dephasing of a qubit via mapping to a lattice model, and solving a simple lattice model via taking an average over realizations of disorder of a unit cell., Comment: 11 pages, 5 figures

The surface of a three dimensional topological insulator (TI) hosts surface states whose properties are determined by a Dirac-like equation. The electronic system on the surface of TI nanowires with polygonal cross-sectional shape adopts the corresponding polygonal shape. In a constant transverse magnetic field, such an electronic system exhibits rich properties as different facets of the polygon experience different values of the magnetic field due to the changing magnetic field projection between facets. We investigate the energy spectrum and transport properties of nanowires where we consider three different polygonal shapes, all showing distinct properties visible in the energy spectrum and transport properties. Here we propose that the wire conductance can be used to differentiate between cross-sectional shapes of the nanowire by rotating the magnetic field around the wire. Distinguishing between the different shapes also works in the presence of impurities as long as conductance steps are discernible, thus revealing the sub-band structure., Comment: 9 pages with 7 figures

Let $W$ be a standard Brownian motion with $W_0 = 0$ and let $b\colon[0,\infty) \to \mathbb{R}$ be a continuous function with $b(0) > 0$. In this article, we look at the classical First Passage Time (FPT) problem, i.e., the question of determining the distribution of $\tau := \inf \{ t\in [0,\infty)\colon W_t \geq b(t) \}.$ More specifically, we revisit the method of images, which we feel has received less attention than it deserves. The main observation of this approach is that the FPT problem is fully solved if a measure $\mu$ exists such that \begin{align*} \int_{(0,\infty)} \exp\left(-\frac{\theta^2}{2t}+\frac{\theta b(t)}{t}\right)\mu(d\theta)=1, \qquad t\in(0,\infty). \end{align*} The goal of this article is to lay the foundation for answering the still open question of the existence and characterisation of such a measure $\mu$ for a given curve $b$. We present a new duality approach that allows us to give sufficient conditions for the existence. Moreover, we introduce a very efficient algorithm for approximating the representing measure $\mu$ and provide a rigorous theoretical foundation.

We theoretically investigate polarization-filtered two-photon correlations for the light emitted by a multichromophoric system undergoing excitation transport under realistic exciton-phonon interactions, and subject to continuous incoherent illumination. We show that for a biomolecular aggregate, such as the Fenna-Matthews Olson (FMO) photosynthetic complex, time-asymmetries in the cross-correlations of photons corresponding to different polarizations can be exploited to probe both quantum coherent transport mechanisms and steady-state coherence properties, which are not witnessed by zero-delay correlations. A classical bound on correlation asymmetry is obtained, which FMO is shown to violate using exact numerical calculations. Our analysis indicates that the dominant contributions to time-asymmetry in such photon cross-correlations are population to coherence transfer for Frenkel-Exciton models. Our results therefore put forward photon correlation asymmetry as a promising approach to investigate coherent contributions to excited-stated dynamics in molecular aggregates and other many-site quantum emitters., Comment: 5 + 16 pages, 3 + 9 figures

Identifying signatures of quantum coherent behaviour in photoactive systems that are maintained in stationary states away from thermal equilibrium is an open problem of wide interest in a variety of physical scenarios, including single photosynthetic complexes subjected to continuous incoherent illumination. Here we consider a prototype light-harvesting heterodimer exhibiting coherent and collective exciton-vibration interactions and show that the second-order frequency-filtered correlations of fluorescence photons provide insightful information on the influence of such coherent interactions for different transitions, thereby yielding fundamentally different photon-counting statistics. Furthermore, we show that coherent vibronic mechanisms strongly affect the asymmetries characteristic of time-resolved photon cross-correlations and manifest themselves in a time-dependent violation of the Cauchy-Schwarz inequality bounding cross-correlations for classically fluctuating fields. We finally discuss how such second-order correlation asymmetry establishes important connections between coherent vibronic interactions, directional exciton population transport, and violation of quantum detailed balance. Our work then indicates that measurement of two-colour photon correlation asymmetry can be an important avenue to investigate quantum behaviour of single photoactive biomolecular and chemical systems under incoherent illumination conditions., Comment: 10 + 8 pages, comments welcome

Let $W$ be a standard Brownian motion with $W_0 = 0$ and let $b: \mathbb{R}_+ \to \mathbb{R}$ be a continuous function with $b(0) > 0$. The first passage time (from below) is then defined as \begin{align*} \tau := \inf \{ t \geq 0 \vert W_t \geq b(t) \}. \end{align*} It is well-known that the distribution $F$ of $\tau$ satisfies a set of Fredholm equations of the first kind, which is used, for example, as a starting point for numerical approaches. For this, it is fundamental that the Fredholm equations have a unique solution. In this article, we prove this in a general setting using analytical methods.