Efficient many-body non-Markovian dynamics of organic polaritons

Funding: P.F.-W. acknowledges support from EPSRC (EP/T518062/1). B.W.L. and J.K. acknowledge support from EPSRC (EP/T014032/1).We show how to simulate a model of many molecules with both strong coupling to many vibrational modes and collective coupling to a single photon mode. We do this by combining process tensor matrix product operator methods with a mean-field approximation which reduces the dimension of the problem. We analyze the steady-state of the model under incoherent pumping to determine the dependence of the polariton lasing threshold on cavity detuning, light-matter coupling strength, and environmental temperature. Moreover, by measuring two-time correlations, we study quadratic fluctuations about the mean-field to calculate the photoluminescence spectrum. Our method enables one to simulate many-body systems with strong coupling to multiple environments, and to extract both static and dynamical properties.Publisher PDFPeer reviewe

Fluctuating epidemics on adaptive networks

A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to connect to other non-infected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.Comment: Submitted to Phys Rev

Sublinear scaling in non-Markovian open quantum systems simulations

Funder: M.C. and E.M.G. acknowledge funding from EPSRC grant no. EP/T01377X/1. B.W.L. and J.K. were supported by EPSRC grant no. EP/T014032/1.While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps n. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spin-boson-type open quantum systems. Based on a divide-and-conquer strategy, our approach requires only (n log n) singular value decompositions for environments with infinite memory. Where the memory can be truncated after nc time steps, a nominal scaling (nc log nc) is found, which is independent of n. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for time-independent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary time-dependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches.Publisher PDFPeer reviewe

Climate change as an intergenerational problem

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences of the United States of America 110 (2013): 4435-4436, doi:10.1073/pnas.1302536110.Predicting climate change is a high priority for society, but such forecasts are notoriously uncertain. Why? Even should climate prove theoretically predictable---by no means certain---the near-absence of adequate observations will preclude its understanding and hence even the hope of useful predictions. Geological and cryospheric records of climate change and our brief recent record of instrumental observations show that the climate system is changeable on all time scales---from a few years out to the age of the earth. Major physical, chemical, and biological processes influence the climate system on decades, centuries, and millennia. Glaciers fluctuate on time scales of years to centuries and beyond. Since the Industrial Revolution, carbon dioxide has been emitted through fossil fuel burning, and it will be absorbed, recycled, and transferred amongst the atmosphere, ocean, and biosphere over decades to thousands of years

Sublinear scaling in non-Markovian open quantum systems simulations

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$. Here, we introduce a numerically exact algorithm to calculate process tensors -- compact representations of environmental influences -- which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent Gaussian environments. Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory. Where the memory can be truncated after $n_c$ time steps, a scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but also has fundamental implications for simulation complexity

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Performance of an environmental test to detect Mycobacterium bovis infection in badger social groups

A study by Courtenay and others (2006) demonstrated that the probability of detecting Mycobacterium bovis by PCR in soil samples from the spoil heaps of main badger setts correlated with the prevalence of excretion (infectiousness) of captured badgers belonging to the social group. It has been proposed that such a test could be used to target badger culling to setts containing infectious animals (Anon 2007). This short communication discusses the issues surrounding this concept, with the intention of dispelling any misconceptions among relevant stakeholders (farmers, policy makers and conservationists)

A change of IL-2 and IL-4 production in patients with Helicobactor pylori infection

Hellcobacter pylori is the most common cause of gastroduodenal inflammation. However, the exact immune pathogenesis is not fully understood. To look for evidence of the immunological mechanism in H. pylori associated disease, we measured cytokine interleukin-2 (IL-2) and IL-4 levels produced by peripheral blood lymphocytes (PBL) and gastric biopsies in 20 subjects with or without H. pylori infection. H. pylori can stimulate IL-2 and IL-4 production from PBL in H. pylori negative as well as H. pylori positive individuals. The spontaneous IL-2 production by PBL and gastric biopsies was greater (p < 0.0025, <0.001)in H. pylori negative individuals than that in H. pylori infected patients. Increased IL-4 levels from PBL in H. pylori infected patients were found in the presence of H. pylori (p < 0.0025). An increased spontaneous production of IL-4 from gastric biopsies was also observed in H. pylori infected patients (p < 0.025). In conclusion, an enhanced type 2 cytokine production was observed in H. pylori infected patients, which may be responsible for H. pylori chronic infection