Fundamental limits on low-temperature quantum thermometry with finite resolution

While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.Comment: Published version. Main text: 12 pages, 5 figures; see also related work by K. Hovhannisyan and L. A. Correa at arXiv:1712.0308

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

On the singular values and eigenvalues of the Fox–Li and related operators

The Fox–Li operator is a convolution operator over a finite interval with a special highly oscillatory kernel. It plays an important role in laser engineering. However, the mathematical analysis of its spectrum is still rather incomplete. In this expository paper we survey part of the state of the art, and our emphasis is on showing how standard Wiener–Hopf theory can be used to obtain insight into the behaviour of the singular values of the Fox–Li operator. In addition, several approximations to the spectrum of the Fox–Li operator are discussed and results on the singular values and eigenvalues of certain related operators are derived

Tensor Product and Permutation Branes on the Torus

We consider B-type D-branes in the Gepner model consisting of two minimal models at k=2. This Gepner model is mirror to a torus theory. We establish the dictionary identifying the B-type D-branes of the Gepner model with A-type Neumann and Dirichlet branes on the torus.Comment: 26 page

Ideal Linear Chain Polymers with Fixed Angular Momentum

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of non-interacting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.Comment: 7 pages, 3 figure

Quantum Thermal Machine as a Thermometer

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines which perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation which allows for precise thermometry down to $\sim$15 mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.Comment: Main text: 5 pages, 4 figures; Supplement: 5 page

Comparison of the epifaunal assemblage of an invasive and native macroalga

The rapid spread of introduced seaweeds is of essential concern, as they can have a deleterious impact on coastal native seaweed and seagrass communities. However, non-indigenous species can generate mixed responses when introduced to native assemblages, and increase habitat complexity, depending on the spatial and ecological context. By taking advantage of the cooccurrence of the native Ulva seaweeds and the non-native Agarophyton vermiculophyllum in the Clonakilty estuary (Cork, Ireland) we aim to assess the differences of the epifaunal community of the native and invasive macroalgal species and how epifaunal biodiversity may be affected by the invasive. In four locations over four sampling occasions, a total of 253 quadrants of algae and epifaunal biomass were sampled. The Ulva dominated sections mainly contained macroalgae with tubular morphotypes and some sporadic patches of laminar Ulva rigida. The average algal biomass of both species was similar, however, the biomass of the red seaweed was highly variable throughout the seasons. The native algal canopy hosted up to four times more epifaunal biomass compared to the invasive rhodophyte. Moreover, the epifaunal community of both canopies differed substantially, whereas deposit-feeding organisms had a higher abundance in Ulva spp. canopies and the carnivorous crab, Carcinus maenas, was much more abundant in A. vermiculophyllum samples. The native green macroalgae hosted more invertebrate taxa, however no difference in biodiversity was found. Increased predation on deposit-feeders and grazers, as well as, the structural and chemical resistance of A. vermiculophyllum against grazing and overgrowth by epiphytes may reduce the trophic transfer from primary production toward higher trophic levels.As introduções de espécies exóticas ocorrem já há vários séculos, de forma intencional para ganho comercial ou involuntariamente, maioritariamente por transporte marítimo como passageiros escondidos em águas de lastro ou agarrados ao casco do navio. A rápida dispersão de algas não-indígenas é uma preocupação básica, já que podem ter impactos nocivos nas comunidades algas e ervas marinhas costeiras indígenas e são, juntamente com as alterações climáticas, um dos fatores de stress mais significativos dos ecossistemas de hoje. Estes impactos incluem a modificação da estrutura da comunidade da fauna, redução de biodiversidade e alteração das dinâmicas de nutrientes estuarinas, que podem, em última instância, acelerar a mudança de macrófitas de crescimento lento para macroalgas efémeras, aumentando o risco de afloramentos de macroalgas. No entanto, as espécies não-indígenas podem gerar respostas mistas quando introduzidas em agrupamentos nativos, e aumentar a complexidade do habitat, dependendo do contexto espacial e ecológico. Os factores de stress antropogénicos como o aumento dos níveis de nutrientes podem intensificar a magnitude de tais eventos e aumentar a sua frequência. A referida eutrofização aparente de sistemas costeiros pode fomentar as invasões de macrófitas, assim como a sua resistência a grazing o que aumenta ainda mais a probabilidade de afloramentos de macroalgas. Duas espécies indígenas de forma laminar (Ulva rigida e Ulva gigantea) e duas espécies indígenas de forma tubular (Ulva prolifera e Ulva compressa) do género Ulva bem como a rodófita não-indígena A.vermiculophyllum foram identificadas no estuário de Clonakilty (Condado de Cork, Irlanda) e estão a formar canópias distintas próximas umas das outras. A identificação de efeitos positivos ou negativos de uma espécie não-indígena em ecossistemas estuarinos e a forma como é controlada teria implicações notáveis nas estratégias de gestão de espécies invasivas fundacionais. Os vários impactos ecológicos na diversidade da epifauna e a utilização de nutrientes precisam de ser avaliados, especialmente no contexto do sobre-enriquecimento de nutrientes antropogénico local e a mudança global para reconhecer e recomendar uma estratégia apropriada (activa ou passiva). Ao tirar proveito da co-ocorrência de algas indígenas e não-indígenas neste estuário, tivemos como objectivos: (i) a comparação de padrões espaciais e temporais na estrutura de comunidades de epifauna em ambas as algas; (ii) caracterizar o seu papel na formação de habitats de ambas as espécies e as suas implicações em diferentes taxa da fauna; (iii) explorar implicações ecológicas para diferentes guildas alimentares e discutir o impacto em cascadas tróficas; e (iv) a avaliação da biodiversidade da epifauna e a riqueza das espécies de macroalgas.(…