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

Management and Service-aware Networking Architectures (MANA) for Future Internet Position Paper: System Functions, Capabilities and Requirements

Future Internet (FI) research and development threads have recently been gaining momentum all over the world and as such the international race to create a new generation Internet is in full swing: GENI, Asia Future Internet, Future Internet Forum Korea, European Union Future Internet Assembly (FIA). This is a position paper identifying the research orientation with a time horizon of 10 years, together with the key challenges for the capabilities in the Management and Service-aware Networking Architectures (MANA) part of the Future Internet (FI) allowing for parallel and federated Internet(s)