Stationary point approach to the phase transition of the classical XY chain with power-law interactions

The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic behavior of the Hessian determinant of H is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szeg\"o-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body Hamiltonian functions. In agreement with this relation, the exact phase transition energy of the model can be read off from the behavior of the Hessian determinant for exponents {\alpha} between zero and one. For {\alpha} between one and two, the phase transition is not manifest in the behavior of the determinant, and it might be necessary to consider larger classes of stationary points.Comment: 9 pages, 6 figure

Measurements of quasi-particle tunneling in the nu = 5/2 fractional quantum Hall state

Some models of the 5/2 fractional quantum Hall state predict that the quasi-particles, which carry the charge, have non-Abelian statistics: exchange of two quasi-particles changes the wave function more dramatically than just the usual change of phase factor. Such non-Abelian statistics would make the system less sensitive to decoherence, making it a candidate for implementation of topological quantum computation. We measure quasi-particle tunneling as a function of temperature and DC bias between counter-propagating edge states. Fits to theory give e*, the quasi-particle effective charge, close to the expected value of e/4 and g, the strength of the interaction between quasi-particles, close to 3/8. Fits corresponding to the various proposed wave functions, along with qualitative features of the data, strongly favor the Abelian 331 state

The DeMaDs Open Source Modeling Framework for Power System Malfunction Detection

Modeling and simulation of electrical power systems are becoming increasingly important approaches for the development and operation of novel smart grid functionalities -- especially with regard to data-driven applications as data of certain operational states or misconfigurations can be next to impossible to obtain. The DeMaDs framework allows for the simulation and modeling of electric power grids and malfunctions therein. Furthermore, it serves as a testbed to assess the applicability of various data-driven malfunction detection methods. These include data mining techniques, traditional machine learning approaches as well as deep learning methods. The framework's capabilities and functionality are laid out here, as well as explained by the means of an illustrative example.Comment: 2023 Open Source Modelling and Simulation of Energy Systems (OSMSES

Topological conditions for discrete symmetry breaking and phase transitions

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here

Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model

The fidelity metric has recently been proposed as a useful and elegant approach to identify and characterize both quantum and classical phase transitions. We study this metric on the manifold of thermal states for the Lipkin-Meshkov-Glick (LMG) model. For the isotropic LMG model, we find that the metric reduces to a Fisher-Rao metric, reflecting an underlying classical probability distribution. Furthermore, this metric can be expressed in terms of derivatives of the free energy, indicating a relation to Ruppeiner geometry. This allows us to obtain exact expressions for the (suitably rescaled) metric in the thermodynamic limit. The phase transition of the isotropic LMG model is signalled by a degeneracy of this (improper) metric in the paramagnetic phase. Due to the integrability of the isotropic LMG model, ground state level crossings occur, leading to an ill-defined fidelity metric at zero temperature.Comment: 18 pages, 3 figure

History dependent magnetoresistance in lightly doped La_{2-x}Sr_{x}CuO_{4} thin films

The in-plane magnetoresistance (MR) in atomically smooth La_{2-x}Sr_{x}CuO_{4} thin films grown by molecular-beam-epitaxy was measured in magnetic fields B up to 9 T over a wide range of temperatures T. The films, with x=0.03 and x=0.05, are insulating, and the positive MR emerges at T<4 K. The positive MR exhibits glassy features, including history dependence and memory, for all orientations of B. The results show that this behavior, which reflects the onset of glassiness in the dynamics of doped holes, is a robust feature of the insulating state.Comment: 4 pages, 4 figures, International School and Workshop on Electronic Crystals (ECRYS-2011); to appear in Physica

Effect of Quantum Confinement on Electron Tunneling through a Quantum Dot

Employing the Anderson impurity model, we study tunneling properties through an ideal quantum dot near the conductance minima. Considering the Coulomb blockade and the quantum confinement on an equal footing, we have obtained current contributions from various types of tunneling processes; inelastic cotunneling, elastic cotunneling, and resonant tunneling of thermally activated electrons. We have found that the inelastic cotunneling is suppressed in the quantum confinement limit, and thus the conductance near its minima is determined by the elastic cotunneling at low temperature ($k_BT \ll \Gamma$, $\Gamma$: dot-reservoir coupling constant), or by the resonant tunneling of single electrons at high temperature ($k_BT \gg \Gamma$).Comment: 11 pages Revtex, 2 Postscript figures, To appear in Phys.Rev.

CO emission from discs around isolated HAeBe and Vega-excess stars

We describe results from a survey for J=3-2 12CO emission from visible stars with an infrared excess. The line is clearly detected in 21 objects, with molecular gas (>10^-3 Jupiter masses) common in targets with infrared excesses >0.01 (>56% of objects). Such high excesses indicate the presence of a disc of opening angle >12 degrees; within this, the optically thick disc prevents CO photodissociation. Two or three stars with associated CO have an excess <0.01, implying a disc opening angle <1 degree. Most line profiles are double-peaked or relatively broad. Model fits, assuming a Keplerian disc, indicate outer radii, R_out, of ~20-300 au. As many as 5 discs have outer radii smaller than the Solar System (50 au), and a further 4 have gas at radii <20 au. R_out is independent of the stellar spectral type (from K through to B9), but is correlated with total dust mass. R_out appears to decrease with time: discs around stars of age 3-7 Myr have a mean radius of ~210 au, whereas discs of age 7-20 Myr are a factor of 3 smaller. The only bona fide debris disc with detected CO is HD9672; this has a double peaked line profile and is the most compact gas disc observed, with a modelled radius 17 au). A fit to HD141569 suggests the gas lies in two rings of radii 90 and 250 au, similar to the scattered light structure. In both AB Aur and HD163296 the sizes of the molecular and dust scattering discs are also similar, suggesting that the gas and small dust grains are co-located.Comment: 16 pages, 5 figures MNRAS - accepte