Renormalization group approach of itinerant electron systems near the Lifshitz point

Using the renormalization approach proposed by Millis for the itinerant electron systems we calculated the specific heat coefficient $\gamma(T)$ for the magnetic fluctuations with susceptibility $\chi^{-1}\sim |\delta+\omega|^\alpha+f(q)$ near the Lifshitz point. The constant value obtained for $\alpha=4/5$ and the logarithmic temperature dependence, specific for the non-Fermi behavior, have been obtained in agreement with the experimental dat.Comment: 6 pages, Revte

Modification of the Charge ordering in Pr1/2_{1/2}Sr1/2_{1/2}MnO3_{3} Nanoparticles

Transport and magnetic properties have been studied in two sets of sol-gel prepared Pr$_{1/2}$Sr$_{1/2}$MnO$_{3}$ nanoparticles having average particle size of 30 nm and 45 nm. Our measurements suggest that the formation of charge ordered state is largely affected due to lowering of particle size, but the ferromagnetic transition temperature ($T_{C}$) remains unaffected.Comment: Accepted in J. Appl. Phy

Pinning potential in highly performant CaKFe4As4 superconductor from DC magnetic relaxation and AC multi-frequency susceptibility studies

We have investigated the pinning potential of high-quality single crystals of superconducting material CaKFe4As4 having high critical current density and very high upper critical field using both magnetization relaxation measurements and frequency-dependent AC susceptibility. Preliminary studies of the superconducting transition and of the isothermal magnetization loops confirmed the high quality of the samples, while temperature dependence of the AC susceptibility in high magnetic fields show absolutely no dependence on the cooling conditions, hence, no magnetic history. From magnetization relaxation measurements were extracted the values of the normalized pinning potential U*, which reveals a clear crossover between elastic creep and plastic creep. The extremely high values of U*, up to 1200 K around the temperature of 20 K lead to a nearly zero value of the probability of thermally-activated flux jumps at temperatures of interest for high-field applications. The values of the creep exponents in the two creep regimes resulted from the analysis of the magnetization relaxation data are in complete agreement with theoretical models. Pinning potentials were also estimated, near the critical temperature, from AC susceptibility measurements, their values being close to those resulted (at the same temperature and DC field) from the magnetization relaxation data

Error bounds and normalising constants for sequential monte carlo samplers in high dimensions

In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. TheSMCsamplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using theSMCsampler and the exact asymptotic relative L2-error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd2). © Applied Probability Trust 2014

Nonequilibrium-induced metal-superconductor quantum phase transition in graphene

We study the effects of dissipation and time-independent nonequilibrium drive on an open superconducting graphene. In particular, we investigate how dissipation and nonequilibrium effects modify the semi-metal-BCS quantum phase transition that occurs at half-filling in equilibrium graphene with attractive interactions. Our system consists of a graphene sheet sandwiched by two semi-infinite three-dimensional Fermi liquid reservoirs, which act both as a particle pump/sink and a source of decoherence. A steady-state charge current is established in the system by equilibrating the two reservoirs at different, but constant, chemical potentials. The nonequilibrium BCS superconductivity in graphene is formulated using the Keldysh path integral formalism, and we obtain generalized gap and number density equations valid for both zero and finite voltages. The behaviour of the gap is discussed as a function of both attractive interaction strength and electron densities for various graphene-reservoir couplings and voltages. We discuss how tracing out the dissipative environment (with or without voltage) leads to decoherence of Cooper pairs in the graphene sheet, hence to a general suppression of the gap order parameter at all densities. For weak enough attractive interactions we show that the gap vanishes even for electron densities away from half-filling, and illustrate the possibility of a dissipation-induced metal-superconductor quantum phase transition. We find that the application of small voltages does not alter the essential features of the gap as compared to the case when the system is subject to dissipation alone (i.e. zero voltage).Comment: 13 pages, 8 figure

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This new working group (WG) was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted; alongside the changed nature of the classroom interactions between the humans (teachers and students) and the chosen technologies. Starting with the assumption that technology resources are being used, the WG explored the nature of these tools and their affordances for the mathematical teaching and learning. The work was framed by the following three pedagogic activities, which are proving to be particularly challenging: introducing and developing understanding of new mathematical topics; managing interaction and communication in mathematics; and assessing mathematics, both formatively and summatively. Three case studies of teachers’ practices were presented to initiate discussions with respect to these challenges and to highlight some existing theoretical and methodological frames

A lagged particle filter for stable filtering of certain high-dimensional state-space models

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with the dimension of the hidden state. Inspired by lag-approximation methods for the smoothing problem, we introduce a lagged approximation of the smoothing distribution that is necessarily biased. For certain classes of SSMs, particularly those that forget the initial condition exponentially fast in time, the bias of our approximation is shown to be uniformly controlled in the dimension and exponentially small in time. We develop a sequential Monte Carlo (SMC) method to recursively estimate expectations with respect to our biased filtering distributions. Moreover, we prove for a class of class of SSMs that can contain dependencies amongst coordinates that as the dimension $d\rightarrow\infty$ the cost to achieve a stable mean square error in estimation, for classes of expectations, is of $\mathcal{O}(Nd^2)$ per-unit time, where $N$ is the number of simulated samples in the SMC algorithm. Our methodology is implemented on several challenging high-dimensional examples including the conservative shallow-water model

Kondo effect in spin-orbit mesoscopic interferometers

We consider a flux-threaded Aharonov-Bohm ring with an embedded quantum dot coupled to two normal leads. The local Rashba spin-orbit interaction acting on the dot electrons leads to a spin-dependent phase factor in addition to the Aharonov-Bohm phase caused by the external flux. Using the numerical renormalization group method, we find a splitting of the Kondo resonance at the Fermi level which can be compensated by an external magnetic field. To fully understand the nature of this compensation effect, we perform a scaling analysis and derive an expression for the effective magnetic field. The analysis is based on a tight-binding model which leads to an effective Anderson model with a spin-dependent density of states for the transformed lead states. We find that the effective field originates from the combined effect of Rashba interaction and magnetic flux and that it contains important corrections due to electron-electron interactions. We show that the compensating field is an oscillatory function of both the spin-orbit and the Aharonov-Bohm phases. Moreover, the effective field never vanishes due to the particle-hole symmetry breaking independently of the gate voltage.Comment: 9 pages, 5 figure

Enhanced critical current density of YBa2Cu3Ox films grown on Nd1/3Eu1/3Gd1/3Ba2Cu3Ox with nano-undulated surface morphology

We report a simple and easily controllable method where a nano-undulated surface morphology of Nd1/3Eu1/3Gd1/3Ba2Cu3Ox (NEG) films leads to a substantial increase in the critical current density in superconducting YBa2Cu3Ox (YBCO) films deposited by pulsed laser deposition on such NEG layers. The enhancement is observed over a wide range of fields and temperatures. Transmission electron microscopy shows that such YBCO films possess a high density of localized areas, typically 20 x 20 nm2 in size, where distortion of atomic planes give rotational (2 to 5 degrees) moire patterns. Their distribution is random and uniform, and expected to be the origin of the enhanced flux pinning. Magneto-optical imaging shows that these films have excellent macroscopic magnetic uniformity.Comment: 4 pages, 4 figure

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This working group (WG), which met for the second time in June 2021, was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted as a result of the COVID-19 pandemic. Following a brief introduction to the aims for the WG, we offer three further case studies of teachers’ practices and an emerging synthesis of the cases according to three pedagogic activities that are proving to be particularly challenging