Signature of antiferromagnetic long-range order in the optical spectrum of strongly correlated electron systems

We show how the onset of a non-Slater antiferromagnetic ordering in a correlated material can be detected by optical spectroscopy. Using dynamical mean-field theory we identify two distinctive features: The antiferromagnetic ordering is associated with an enhanced spectral weight above the optical gap, and well separated spin-polaron peaks emerge in the optical spectrum. Both features are indeed observed in LaSrMnO_4 [G\"ossling et al., Phys. Rev. B 77, 035109 (2008)]Comment: 11 pages, 9 figure

From infinite to two dimensions through the functional renormalization group

We present a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, i.e., the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, this allows for a systematic inclusion of non-local correlations via the flow equations of the fRG, after the local correlations are taken into account non-perturbatively by the DMFT. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half-filling.Comment: 5 pages, 4 figure

Time-dependent wave equations on graded groups

In this paper we consider the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent H\"older propagation speeds. The examples are the time-dependent wave equation for the sub-Laplacian on the Heisenberg group or on general stratified Lie groups, or $p$-evolution equations for higher order operators, already in all these cases our results being new. We establish sharp well-posedness results in the spirit of the classical result by Colombini, de Giorgi and Spagnolo. In particular, we describe an interesting loss of regularity phenomenon depending on the step of the group and on the order of the considered operator

Non-Markovian Memory Strength Bounds Quantum Process Recoverability

Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.Comment: 8 pages, 7 pages of appendices, 5 figures. Close to the published versio

Modelling the impact of close-out netting on bank portfolios

The stochastic volatility of daily foreign exchange (FX) derivatives poses a number of risks for the international banking community. Settlement risk, liquidity risk and capital adequacy are just a few immediate concerns that arise from such volatility. This thesis examines the impact of close-out netting on minimising the stochastic volatility of inter-bank FX derivatives. The problem with close-out netting is that although it is a simple formula of taking the differences between two banks at one point in time, it is the stochastic and volatile nature of FX rates that makes measuring the full impact of netting difficult. The objective of this thesis is to establish a realistic international banking framework or modelling environment in which close-out netting can be scientifically applied and examined. Five international daily FX rates will be used as sufficient approximations for five international banks. A generalised autoregressive conditionally heteroschedastic (GARCH) modelling approach is adopted as a robust and rich FX volatility paradigm. Then through Monte Carlo simulation of the resulting fitted GARCH models, we generate the distributions -with and without close-out netting. The findings of this thesis are interesting, showing that close-out netting is far more than just a simple mathematical process. Netting surely does reduce each bank's exposure to FX volatility, however, its multivariate nature reveals some important results for banking risk research and bank analysts

Oncoplastic conservative surgery for breast cancer: long-term outcomes of our first ten years experience

The main goal of oncoplastic breast surgery (OBS) is to optimize cosmetic outcomes and reduce patient morbidity, while still providing an oncologically-safe surgical outcome and extending the target population of conservative surgery. Although the growing number of reported experiences with oncoplastic surgery, few studies account for the long-term outcomes