Generalised Quantum Waveguides

We study general quantum waveguides and establish explicit effective Hamiltonians for the Laplacian on these spaces. A conventional quantum waveguide is an $\varepsilon$-tubular neighbourhood of a curve in $\mathbb{R}^3$ and the object of interest is the Dirichlet Laplacian on this tube in the asymptotic limit $\varepsilon\to0$. We generalise this by considering fibre bundles $M$ over a $d$-dimensional submanifold $B\subset\mathbb{R}^{d+k}$ with fibres diffeomorphic to $F\subset\mathbb{R}^k$, whose total space is embedded into an $\varepsilon$-neighbourhood of $B$. From this point of view $B$ takes the role of the curve and $F$ that of the disc-shaped cross-section of a conventional quantum waveguide. Our approach allows, among other things, for waveguides whose cross-sections $F$ are deformed along $B$ and also the study of the Laplacian on the boundaries of such waveguides. By applying recent results on the adiabatic limit of Schr\"odinger operators on fibre bundles we show, in particular, that for small energies the dynamics and the spectrum of the Laplacian on $M$ are reflected by the adiabatic approximation associated to the ground state band of the normal Laplacian. We give explicit formulas for the according effective operator on $L^2(B)$ in various scenarios, thereby improving and extending many of the known results on quantum waveguides and quantum layers in $\mathbb{R}^3$

Diagnosing Fractionalization from the Spin Dynamics of Z2Z_2 Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations

Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice quantum spin-$1/2$ model, which is known to harbor an extended $Z_2$ quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit-cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the $Z_2$ quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.Comment: 6 pages, 9 figures, v2: published versio

The adiabatic limit of the connection Laplacian

We study the behaviour of Laplace-type operators H on a complex vector bundle E $\rightarrow$ M in the adiabatic limit of the base space. This space is a fibre bundle M $\rightarrow$ B with compact fibres and the limit corresponds to blowing up directions perpendicular to the fibres by a factor 1/$\epsilon$. Under a gap condition on the fibre-wise eigenvalues we prove existence of effective operators that provide asymptotics to any order in $\epsilon$ for H (with Dirichlet boundary conditions), on an appropriate almost-invariant subspace of L${}^2$(E).Comment: To appear in the Journal of Geometric Analysi

Rapid prediction of NMR spectral properties with quantified uncertainty

open access articleAccurate calculation of specific spectral properties for NMR is an important step for molecular structure elucidation. Here we report the development of a novel machine learning technique for accurately predicting chemical shifts of both 1H and 13C nuclei which exceeds DFT-accessible accuracy for 13C and 1H for a subset of nuclei, while being orders of magnitude more performant. Our method produces estimates of uncertainty, allowing for robust and confident predictions, and suggests future avenues for improved performance

Competition between employed and unemployed job applicants: Swedish evidence

We use the Swedish Job Applicant Database to empirically investigate whether being unemployed per se reduces the probability to get contacted by a firm. This database contains personal characteristics and preferences over the type of job the applicant wants to find. The data is submitted both by employed and unemployed workers over the Internet by the applicants themselves. This means that we have access to exactly the same information as firms have when they choose whom to contact. Our results show that an unemployed applicant faces a lower probability to get contacted by a firm than an otherwise identical employed applicant, thus supporting the claim that firms view employment status as an important signal for productivity.Employed and unemployed job seekers; discrimination

Detecting discrimination in the hiring process: evidence from an Internet-based search channel

This paper uses data from an Internet-based CV database to investigate how factors which may be used as a basis for discrimination, such as the searchers’ ethnicity, gender, age and employment status, affect the number of contacts they receive from firms. Since we have access to essentially the same information as the firms, we can handle the problems associated with unobserved heterogeneity better than most existing studies of discrimination. We find that, even when we control for all other differences, searchers who have non-Nordic names, are old or unemployed receive significantly fewer contacts. Moreover, we find that this matters for the hiring outcome: Searchers who receive more contacts have a higher probability of actually getting hired.Job search; Unobserved heterogeneity; Discrimination

Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section

We show how to translate recent results on effective Hamiltonians for quantum systems constrained to a submanifold by a sharply peaked potential to quantum systems on thin Dirichlet tubes. While the structure of the problem and the form of the effective Hamiltonian stays the same, the difficulties in the proofs are different.Comment: 6 pages, 1 figur

Learning stable and predictive structures in kinetic systems: Benefits of a causal approach

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well established approaches focusing solely on predictive performance, especially for out-of-sample generalization

pp→A→Zhpp\to A\to Zh and the wrong-sign limit of the Two-Higgs-Doublet Model

We point out the importance of the decay channels $A\to Zh$ and $H\to VV$ in the wrong-sign limit of the Two-Higgs-Doublet Model (2HDM) of type II. They can be the dominant decay modes at moderate values of $\tan\beta$, even if the (pseudo)scalar mass is above the threshold where the decay into a pair of top quarks is kinematically open. Accordingly, large cross sections $pp\to A\to Zh$ and $pp\to H\to VV$ are obtained and currently probed by the LHC experiments, yielding conclusive statements about the remaining parameter space of the wrong-sign limit. In addition, mild excesses - as recently found in the ATLAS analysis $b\bar b \to A\to Zh$ - could be explained. The wrong-sign limit makes other important testable predictions for the light Higgs boson couplings.Comment: 19 pages, 6 figures, v2: journal versio