Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images

Similarity measure is one of the main factors that affect the accuracy of intensity-based 2D/3D registration of X-ray fluoroscopy to CT images. Information theory has been used to derive similarity measure for image registration leading to the introduction of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measure only takes intensity values into account without considering spatial information and its robustness is questionable. Previous attempt to incorporate spatial information into mutual information either requires computing the entropy of higher dimensional probability distributions, or is not robust to outliers. In this paper, we show how to incorporate spatial information into mutual information without suffering from these problems. Using a variational approximation derived from the Kullback-Leibler bound, spatial information can be effectively incorporated into mutual information via energy minimization. The resulting similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experimental results are presented on datasets of two applications: (a) intra-operative patient pose estimation from a few (e.g. 2) calibrated fluoroscopic images, and (b) post-operative cup alignment estimation from single X-ray radiograph with gonadal shielding.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Thermal right-handed neutrino self-energy in the non-relativistic regime

Recently the issue of radiative corrections to leptogenesis has been raised. Considering the "strong washout" regime, in which OPE-techniques permit to streamline the setup, we report the thermal self-energy matrix of heavy right-handed neutrinos at NLO (resummed 2-loop level) in Standard Model couplings. The renormalized expression describes flavour transitions and "inclusive" decays of chemically decoupled right-handed neutrinos. Although CP-violation is not addressed, the result may find use in existing leptogenesis frameworks.

Hierarchical segmentation-assisted multimodal registration for MR brain images

Information theory-based metric such as mutual information (MI) is widely used as similarity measurement for multimodal registration. Nevertheless, this metric may lead to matching ambiguity for non-rigid registration. Moreover, maximization of MI alone does not necessarily produce an optimal solution. In this paper, we propose a segmentation-assisted similarity metric based on point-wise mutual information (PMI). This similarity metric, termed SPMI, enhances the registration accuracy by considering tissue classification probabilities as prior information, which is generated from an expectation maximization (EM) algorithm. Diffeomorphic demons is then adopted as the registration model and is optimized in a hierarchical framework (H-SPMI) based on different levels of anatomical structure as prior knowledge. The proposed method is evaluated using Brainweb synthetic data and clinical fMRI images. Both qualitative and quantitative assessment were performed as well as a sensitivity analysis to the segmentation error. Compared to the pure intensity-based approaches which only maximize mutual information, we show that the proposed algorithm provides significantly better accuracy on both synthetic and clinical data.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Information Integration Theory and the Construction of Individually Perceived Group Efficacy

According to Bandura (1997) efficacy beliefs are a primary determinant of motivation. Still, very little is known about the processes through which people integrate situational factors to form efficacy beliefs (Myers & Feltz, 2007). The aim of this study was to gain insight into the cognitive construction of subjective group-efficacy beliefs. Only with a sound understanding of those processes is there a sufficient base to derive psychological interventions aimed at group-efficacy beliefs. According to cognitive theories (e.g., Miller, Galanter, & Pribram, 1973) individual group-efficacy beliefs can be seen as the result of a comparison between the demands of a group task and the resources of the performing group. At the center of this comparison are internally represented structures of the group task and plans to perform it. The empirical plausibility of this notion was tested using functional measurement theory (Anderson, 1981). Twenty-three students (M = 23.30 years; SD = 3.39; 35 % females) of the University of Bern repeatedly judged the efficacy of groups in different group tasks. The groups consisted of the subjects and another one to two fictive group members. The latter were manipulated by their value (low, medium, high) in task-relevant abilities. Data obtained from multiple full factorial designs were structured with individuals as second level units and analyzed using mixed linear models. The task-relevant abilities of group members, specified as fixed factors, all had highly significant effects on subjects’ group-efficacy judgments. The effect sizes of the ability factors showed to be dependent on the respective abilities’ importance in a given task. In additive tasks (Steiner, 1972) group resources were integrated in a linear fashion whereas significant interaction between factors was obtained in interdependent tasks. The results also showed that people take into account other group members’ efficacy beliefs when forming their own group-efficacy beliefs. The results support the notion that personal group-efficacy beliefs are obtained by comparing the demands of a task with the performing groups’ resources. Psychological factors such as other team members’ efficacy beliefs are thereby being considered task relevant resources and affect subjective group-efficacy beliefs. This latter finding underlines the adequacy of multidimensional measures. While the validity of collective efficacy measures is usually estimated by how well they predict performances, the results of this study allow for a somewhat internal validity criterion. It is concluded that Information Integration Theory holds potential to further help understand people’s cognitive functioning in sport relevant situations.

Modern charge density studies: the entanglement of experiment and theory

This tutorial review article is intended to provide a general guidance to a reader interested to learn about the methodologies to obtain accurate electron density mapping in molecules and crystalline solids, from theory or from experiment, and to carry out a sensible interpretation of the results, for chemical, biochemical or materials science applications. The review mainly focuses on X-ray diffraction techniques and refinement of experimental models, in particular multipolar models. Neutron diffraction, which was widely used in the past to fix accurate positions of atoms, is now used for more specific purposes. The review illustrates three principal analyses of the experimental or theoretical electron density, based on quantum chemical, semi-empirical or empirical interpretation schemes, such as the quantum theory of atoms in molecules, the semi-classical evaluation of interaction energies and the Hirshfeld analysis. In particular, it is shown that a simple topological analysis based on a partition of the electron density cannot alone reveal the whole nature of chemical bonding. More information based on the pair density is necessary. A connection between quantum mechanics and observable quantities is given in order to provide the physical grounds to explain the observations and to justify the interpretations.