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.

Quantum Simulation of Non-Abelian Lattice Gauge Theories

We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson’s classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.

Towards quantum simulating QCD

Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.

Benchmark problems for reactive transport modeling of the generation and attenuation of acid rock drainage

Acid rock drainage (ARD) is a problem of international relevance with substantial environmental and economic implications. Reactive transport modeling has proven a powerful tool for the process-based assessment of metal release and attenuation at ARD sites. Although a variety of models has been used to investigate ARD, a systematic model intercomparison has not been conducted to date. This contribution presents such a model intercomparison involving three synthetic benchmark problems designed to evaluate model results for the most relevant processes at ARD sites. The first benchmark (ARD-B1) focuses on the oxidation of sulfide minerals in an unsaturated tailing impoundment, affected by the ingress of atmospheric oxygen. ARD-B2 extends the first problem to include pH buffering by primary mineral dissolution and secondary mineral precipitation. The third problem (ARD-B3) in addition considers the kinetic and pH-dependent dissolution of silicate minerals under low pH conditions. The set of benchmarks was solved by four reactive transport codes, namely CrunchFlow, Flotran, HP1, and MIN3P. The results comparison focused on spatial profiles of dissolved concentrations, pH and pE, pore gas composition, and mineral assemblages. In addition, results of transient profiles for selected elements and cumulative mass loadings were considered in the intercomparison. Despite substantial differences in model formulations, very good agreement was obtained between the various codes. Residual deviations between the results are analyzed and discussed in terms of their implications for capturing system evolution and long-term mass loading predictions.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

Renal Blood Oxygenation Level-dependent Imaging in Longitudinal Follow-up of Donated and Remaining Kidneys

Purpose To determine renal oxygenation changes associated with uninephrectomy and transplantation in both native donor kidneys and transplanted kidneys by using blood oxygenation level-dependent (BOLD) MR imaging. Materials and Methods The study protocol was approved by the local ethics committee. Thirteen healthy kidney donors and their corresponding recipients underwent kidney BOLD MR imaging with a 3-T imager. Written informed consent was obtained from each subject. BOLD MR imaging was performed in donors before uninephrectomy and in donors and recipients 8 days, 3 months, and 12 months after transplantation. R2* values, which are inversely related to tissue partial pressure of oxygen, were determined in the cortex and medulla. Longitudinal R2* changes were statistically analyzed by using repeated measures one-way analysis of variance with post hoc pair-wise comparisons. Results R2* values in the remaining kidneys significantly decreased early after uninephrectomy in both the medulla and cortex (P < .003), from 28.9 sec(-1) ± 2.3 to 26.4 sec(-1) ± 2.5 in the medulla and from 18.3 sec(-1) ± 1.5 to 16.3 sec(-1) ± 1.0 in the cortex, indicating increased oxygen content. In donors, R2* remained significantly decreased in both the medulla and cortex at 3 (P < .01) and 12 (P < .01) months. In transplanted kidneys, R2* remained stable during the first year after transplantation, with no significant change. Among donors, cortical R2* was found to be negatively correlated with estimated glomerular filtration rate (R = -0.47, P < .001). Conclusion The results suggest that BOLD MR imaging may potentially be used to monitor renal functional changes in both remaining and corresponding transplanted kidneys. (©) RSNA, 2016.

Primitive ontology and quantum state in the GRW matter density theory

The paper explains in what sense the GRW matter density theory (GRWm) is a primitive ontology theory of quantum mechanics and why, thus conceived, the standard objections against the GRW formalism do not apply to GRWm. We consider the different options for conceiving the quantum state in GRWm and argue that dispositionalism is the most attractive one.

Advanced Physical Chemistry Problems (II), Hydrogen Atom and Hyrdrogen Molecular Ion

Slightly advanced problems in Physical Chemistry, herein concerning the H-atom and the Hydrogen Molecular Cation, are presented and discussed.

A GENETIC MARKER STUDY OF NON - INSULIN DEPENDENT DIABETICS IN THE MEXICAN-AMERICAN COMMUNITY FROM STARR COUNTY, TEXAS (PLASMA GLUCOSE, HEMOGLOBIN ANALYSIS)

Diabetes mellitus occurs in two forms, insulin-dependent (IDDM, formerly called juvenile type) and non-insulin dependent (NIDDM, formerly called adult type). Prevalence figures from around the world for NIDDM, show that all societies and all races are affected; although uncommon in some populations (.4%), it is common (10%) or very common (40%) in others (Tables 1 and 2).^ In Mexican-Americans in particular, the prevalence rates (7-10%) are intermediate to those in Caucasians (1-2%) and Amerindians (35%). Information about the distribution of the disease and identification of high risk groups for developing glucose intolerance or its vascular manifestations by the study of genetic markers will help to clarify and solve some of the problems from the public health and the genetic point of view.^ This research was designed to examine two general areas in relation to NIDDM. The first aims to determine the prevalence of polymorphic genetic markers in two groups distinguished by the presence or absence of diabetes and to observe if there are any genetic marker-disease association (univariate analysis using two by two tables and logistic regression to study the individual and joint effects of the different variables). The second deals with the effect of genetic differences on the variation in fasting plasma glucose and percent glycosylated hemoglobin (HbAl) (analysis of Covariance for each marker, using age and sex as covariates).^ The results from the first analysis were not statistically significant at the corrected p value of 0.003 given the number of tests that were performed. From the analysis of covariance of all the markers studied, only Duffy and Phosphoglucomutase were statistically significant but poor predictors, given that the amount they explain in terms of variation in glycosylated hemoglobin is very small.^ Trying to determine the polygenic component of chronic disease is not an easy task. This study confirms the fact that a larger and random or representative sample is needed to be able to detect differences in the prevalence of a marker for association studies and in the genetic contribution to the variation in glucose and glycosylated hemoglobin. The importance that ethnic homogeneity in the groups studied and standardization in the methodology will have on the results has been stressed. ^

The lead salt quantum dot intermediate band solar cell

We propose a new kind of quantum dot (QD) materials for the implementation of the intermediate band solar cell (IBSC) [1]. The materials are formed by lead salt QDs of the family IV-VI (PbTe, PbSe or PbS) embedded in a semiconductor of the family II-VI (Cd1-xMgxTe, CdxZn1-xTe, and CdS1-xSex or ZnSe1-xTex, respectively). These QDs are not nucleated due to lattice mismatch, as it is the case of the InAs/GaAs QD material system grown by the Stranski-Krastanov (S-K) mode. In these materials, the QDs precipitate due to the difference in lattice type: the QD lead salt material crystallizes in the rocksalt structure, while the II-VI host material has the zincblende structure [2]. Therefore, it is possible to use lattice-matched QD/host combinations, avoiding all the strain-related problems found in previous QD-IBSC developments. In this paper we discuss the properties of the lead salt QD materials and propose that they are appropriate to overcome the fundamental drawbacks of present III-V-based QD-IBSC prototypes. We also calculate the band diagram for some examples of IV-VI/II-VI QD materials. The detailed balance efficiency limit of QD-IBSCs based on the studied materials is found to be over 60% under maximum concentration.

One dimensional exciton luminescence induced by extended defects in nonpolar (Al,Ga)N/GaN quantum wells

In this study, we present the optical properties of nonpolar GaN/(Al,Ga)N single quantum wells (QWs) grown on either a- or m-plane GaN templates for Al contents set below 15%. In order to reduce the density of extended defects, the templates have been processed using the epitaxial lateral overgrowth technique. As expected for polarization-free heterostructures, the larger the QW width for a given Al content, the narrower the QW emission line. In structures with an Al content set to 5 or 10%, we also observe emission from excitons bound to the intersection of I1-type basal plane stacking faults (BSFs) with the QW. Similarly to what is seen in bulk material, the temperature dependence of BSF-bound QW exciton luminescence reveals intra-BSF localization. A qualitative model evidences the large spatial extension of the wavefunction of these BSF-bound QW excitons, making them extremely sensitive to potential fluctuations located in and away from BSF. Finally, polarization-dependent measurements show a strong emission anisotropy for BSF-bound QW excitons, which is related to their one-dimensional character and that confirms that the intersection between a BSF and a GaN/(Al,Ga)N QW can be described as a quantum wire.

Highly efficient potentiometric glucose biosensor based on functionalized InN quantum dots

We present a fast, highly sensitive, and efficient potentiometric glucose biosensor based on functionalized InN quantum-dots (QDs). The InN QDs are grown by molecular beam epitaxy. The InN QDs are bio-chemically functionalized through physical adsorption of glucose oxidase (GOD). GOD enzyme-coated InN QDs based biosensor exhibits excellent linear glucose concentration dependent electrochemical response against an Ag/AgCl reference electrode over a wide logarithmic glucose concentration range (1 × 10−5 M to 1 × 10−2 M) with a high sensitivity of 80 mV/decade. It exhibits a fast response time of less than 2 s with good stability and reusability and shows negligible response to common interferents such as ascorbic acid and uric acid. The fabricated biosensor has full potential to be an attractive candidate for blood sugar concentration detection in clinical diagnoses.

InAs/AlGaAs quantum dot intermediate band solar cells with enlarged sub-bandgaps

In the last decade several prototypes of intermediate band solar cells (IBSCs) have been manufactured. So far, most of these prototypes have been based on InAs/GaAs quantum dots (QDs) in order to implement the IB material. The key operation principles of the IB theory are two photon sub-bandgap (SBG) photocurrent, and output voltage preservation, and both have been experimentally demonstrated at low temperature. At room temperature (RT), however, thermal escape/relaxation between the conduction band (CB) and the IB prevents voltage preservation. To improve this situation, we have produced and characterized the first reported InAs/AlGaAs QD-based IBSCs. For an Al content of 25% in the host material, we have measured an activation energy of 361 meV for the thermal carrier escape. This energy is about 250 meV higher than the energies found in the literature for InAs/GaAs QD, and almost 140 meV higher than the activation energy obtained in our previous InAs/GaAs QD-IBSC prototypes including a specifically designed QD capping layer. This high value is responsible for the suppression of the SBG quantum efficiency under monochromatic illumination at around 220 K. We suggest that, if the energy split between the CB and the IB is large enough, activation energies as high as to suppress thermal carrier escape at room temperature (RT) can be achieved. In this respect, the InAs/AlGaAs system offers new possibilities to overcome some of the problems encountered in InAs/GaAs and opens the path for QD-IBSC devices capable of achieving high efficiency at RT.