The numerical renormalization group method for quantum impurity systems

In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.Comment: 55 pages, 27 figures, submitted to Rev. Mod. Phy

Mean-Field Limits Beyond Ordinary Differential Equations

16th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2016, Bertinoro, Italy, June 20-24, 2016, Advanced LecturesInternational audienceWe study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation (ODE) under two conditions: (1) that the dynamics is smooth; and (2) that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents. This paper reviews recent work showing what happens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton

The relationship between chronic type III acromioclavicular joint dislocation and cervical spine pain

<p>Abstract</p> <p>Background</p> <p>This study was aimed at evaluating whether or not patients with chronic type III acromioclavicular dislocation develop cervical spine pain and degenerative changes more frequently than normal subjects.</p> <p>Methods</p> <p>The cervical spine of 34 patients with chronic type III AC dislocation was radiographically evaluated. Osteophytosis presence was registered and the narrowing of the intervertebral disc and cervical lordosis were evaluated. Subjective cervical symptoms were investigated using the Northwick Park Neck Pain Questionnaire (NPQ). One-hundred healthy volunteers were recruited as a control group.</p> <p>Results</p> <p>The rate and distribution of osteophytosis and narrowed intervertebral disc were similar in both of the groups. Patients with chronic AC dislocation had a lower value of cervical lordosis. NPQ score was 17.3% in patients with AC separation (100% = the worst result) and 2.2% in the control group (p < 0.05). An inverse significant nonparametric correlation was found between the NPQ value and the lordosis degree in the AC dislocation group (p = 0.001) wheras results were not correlated (p = 0.27) in the control group.</p> <p>Conclusions</p> <p>Our study shows that chronic type III AC dislocation does not interfere with osteophytes formation or intervertebral disc narrowing, but that it may predispose cervical hypolordosis. The higher average NPQ values were observed in patients with chronic AC dislocation, especially in those that developed cervical hypolordosis.</p

Modeling Mechanisms of In Vivo Variability in Methotrexate Accumulation and Folate Pathway Inhibition in Acute Lymphoblastic Leukemia Cells

Methotrexate (MTX) is widely used for the treatment of childhood acute lymphoblastic leukemia (ALL). The accumulation of MTX and its active metabolites, methotrexate polyglutamates (MTXPG), in ALL cells is an important determinant of its antileukemic effects. We studied 194 of 356 patients enrolled on St. Jude Total XV protocol for newly diagnosed ALL with the goal of characterizing the intracellular pharmacokinetics of MTXPG in leukemia cells; relating these pharmacokinetics to ALL lineage, ploidy and molecular subtype; and using a folate pathway model to simulate optimal treatment strategies. Serial MTX concentrations were measured in plasma and intracellular MTXPG concentrations were measured in circulating leukemia cells. A pharmacokinetic model was developed which accounted for the plasma disposition of MTX along with the transport and metabolism of MTXPG. In addition, a folate pathway model was adapted to simulate the effects of treatment strategies on the inhibition of de novo purine synthesis (DNPS). The intracellular MTXPG pharmacokinetic model parameters differed significantly by lineage, ploidy, and molecular subtypes of ALL. Folylpolyglutamate synthetase (FPGS) activity was higher in B vs T lineage ALL (p<0.005), MTX influx and FPGS activity were higher in hyperdiploid vs non-hyperdiploid ALL (p<0.03), MTX influx and FPGS activity were lower in the t(12;21) (ETV6-RUNX1) subtype (p<0.05), and the ratio of FPGS to γ-glutamyl hydrolase (GGH) activity was lower in the t(1;19) (TCF3-PBX1) subtype (p<0.03) than other genetic subtypes. In addition, the folate pathway model showed differential inhibition of DNPS relative to MTXPG accumulation, MTX dose, and schedule. This study has provided new insights into the intracellular disposition of MTX in leukemia cells and how it affects treatment efficacy

International money markets: eurocurrencies

Eurocurrencies are international markets for short-term wholesale bank deposits and loans. They emerged in Western Europe in the late 1950s and rapidly reached a global scale. A Eurocurrency is a form of bank money: an unsecured short-term bank debt denominated in a currency (for instance, US dollars) but issued by banks operating offshore, in a geographical location or a legal space situated outside of the jurisdiction of the national authorities presiding over that currency (for instance, the Federal Reserve). In Eurocurrency markets, banks intermediate mainly between foreign residents. They borrow funds by "accepting" foreign currency deposits and lend foreign currency-denominated funds by "placing" deposits with other banks, by granting short-term loans or investing in other liquid assets. Historically, Eurodollars accounted for the largest share of Eurocurrencies, although other international currencies (Deutsche Marks, Japanese yens, and especially Euros since 1999) played an important role. Eurocurrency markets were a manifestation of financial integration and interdependence in a globalizing economy and performed critical functions in the distribution and creation of international liquidity. At the same time, their fast growth was a recurrent source of concerns for central bankers and policymakers due to their implications for macroeconomic policies and financial stability. This chapter analyzes different aspects of the historical development of Eurocurrency markets and their role in the international monetary and financial system. The first part discusses theoretical interpretations, presents estimates of markets' size, describes their structure, and explains the determinants of their growth. The second part analyzes the spread between Eurodollar rates and other US money market rates, the role of arbitrage, the evolution of risk factors, and the causes of historical episodes of stress and contagion in the interbank market. The last part discusses political economy issues, such as the role of governments and market forces in the emergence of Eurodollars in the 1950s and the failed attempts to impose multilateral controls on Eurocurrency markets in the 1970s

Three-orbital Kondo effect in single quantum dot system with plural electrons

We study the Kondo effect and related transport properties in orbitally degenerate vertical quantum dot systems with plural electrons. Applying the non-crossing approximation to the three-orbital Anderson impurity model with the finite Coulomb interaction and Hund-coupling, we investigate the magnetic-field dependence of the conductance and thermopower. We also introduce an additional orbital splitting to take account of the realistic many-body effect in the vertical quantum dot system. It is clarified how the three-orbital Kondo effect influences the transport properties via the modulation of the Kondo temperature and unitary limit of transport quantities due to the change of the symmetry in the system.Comment: 11 pages, 10 figures, accepted for publication in J. Phys. Soc. Jp