Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

The Hilbert basis method for D-flat directions and the superpotential

We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.Comment: 11 pages; a related mathematica code can be found at http://einrichtungen.ph.tum.de/T30e/codes/NonAbelianHilbert

Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage

We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics - ideal fluid dynamics vs. non-equilibrium transport theory - will be explored. The freeze-out and initial state parameter dependences are investigated for different observables. Furthermore, the time evolution of the baryon density and particle yields are discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.Comment: 20 pages, 21 figures, 1 additional figure, minor corrections and revised figures for clarity, version published in PR

Energy Dependence of High Moments for Net-proton Distributions

High moments of multiplicity distributions of conserved quantities are predicted to be sensitive to critical fluctuations. To understand the effect of the complicated non-critical physics backgrounds on the proposed observable, we have studied various moments of net-proton distributions with AMPT, Hijing, Therminator and UrQMD models, in which no QCD critical point physics is implemented. It is found that the centrality evolution of various moments of net-proton distributions can be uniformly described by a superposition of emission sources. In addition, in the absence of critical phenomena, some moment products of net-proton distribution, related to the baryon number susceptibilities ratio in Lattice QCD calculation, are predicted to be constant as a function of the collision centrality. We argue that a non-monotonic dependence of the moment products as a function collision centrality and the beam energy may be used to locate the QCD critical point.Comment: SQM2009 Proceeding, 6 pages, 5 figure

Modifications to the University of Michigan 83‐Inch Cyclotron to Improve Beam Quality

Recent studies of the internal and extracted beams at the higher energies (up to 40‐MeV deuterons and 80‐MeV α‐particles) led us to convert the dee system of the 83‐inch cyclotron from two 150° dees to one 180° dee. The primary purpose was to remove from the deflector channel the rf dee voltage, which because of its phase opposes the dc deflector voltage and in addition introduces an energy spread in the extracted beam. The one‐dee system offers further advantages. The equivalent first harmonic due to a gap‐crossing driving force which is a function of the dee geometry and dee voltage balance in the two‐dee system, is essentially eliminated, and control of the central orbits, in particular the selection of phase width, is facilitated. The measured values of the beam quality and energy spread are in good agreement with calculations. These results, together with the diagnostic instrumentation used in obtaining them, are described.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87291/2/366_1.pd

Who is the best player ever? A complex network analysis of the history of professional tennis

We consider all matches played by professional tennis players between 1968 and 2010, and, on the basis of this data set, construct a directed and weighted network of contacts. The resulting graph shows complex features, typical of many real networked systems studied in literature. We develop a diffusion algorithm and apply it to the tennis contact network in order to rank professional players. Jimmy Connors is identified as the best player of the history of tennis according to our ranking procedure. We perform a complete analysis by determining the best players on specific playing surfaces as well as the best ones in each of the years covered by the data set. The results of our technique are compared to those of two other well established methods. In general, we observe that our ranking method performs better: it has a higher predictive power and does not require the arbitrary introduction of external criteria for the correct assessment of the quality of players. The present work provides a novel evidence of the utility of tools and methods of network theory in real applications.Comment: 10 pages, 4 figures, 4 table

Quantitative law describing market dynamics before and after interest-rate change

We study the behavior of U.S. markets both before and after U.S. Federal Open Market Committee (FOMC) meetings, and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the announcement is described by an analogue of the Omori earthquake law. We quantify the rate n(t) of aftershocks following an interest rate change at time T, and find power-law decay which scales as n(t-T) (t-T)^-$\Omega$, with $\Omega$ positive. Surprisingly, we find that the same law describes the rate n'(|t-T|) of "pre-shocks" before the interest rate change at time T. This is the first study to quantitatively relate the size of the market response to the news which caused the shock and to uncover the presence of quantifiable preshocks. We demonstrate that the news associated with interest rate change is responsible for causing both the anticipation before the announcement and the surprise after the announcement. We estimate the magnitude of financial news using the relative difference between the U. S. Treasury Bill and the Federal Funds Effective rate. Our results are consistent with the "sign effect," in which "bad news" has a larger impact than "good news." Furthermore, we observe significant volatility aftershocks, confirming a "market underreaction" that lasts at least 1 trading day.Comment: 16 pages (2-column), 9 Figures, 1 Table; Changes in final version made in response to referee comment

The Cross-Sectional Association between Diet Quality and Depressive Symptomology amongst Fijian Adolescents

OBJECTIVE: To examine the relationship between diet quality and depressive symptomology amongst a community-based sample of Fijian adolescents. METHODS: Participants included 7,237 adolescents (52.6% girls; mean age 15.6 years) at baseline (2005) and 2,948 (56% girls; mean age 17.4 years) at follow-up (2007/2008), from the Pacific Obesity Prevention in Communities Project. Intervention schools (n = 7) were selected from Nasinu, near Suva on the main Fijian island Viti Levu, and comparison schools (n = 11) were chosen from towns on the opposite, west side of the island. A dietary questionnaire was used to measure diet quality. Factor analysis clustered dietary variables into two unique and independent factors, referred to as healthy diet quality and unhealthy diet quality. Depressive symptomology was assessed via the emotional subscale of the Paediatric Quality of Life Inventory. Both measures were self-reported and self-administered. Multiple linear regression was used to test cross-sectional associations (at baseline and follow-up) between diet quality and depressive symptomology. Variables controlled for included gender, age, ethnicity, study condition, BMI-z scores, and physical activity. FINDINGS: Strong, positive dose-response associations between healthy diet and high emotional scores (lower depressive symptomology) were found in cross-sectional analyses at baseline and follow-up, among boys and girls. No association was found between emotional health and unhealthy diet. CONCLUSIONS: This study suggests that cross-sectional relationships exist between a high quality diet during adolescence and less depressive symptoms, however more evidence is required to determine if these two variables are linked causally. Trial population health strategies that use dietary interventions as a mechanism for mental health promotion provide an opportunity to further test these associations. If this is indeed a true relationship, these forms of interventions have the potential to be inexpensive and have substantial reach, especially in Low and Middle Income Countries. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry ACTRN12608000345381