Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical review appearing in the proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri sul Mare (Salerno, Italy, October 2004

Puberty: Is Your Gingiva Having Mood Swings?

Objectives/aim: The purpose of this paper is to explore the effects on the different pathological changes in the oral cavity due to puberty, in both males and females. Hormonal changes caused by menstrual cycles, ovulation, the use contraceptives, and increased testosterone and estrogen levels. Methods: This topic will be analyzed by thoroughly reviewing research on articles that relate to the oral health of individuals specifically between the ages of 12-18 years old. Results: Research presents significant evidence that supports changes occurring in the oral cavity during an individual’s stage of puberty. These stages include ovulation, pre-menstruation, menstruation and males transitioning through puberty. During the puberty stage adolescents are more prone to have increased gingival crevicular fluid (GCF), gingival index, and bleeding on probing while research has shown no significant findings on plaque indexes or probing depths. Changes occurring during the menstrual cycle tend to influence the periodontium and induce inflammatory conditions as well. While the periodontium and inflammatory cytokines play a major role in the effects during puberty, changes in diet during this phase can increase the risk of developing caries as well. Conclusion: When adolescents are transitioning into adulthood, there are multiple changes their body goes through. During the literature review, many changes happen during puberty significantly affecting the oral cavity were discovered. These changes have both positive and negative effects. Variations in hormone levels and diet greatly influence the health of the oral cavity and can be a deciding factor on development or severity of oral disease.https://scholarscompass.vcu.edu/denh_student/1008/thumbnail.jp

Analysis of monotonicity properties of some rule interestingness measures

One of the crucial problems in the field of knowledge discovery is development of good interestingness measures for evaluation of the discovered patterns. In this paper, we consider quantitative, objective interestingness measures for "if..., then... " association rules. We focus on three popular interestingness measures, namely rule interest function of Piatetsky-Shapiro, gain measure of Fukuda et al., and dependency factor used by Pawlak. We verify whether they satisfy the valuable property M of monotonic dependency on the number of objects satisfying or not the premise or the conclusion of a rule, and property of hypothesis symmetry (HS). Moreover, analytically and through experiments we show an interesting relationship between those measures and two other commonly used measures of rule support and anti-support

Unicast Barrage Relay Networks: Outage Analysis and Optimization

Barrage relays networks (BRNs) are ad hoc networks built on a rapid cooperative flooding primitive as opposed to the traditional point-to-point link abstraction. Controlled barrage regions (CBRs) can be used to contain this flooding primitive for unicast and multicast, thereby enabling spatial reuse. In this paper, the behavior of individual CBRs is described as a Markov process that models the potential cooperative relay transmissions. The outage probability for a CBR is found in closed form for a given topology, and the probability takes into account fading and co-channel interference (CCI) between adjacent CBRs. Having adopted this accurate analytical framework, this paper proceeds to optimize a BRN by finding the optimal size of each CBR, the number of relays contained within each CBR, the optimal relay locations when they are constrained to lie on a straight line, and the code rate that maximizes the transport capacity.Comment: 7 pages, 4 figures, 1 table, in IEEE Military Commun. Conf. (MILCOM), 201

Quantification of Order in the Lennard-Jones System

We conduct a numerical investigation of structural order in the shifted-force Lennard-Jones system by calculating metrics of translational and bond-orientational order along various paths in the phase diagram covering equilibrium solid, liquid, and vapor states. A series of non-equilibrium configurations generated through isochoric quenches, isothermal compressions, and energy minimizations are also considered. Simulation results are analyzed using an ordering map representation [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000); Truskett et al., Phys. Rev. E 62, 993 (2000)] that assigns to both equilibrium and non-equilibrium states coordinates in an order metric plane. Our results show that bond-orientational order and translational order are not independent for simple spherically symmetric systems at equilibrium. We also demonstrate quantitatively that the Lennard-Jones and hard sphere systems sample the same configuration space at supercritical densities. Finally, we relate the structural order found in fast-quenched and minimum-energy configurations (inherent structures).Comment: 35 pages, 8 figure

Time evolution of one-dimensional Quantum Many Body Systems

The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.Comment: Contribution for the conference proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors" held in Vietri sul Mare (Salerno, Italy) in October 200

Correlations and enlarged superconducting phase of tt-J⊥J_\perp chains of ultracold molecules on optical lattices

We compute physical properties across the phase diagram of the $t$-$J_\perp$ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group (DMRG) indicate that superconductivity is enhanced when the Ising component $J_z$ of the spin-spin interaction and the charge component $V$ are tuned to zero, and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.Comment: published version with minor modification