Real-space renormalization group study of the Hubbard model on a non-bipartite lattice

We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of $U/t \approx 12.5$

Entanglement Switch for Dipole Arrays

We propose a new entanglement switch of qubits consisting of electric dipoles, oriented along or against an external electric field and coupled by the electric dipole-dipole interaction. The pairwise entanglement can be tuned and controlled by the ratio of the Rabi frequency and the dipole-dipole coupling strength. Tuning the entanglement can be achieved for one, two and three-dimensional arrangements of the qubits. The feasibility of building such an entanglement switch is also discussed.Comment: 6 pages and 4 figures. To be published on Journal of Chemical Physic

Simulated Quantum Computation of Global Minima

Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations $N$ reduced from O(N) in classical simulation to $O(\sqrt{N})$ in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.Comment: 6 figures. Molecular Physics, in pres

Effects of joint orientation in tunneling

This research is focused on the effects of joint orientation with respect to the direction of tunnel axis. It is expected that the stability of surrounding rock is affected by the strike and dip of the joints and the direction of the tunnel axis, whether it is with the dip or against dip etc. similarly the spacing of joints will also affect the stability. The orientation of joints in different directions can form blocks liable to fall. The objective of this research project is to determine the degree of influence of joints' strike and dip orientation in tunneling. Field works related to this project was carried out at the Bogala Graphite Lanka Ltd. Tunnel mapping and other observations related to the project were made at 489.6m level in Bogata mine. Models were made with joint spacing of 15mm with two joint sets (joint sets parallel to tunnel axis and joint sets perpendicular to tunnel axis). Tunnels were created with 90mm diameter with dip angles of joints are 00,300,600,and 900. The tunnels models are loaded using UCS machine and observed the behavior of rock mass around the tunnels during loading. From the results the most preferable dip angle for the joint strike perpendicular to the tunnel axis would be the 900 and for the joint strike parallel to the tunnel axis would be 00

The Effects of Methylphenidate on Cognitive Control in Active Methamphetamine Dependence Using Functional Magnetic Resonance Imaging

Methamphetamine (MA) dependence is associated with cognitive deficits. Methylphenidate (MPH) has been shown to improve inhibitory control in healthy and cocaine-dependent subjects. This study aimed to understand the neurophysiological effects before and after acute MPH administration in active MA-dependent and control subjects. Fifteen MA-dependent and 18 control subjects aged 18–46 years were scanned using functional magnetic resonance imaging before and after either a single oral dose of MPH (18 mg) or placebo while performing a color-word Stroop task. Baseline accuracy was lower (p = 0.026) and response time (RT) was longer (p < 0.0001) for the incongruent compared to congruent condition, demonstrating the task probed cognitive control. Increased activation of the dorsolateral prefrontal cortex (DLPFC) and parietal cortex during the incongruent and Stroop effect conditions, respectively was observed in MA-dependent compared to control subjects (p < 0.05), suggesting the need to recruit neural resources within these regions for conflict resolution. Post- compared to pre-MPH treatment, increased RT and DLPFC activation for the Stroop effect were observed in MA-dependent subjects (p < 0.05). In comparison to MPH-treated controls and placebo-treated MA-dependent subjects, MPH-treated MA-dependent subjects showed decreased activation of parietal and occipital regions during the incongruent and Stroop effect conditions (p < 0.05). These findings suggest that in MA-dependent subjects, MPH facilitated increased recruitment of the DLPFC for Stroop conflict resolution, and a decreased need for recruitment of neural resources in parietal and occipital regions compared to the other groups, while maintaining a comparable level of task performance to that achieved pre-drug administration. Due to the small sample size, the results from this study are preliminary; however, they inform us about the effects of MPH on the neural correlates of cognitive control in active MA-dependent subjects

Finite size scaling for quantum criticality using the finite-element method

Finite size scaling for the Schr\"{o}dinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite element method was shown to be a powerful numerical method for ab initio electronic structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, density functional theory under the local density approximation, and an "exact"' formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee, accepted in Phys. Rev.