A Monte Carlo study of the triangular lattice gas with the first- and the second-neighbor exclusions

We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application,we study the hard-core lattice gas on the triangular lattice with the first- and the second-neighbor exclusions. The data are analyzed by finite-size scaling, but the possible existence of logarithmic corrections is not considered due to the limited data. We determine the critical chemical potential as $\mu_c=1.75682 (2)$ and the critical particle density as $\rho_c=0.180(4)$. The thermal and magnetic exponents $y_t=1.51(1) \approx 3/2$ and $y_h=1.8748 (8) \approx 15/8$, estimated from Binder ratio $Q$ and susceptibility $\chi$, strongly support the general belief that the model is in the 4-state Potts universality class. On the other hand, the analyses of energy-like quantities yield the thermal exponent $y_t$ ranging from $1.440(5)$ to $1.470(5)$. These values differ significantly from the expected value 3/2, and thus imply the existence of logarithmic corrections.Comment: 4 figures 2 table

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit coupling

We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective-2D scattering amplitude and the algebraic equations for the two-atom bound state energy. Based on these results, we further derive the effective 2D interaction potential between two ultracold atoms in the quasi-2D confinement with Rashba SOC. These results are crucial for the control of the 2D effective physics in quasi-2D geometry via the confinement intensity and the atomic three-dimensional scattering length.Comment: 13pages, 5 figure

Influence of crystal structure on charge carrier effective masses in BiFeO3_3

Ferroelectric-based photovoltaics have shown great promise as a source of renewable energy, thanks to their in-built charge separation capability, yet their efficiency is often limited by low charge carrier mobilities. In this work, we compare the photovoltaic prospects of various phases of the multiferroic material BiFeO$_3$ by evaluating their charge carrier effective masses using first-principles simulations. We identify a tetragonal phase with the promising combination of a large spontaneous polarisation and relatively light charge carriers. From a systematic study of the octahedral distortions present in BiFeO$_3$, we explain the relationship between structure and effective masses in terms of the changes to the orbital character and overlap at the band edges that result from changes in the geometry. The findings in this study provide some design principles to engineer desired effective masses in BiFeO$_3$ and similar materials through manipulation of their crystal structures in experimentally accessible ways.Comment: 12 pages, 10 figure

Weak phase stiffness and mass divergence of superfluid in underdoped cuprates

Despite more than two decades of intensive investigations, the true nature of high temperature (high-$T_c$) superconductivity observed in the cuprates remains elusive to the researchers. In particular, in the so-called `underdoped' region, the overall behavior of superconductivity deviates $qualitatively$ from the standard theoretical description pioneered by Bardeen, Cooper and Schrieffer (BCS). Recently, the importance of phase fluctuation of the superconducting order parameter has gained significant support from various experiments. However, the microscopic mechanism responsible for the surprisingly soft phase remains one of the most important unsolved puzzles. Here, opposite to the standard BCS starting point, we propose a simple, solvable low-energy model in the strong coupling limit, which maps the superconductivity literally into a well-understood physics of superfluid in a special dilute bosonic system of local pairs of doped holes. In the prototypical material (La$_{1-\delta}$Sr$_\delta$)$_2$CuO$_4$, without use of any free parameter, a $d$-wave superconductivity is obtained for doping above $\sim 5.2\%$, below which unexpected incoherent $p$-wave pairs dominate. Throughout the whole underdoped region, very soft phases are found to originate from enormous mass enhancement of the pairs. Furthermore, a striking mass divergence is predicted that dictates the occurrence of the observed quantum critical point. Our model produces properties of the superfluid in good agreement with the experiments, and provides new insights into several current puzzles. Owing to its simplicity, this model offers a paradigm of great value in answering the long-standing challenges in underdoped cuprates

Morphology of rain water channelization in systematically varied model sandy soils

We visualize the formation of fingered flow in dry model sandy soils under different raining conditions using a quasi-2d experimental set-up, and systematically determine the impact of soil grain diameter and surface wetting property on water channelization phenomenon. The model sandy soils we use are random closely-packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates into a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in water infiltration depth, water channel width, and water channel separation. At a fixed raining condition, we combine the effects of grain diameter and surface hydrophobicity into a single parameter and determine its influence on water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to rain water channelization phenomenon, including pre-wetting sandy soils at different level before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers

Functional Forms for the Squeeze and the Time-Displacement Operators

Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$, $\gamma$, and $\delta$ are explicitly determined. Applications are discussed.Comment: 10 pages, LaTe

Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine

When a reciprocating heat engine is started it eventually settles to a stable mode of operation. The approach of a first principle quantum heat engine toward this stable limit cycle is studied. The engine is based on a working medium consisting of an ensemble of quantum systems composed of two coupled spins. A four stroke cycle of operation is studied, with two {\em isochore} branches where heat is transferred from the hot/cold baths and two {\em adiabats} where work is exchanged. The dynamics is generated by a completely positive map. It has been shown that the performance of this model resembles an engine with intrinsic friction. The quantum conditional entropy is employed to prove the monotonic approach to a limit cycle. Other convex measures, such as the quantum distance display the same monotonic approach. The equations of motion of the engine are solved for the different branches and are combined to a global propagator that relates the state of the engine in the beginning of the cycle to the state after one period of operation of the cycle. The eigenvalues of the propagator define the rate of relaxation toward the limit cycle. A longitudinal and transverse mode of approach to the limit cycle is identified. The entropy balance is used to explore the necessary conditions which lead to a stable limit cycle. The phenomena of friction can be identified with a zero change in the von Neumann entropy of the working medium.Comment: 29 pages and six figure

Bulk-fragment and tube-like structures of AuN (N=2-26)

Using the relativistic all-electron density-functional calculations on the AuN (N=2-26) in the generalized gradient approximation, combined with the guided simulated annealing, we have found that the two- to three-dimensional structural transition for AuN occurs between N=13 and 15, and the AuN (16<= N <=25) prefer also the pyramid-based bulk fragment structures in addition to the Au20. More importantly, the tubelike structures are found to be the most stable for Au24 and Au26, offering another powerful structure competitor with other isomers, e.g., amorphous, bulk fragment, and gold fullerene. The mechanism to cause these unusual AuN may be attributed to the stronger s-d hybridization and the d-d interaction enhanced by the relativistic effects.Comment: 12 pages and 3 figure