Self-assembled island formation in heteroepitaxial growth

We investigate island formation during heteroepitaxial growth using an atomistic model that incorporates deposition, activated diffusion and stress relaxation. For high misfit the system naturally evolves into a state characterized by a narrow island size distribution. The simulations indicate the existence of a strain assisted kinetic mechanism responsible for the self-assembling process, involving enhanced detachment of atoms from the edge of large islands and biased adatom diffusion.Comment: ReVTeX, 10 pages, 3 ps figure

Casimir pistons with hybrid boundary conditions

The Casimir effect giving rise to an attractive or repulsive force between the configuration boundaries that confine the massless scalar field is reexamined for one to three-dimensional pistons in this paper. Especially, we consider Casimir pistons with hybrid boundary conditions, where the boundary condition on the piston is Neumann and those on other surfaces are Dirichlet. We show that the Casimir force on the piston is always repulsive, in contrast with the same problem where the boundary conditions are Dirichlet on all surfaces.Comment: 8 pages, 4 figures,references added, minor typos correcte

Coherent transport on Apollonian networks and continuous-time quantum walks

We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks less than the second generation the coherent transport shows perfect revivals when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.Comment: 5 pages, 6 figues. Submitted to Phys. ReV.

Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles

A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space (which includes energy and time as independent coordinates) for all three adiabatic invariants. First, the guiding-center equations of motion for a relativistic particle are derived from the particle Lagrangian. Covariant aspects of the resulting relativistic guiding-center equations of motion are discussed and contrasted with previous works. Next, the second and third invariants for the bounce motion and drift motion, respectively, are obtained by successively removing the bounce phase and the drift phase from the guiding-center Lagrangian. First-order corrections to the second and third adiabatic invariants for a relativistic particle are derived. These results simplify and generalize previous works to all three adiabatic motions of relativistic magnetically-trapped particles.Comment: 20 pages, LaTeX, to appear in Physics of Plasmas (Aug, 2007

The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime

The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper\cite{Feng}. In this paper, the Casimir effect of the quantum spring is investigated in $(D+1)$-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any $D$, which indicate a $Z_2$ symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the $\zeta$-function. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes.Comment: 9 pages, 5 figures, v2, massive case added, refs. adde

Continuous-time quantum walks on one-dimension regular networks

In this paper, we consider continuous-time quantum walks (CTQWs) on one-dimension ring lattice of N nodes in which every node is connected to its 2m nearest neighbors (m on either side). In the framework of the Bloch function ansatz, we calculate the spacetime transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walk (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter m for both the CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slow with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long time limit, depending on the network size N and connectivity parameter m, the limiting probability distributions of CTQWs show various paterns. When the network size N is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter m.Comment: Typos corrected and Phys. ReV. E comments considered in this versio

Ground state and edge excitations of quantum Hall liquid at filling factor 2/3

We present a numerical study of fractional quantum Hall liquid at Landau level filling factor $\nu=2/3$ in a microscopic model including long-range Coulomb interaction and edge confining potential, based on the disc geometry. We find the ground state is accurately described by the particle-hole conjugate of a $\nu=1/3$ Laughlin state. We also find there are two counter-propagating edge modes, and the velocity of the forward-propagating mode is larger than the backward-propagating mode. The velocities have opposite responses to the change of the background confinement potential. On the other hand changing the two-body Coulomb potential has qualitatively the same effect on the velocities; for example we find increasing layer thickness (which softens of the Coulomb interaction) reduces both the forward mode and the backward mode velocities.Comment: 12 pages, 13 figure

A cost-based maritime container assignment model and port choice

A recently proposed frequency-based maritime container assignment model (Bell et al, 2011) seeks an assignment of full and empty containers to paths that minimises expected container travel time, whereas containers are in practice more likely to be assigned to minimise expected cost. There are significant economies of scale in the maritime transport of containers; the cost per container per unit time falls with increasing ship occupancy and larger ships when full cost less per container per unit time than smaller ships. A cost-based container assignment model is proposed here. The objective is to assign containers to maritime routes to minimize sailing costs plus expected dwell costs at the ports of origin and transhipment. The constraints in the model are extended to include route as well as port capacity constraints. Although the cost per container per unit time depends on ship occupancy, it is shown that the problem remains a linear program. A small numerical example is presented to illustrate the properties of the model. The paper concludes by considering the many applications of the proposed maritime container assignment model

Comparison of Power Dependence of Microwave Surface Resistance of Unpatterned and Patterned YBCO Thin Film

The effect of the patterning process on the nonlinearity of the microwave surface resistance $R_S$ of YBCO thin films is investigated. With the use of a sapphire dielectric resonator and a stripline resonator, the microwave $R_S$ of YBCO thin films was measured before and after the patterning process, as a function of temperature and the rf peak magnetic field in the film. The microwave loss was also modeled, assuming a $J_{rf}^2$ dependence of $Z_S(J_{rf})$ on current density $J_{rf}$. Experimental and modeled results show that the patterning has no observable effect on the microwave residual $R_S$ or on the power dependence of $R_S$.Comment: Submitted to IEEE Trans. MT

The Universal Edge Physics in Fractional Quantum Hall Liquids

The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been unambiguously observed in experiments in two-dimensional electron gases based on GaAs/GaAlAs heterostructures or quantum wells. One plausible cause is the fractional quantum Hall edge reconstruction, which introduces non-chiral edge modes. The coupling between counterpropagating edge modes can modify the exponent of the $I$-$V$ characteristics. By comparing the $\nu=1/3$ fractional quantum Hall states in modulation-doped semiconductor devices and in graphene devices, we show that the graphene-based systems have an experimental accessible parameter region to avoid the edge reconstruction, which is suitable for the exploration of the universal edge tunneling exponent predicted by the chiral Luttinger liquid theory.Comment: 7 pages, 6 figure