657 research outputs found
Iterated two-phase local search for the Set-Union Knapsack Problem
Many practical decision-making problems involve selecting a subset of objects from a set of candidate objects such that the selected objects optimize a given objective while satisfying some constraints. Knapsack problems such as the Set-union Knapsack Problem (SUKP) are general models that allow such decision-making problems to be conveniently formulated. Given a set of weighted elements and a set of items with profits where each item is composed of a subset of elements, the SUKP aims to pack a subset of items in a capacity-constrained knapsack in a way that the total profit of the selected items is maximized while their weights do not exceed the knapsack capacity. In this work, we present an effective iterated two-phase local search algorithm for this NP-hard problem. The proposed algorithm iterates through two complementary search phases: a local optima exploration phase to discover local optimal solutions, and a local optima escaping phase to drive the search to unexplored regions. We show the competitiveness of the algorithm compared to the state-of-the-art methods in the literature. Specifically, the algorithm discovers 18 improved best results (new lower bounds) for the 30 benchmark instances and matches the best-known results for the 12 remaining instances. We also report the first computational results with the general CPLEX solver, including 6 proven optimal solutions. Finally, we investigate the impacts of the key ingredients of the algorithm on its performance
Resonant scattering on impurities in the Quantum Hall Effect
We develop a new approach to carrier transport between the edge states via
resonant scattering on impurities, which is applicable both for short and long
range impurities. A detailed analysis of resonant scattering on a single
impurity is performed. The results are used for study of the inter-edge
transport by multiple resonant hopping via different impurities' sites. It is
shown that the total conductance can be found from an effective Schroedinger
equation with constant diagonal matrix elements in the Hamiltonian, where the
complex non-diagonal matrix elements are the amplitudes of a carrier hopping
between different impurities. It is explicitly demonstrated how the complex
phase leads to Aharonov-Bohm oscillations in the total conductance. Neglecting
the contribution of self-crossing resonant-percolation trajectories, one finds
that the inter-edge carrier transport is similar to propagation in
one-dimensional system with off-diagonal disorder. We demonstrated that each
Landau band has an extended state , while all other states are
localized. The localization length behaves as .Comment: RevTex 41 pages; 3 Postscript figure on request; Final version
accepted for publication in Phys. Rev. B. A new section added contained a
comparison with other method
Universal flow diagram for the magnetoconductance in disordered GaAs layers
The temperature driven flow lines of the diagonal and Hall magnetoconductance
data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers
with different thicknesses. The flow lines are quantitatively well described by
a recent universal scaling theory developed for the case of duality symmetry.
The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a
spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator
or the QHE state at low temperatures happens along a semicircle separatrix
G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at
(G_{xx},G_{xy})=(1,1).Comment: 10 pages, 5 figures, submitted to Phys. Rev. Let
Geometric measure of entanglement and applications to bipartite and multipartite quantum states
The degree to which a pure quantum state is entangled can be characterized by
the distance or angle to the nearest unentangled state. This geometric measure
of entanglement, already present in a number of settings (see Shimony 1995 and
Barnum and Linden 2001), is explored for bipartite and multipartite pure and
mixed states. The measure is determined analytically for arbitrary two-qubit
mixed states and for generalized Werner and isotropic states, and is also
applied to certain multipartite mixed states. In particular, a detailed
analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W
states. Along the way, we point out connections of the geometric measure of
entanglement with entanglement witnesses and with the Hartree approximation
method.Comment: 13 pages, 11 figures, this is a combination of three previous
manuscripts (quant-ph/0212030, quant-ph/0303079, and quant-ph/0303158) made
more extensive and coherent. To appear in PR
Electron Localization in a 2D System with Random Magnetic Flux
Using a finite-size scaling method, we calculate the localization properties
of a disordered two-dimensional electron system in the presence of a random
magnetic field. Below a critical energy all states are localized and the
localization length diverges when the Fermi energy approaches the
critical energy, {\it i.e.} . We find that
shifts with the strength of the disorder and the amplitude of the random
magnetic field while the critical exponent () remains unchanged
indicating universality in this system. Implications on the experiment in
half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request),
#phd1
Mott Transition in An Anyon Gas
We introduce and analyze a lattice model of anyons in a periodic potential
and an external magnetic field which exhibits a transition from a Mott
insulator to a quantum Hall fluid. The transition is characterized by the anyon
statistics, , which can vary between Fermions, , and Bosons,
. For bosons the transition is in the universality class of the
classical three-dimensional XY model. Near the Fermion limit, the transition is
described by a massless Dirac theory coupled to a Chern-Simons gauge
field. Analytic calculations perturbative in , and also a large
N-expansion, show that due to gauge fluctuations, the critical properties of
the transition are dependent on the anyon statistics. Comparison with previous
calcualations at and near the Boson limit, strongly suggest that our lattice
model exhibits a fixed line of critical points, with universal critical
properties which vary continuosly and monotonically as one passes from Fermions
to Bosons. Possible relevance to experiments on the transitions between
plateaus in the fractional quantum Hall effect and the magnetic field-tuned
superconductor-insulator transition are briefly discussed.Comment: text and figures in Latex, 41 pages, UBCTP-92-28, CTP\#215
Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level
Field-theoretical methods have been shown to be useful in constructing simple
effective theories for two-dimensional (2D) systems. These effective theories
are usually studied by perturbing around a mean-field approximation, so the
question whether such an approximation is meaningful arises immediately. We
here study 2D interacting electrons in a half-filled Landau level mapped onto
interacting hard-core bosons in a magnetic field. We argue that an interacting
hard-core boson system in a uniform external field such that there is one flux
quantum per particle (unit filling) exhibits an integer quantum Hall effect. As
a consequence, the mean-field approximation for mapping electrons at
half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.
Geometric Entanglement of Symmetric States and the Majorana Representation
Permutation-symmetric quantum states appear in a variety of physical
situations, and they have been proposed for quantum information tasks. This
article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the
maximally entangled symmetric states of up to twelve qubits were explored, and
their amount of geometric entanglement determined by numeric and analytic
means. For this the Majorana representation, a generalization of the Bloch
sphere representation, can be employed to represent symmetric n qubit states by
n points on the surface of a unit sphere. Symmetries of this point distribution
simplify the determination of the entanglement, and enable the study of quantum
states in novel ways. Here it is shown that the duality relationship of
Platonic solids has a counterpart in the Majorana representation, and that in
general maximally entangled symmetric states neither correspond to anticoherent
spin states nor to spherical designs. The usability of symmetric states as
resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science
(LNCS
Thermodynamics of an Anyon System
We examine the thermal behavior of a relativistic anyon system, dynamically
realized by coupling a charged massive spin-1 field to a Chern-Simons gauge
field. We calculate the free energy (to the next leading order), from which all
thermodynamic quantities can be determined. As examples, the dependence of
particle density on the anyon statistics and the anyon anti-anyon interference
in the ideal gas are exhibited. We also calculate two and three-point
correlation functions, and uncover certain physical features of the system in
thermal equilibrium.Comment: 18 pages; in latex; to be published in Phys. Rev.
Electrochemical capacitance of a leaky nano-capacitor
We report a detailed theoretical investigation on electrochemical capacitance
of a nanoscale capacitor where there is a DC coupling between the two
conductors. For this ``leaky'' quantum capacitor, we have derived general
analytic expressions of the linear and second order nonlinear electrochemical
capacitance within a first principles quantum theory in the discrete potential
approximation. Linear and nonlinear capacitance coefficients are also derived
in a self-consistent manner without the latter approximation and the
self-consistent analysis is suitable for numerical calculations. At linear
order, the full quantum formula improves the semiclassical analysis in the
tunneling regime. At nonlinear order which has not been studied before for
leaky capacitors, the nonlinear capacitance and nonlinear nonequilibrium charge
show interesting behavior. Our theory allows the investigation of crossover of
capacitance from a full quantum to classical regimes as the distance between
the two conductors is changed
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