4,013 research outputs found
Rheology and dynamical heterogeneity in frictionless beads at jamming density
We investigate the rheological properties of an assembly of inelastic (but
frictionless) particles close to the jamming density using numerical
simulation, in which uniform steady states with a constant shear rate
is realized. The system behaves as a power-law fluid and the
relevant exponents are estimated; e.g., the shear stress is proportional to
, where . It is also found that
the relaxation time and the correlation length of the velocity
increase obeying power laws: and
, where and
Scaling Theory of Antiferromagnetic Heisenberg Ladder Models
The antiferromagnetic Heisenberg model on multi-leg ladders is
investigated. Criticality of the ground-state transition is explored by means
of finite-size scaling. The ladders with an even number of legs and those with
an odd number of legs are distinguished clearly. In the former, the energy gap
opens up as , where is the strength of the
antiferromagnetic inter-chain coupling. In the latter, the critical phase with
the central charge extends over the whole region of .Comment: 12 pages with 9 Postscript figures. To appear in J. Phys. A: Math.
Ge
A variational approach to Ising spin glasses in finite dimensions
We introduce a hierarchical class of approximations of the random Ising spin
glass in dimensions. The attention is focused on finite clusters of spins
where the action of the rest of the system is properly taken into account. At
the lower level (cluster of a single spin) our approximation coincides with the
SK model while at the highest level it coincides with the true -dimensional
system. The method is variational and it uses the replica approach to spin
glasses and the Parisi ansatz for the order parameter. As a result we have
rigorous bounds for the quenched free energy which become more and more precise
when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J.
Phys. A: Math. Ge
Maximization of thermal entanglement of arbitrarily interacting two qubits
We investigate the thermal entanglement of interacting two qubits. We
maximize it by tuning a local Hamiltonian under a given interaction
Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form
which dose not depend on the temperature and that the corresponding optimized
thermal entanglement decays as at high temperatures. We also find
that at low temperatures the thermal entanglement is maximum without any local
Hamiltonians and that the second derivative of the maximized thermal
entanglement changes discontinuously at the boundary between the high- and
low-temperature phases.Comment: 23 pages, 4 figure
Supernova Resonance-Scattering Profiles in the Presence of External Illumination
We discuss a simple model for the formation of a supernova spectral line by
resonance scattering in the presence of external illumination of the
line-forming region by light from circumstellar interaction (toplighting). The
simple model provides a clear understanding of the most conspicuous toplighting
effect: a rescaling or, as we prefer, a ``muting'' of the line profile relative
to the continuum. This effect would be present in more realistic models, but
would be harder to isolate. An analytic expression for a muting factor for a
P-Cygni line is derived that depends on the ratio E of the toplighting specific
intensity to the specific intensity from the supernova photosphere. If E<1, the
line profile is reduced in scale or ``muted''. If E=1, the line profile
vanishes altogether. If E>1, the line profile flips vertically: then having an
absorption component near the observer-frame line center wavelength and a
blueshifted emission component.Comment: accepted for publication in PAS
Complex periodic potentials with real band spectra
This paper demonstrates that complex PT-symmetric periodic potentials possess
real band spectra. However, there are significant qualitative differences in
the band structure for these potentials when compared with conventional real
periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x),
(N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are
periodic wave functions but no antiperiodic wave functions. Numerical analysis
and higher-order WKB techniques are used to establish these results.Comment: 8 pages, 7 figures, LaTe
Electronic Structure of Multiple Dots
We calculate, via spin density functional theory (SDFT) and exact
diagonalization, the eigenstates for electrons in a variety of external
potentials, including double and triple dots. The SDFT calculations employ
realistic wafer profiles and gate geometries and also serve as the basis for
the exact diagonalization calculations. The exchange interaction J between
electrons is the difference between singlet and triplet ground state energies
and reflects competition between tunneling and the exchange matrix element,
both of which result from overlap in the barrier. For double dots, a
characteristic transition from singlet ground state to triplet ground state
(positive to negative J) is calculated. For the triple dot geometry with 2
electrons we also find the electronic structure with exact diagonalization. For
larger electron number (18 and 20) we use only SDFT. In contrast to the double
dot case, the triple dot case shows a quasi-periodic fluctuation of J with
magnetic field which we attribute to periodic variations of the basis states in
response to changing flux quanta threading the triple dot structure.Comment: 3 pages, 4 figure
Semiconductor quantum dots for electron spin qubits
We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates
Non-Hermitian Delocalization and Eigenfunctions
Recent literature on delocalization in non-Hermitian systems has stressed
criteria based on sensitivity of eigenvalues to boundary conditions and the
existence of a non-zero current. We emphasize here that delocalization also
shows up clearly in eigenfunctions, provided one studies the product of left-
and right-eigenfunctions, as required on physical grounds, and not simply the
squared modulii of the eigenfunctions themselves. We also discuss the right-
and left-eigenfunctions of the ground state in the delocalized regime and
suggest that the behavior of these functions, when considered separately, may
be viewed as ``intermediate'' between localized and delocalized.Comment: 8 pages, 11 figures include
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