1,504 research outputs found
(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite
The scaling of friction with the contact size and (in)commensurabilty of
nanoscopic and mesoscopic crystals on a regular substrate are investigated
analytically for triangular nanocrystals on hexagonal substrates. The crystals
are assumed to be stiff, but not completely rigid. Commensurate and
incommensurate configurations are identified systematically. It is shown that
three distinct friction branches coexist, an incommensurate one that does not
scale with the contact size () and two commensurate ones which scale
differently (with and ) and are associated with various
combinations of commensurate and incommensurate lattice parameters and
orientations. This coexistence is a direct consequence of the two-dimensional
nature of the contact layer, and such multiplicity exists in all geometries
consisting of regular lattices. To demonstrate this, the procedure is repeated
for rectangular geometry. The scaling of irregularly shaped crystals is also
considered, and again three branches are found (). Based
on the scaling properties, a quantity is defined which can be used to classify
commensurability in infinite as well as finite contacts. Finally, the
consequences for friction experiments on gold nanocrystals on graphite are
discussed
Ground state wavefunction of the quantum Frenkel-Kontorova model
The wavefunction of an incommensurate ground state for a one-dimensional
discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero
temperature is calculated by the quantum Monte Carlo method. It is found that
the ground state wavefunction crosses over from an extended state to a
localized state when the coupling constant exceeds a certain critical value.
So, although the quantum fluctuation has smeared out the breaking of
analyticity transition as observed in the classical case, the remnant of this
transition is still discernible in the quantum regime.Comment: 5 Europhys pages, 3 EPS figures, accepted for publication in
Europhys. Letter
Correlated metallic two particle bound states in quasiperiodic chains
Single particle states in a chain with quasiperiodic potential show a
metal-insulator transition upon the change of the potential strength. We
consider two particles with local interaction in the single particle insulating
regime. The two particle states change from being localized to delocalized upon
an increase of the interaction strength to a nonperturbative finite value. At
even larger interaction strength the states become localized again. This
transition of two particle bound states into a correlated metal is due to a
resonant mixing of the noninteracting two particle eigenstates. In the
discovered correlated metal states two particles move coherently together
through the whole chain, therefore contributing to a finite conductivity.Comment: 4 pages, 4 figure
Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
One-dimensional quasiperiodic systems, such as the Harper model and the
Fibonacci quasicrystal, have long been the focus of extensive theoretical and
experimental research. Recently, the Harper model was found to be topologically
nontrivial. Here, we derive a general model that embodies a continuous
deformation between these seemingly unrelated models. We show that this
deformation does not close any bulk gaps, and thus prove that these models are
in fact topologically equivalent. Remarkably, they are equivalent regardless of
whether the quasiperiodicity appears as an on-site or hopping modulation. This
proves that these different models share the same boundary phenomena and
explains past measurements. We generalize this equivalence to any
Fibonacci-like quasicrystal, i.e., a cut and project in any irrational angle.Comment: 7 pages, 2 figures, minor change
Order in extremal trajectories
Given a chaotic dynamical system and a time interval in which some quantity
takes an unusually large average value, what can we say of the trajectory that
yields this deviation? As an example, we study the trajectories of the
archetypical chaotic system, the baker's map. We show that, out of all
irregular trajectories, a large-deviation requirement selects (isolated) orbits
that are periodic or quasiperiodic. We discuss what the relevance of this
calculation may be for dynamical systems and for glasses
Chaotic quasi-collision trajectories in the 3-centre problem
We study a particular kind of chaotic dynamics for the planar 3-centre
problem on small negative energy level sets. We know that chaotic motions
exist, if we make the assumption that one of the centres is far away from the
other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this
result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we
change the assumption on the third centre: we do not make any hypothesis on its
position, and we obtain a perturbation of the 2-centre problem by assuming its
intensity to be very small. Then, for a dense subset of possible positions of
the perturbing centre on the real plane, we prove the existence of uniformly
hyperbolic invariant sets of periodic and chaotic almost collision orbits by
the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr.
77 (2000), 49--75). To apply it, we must preliminarily construct chains of
collision arcs in a proper way. We succeed in doing that by the classical
regularisation of the 2-centre problem and the use of the periodic orbits of
the regularised problem passing through the third centre.Comment: 22 pages, 6 figure
Magnetization of two coupled rings
We investigate the persistent currents and magnetization of a mesoscopic
system consisting of two clean metallic rings sharing a single contact point in
a magnetic field. Many novel features with respect to the single-ring geometry
are underlined, including the explicit dependence of wavefunctions on the
Aharonov-Bohm fluxes, the complex pattern of twofold and threefold
degeneracies, the key role of length and flux commensurability, and in the case
of commensurate ring lengths the occurrence of idle levels which do not carry
any current. Spin-orbit interactions, induced by the electric fields of charged
wires threading the rings, give rise to a peculiar version of the
Aharonov-Casher effect where, unlike for a single ring, spin is not conserved.
Remarkably enough, this can only be realized when the Aharonov-Bohm fluxes in
both rings are neither integer nor half-integer multiples of the flux quantum.Comment: 27 pages, 10 figures, 4 tables. A few references added and other
minor change
Asymptotic entanglement in 1D quantum walks with a time-dependent coined
Discrete-time quantum walk evolve by a unitary operator which involves two
operators a conditional shift in position space and a coin operator. This
operator entangles the coin and position degrees of freedom of the walker. In
this paper, we investigate the asymptotic behavior of the coin position
entanglement (CPE) for an inhomogeneous quantum walk which determined by two
orthogonal matrices in one-dimensional lattice. Free parameters of coin
operator together provide many conditions under which a measurement perform on
the coin state yield the value of entanglement on the resulting position
quantum state. We study the problem analytically for all values that two free
parameters of coin operator can take and the conditions under which
entanglement becomes maximal are sought.Comment: 23 pages, 4 figures, accepted for publication in IJMPB. arXiv admin
note: text overlap with arXiv:1001.5326 by other author
Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain
We study numerically and analytically the classical one-dimensional
Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon
gap. Our results show the existence of exponentially many static equilibrium
configurations which are exponentially close to the energy of the ground state.
The energies of these configurations form a fractal quasi-degenerate band
structure which is described on the basis of elementary excitations. Contrary
to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure
Yukawa particles confined in a channel and subject to a periodic potential: ground state and normal modes
We consider a classical system of two-dimensional (2D) charged particles,
which interact through a repulsive Yukawa potential ,
confined in a parabolic channel which limits the motion of the particles in the
-direction. Along the -direction, the particles are also subject to a
periodic potential substrate. The ground state configurations and the normal
mode spectra of the system are obtained as function of the periodicity and
strength of the periodic potential (), and density. An interesting set of
tunable ground state configurations are found, with first and second order
structural transitions between them. A magic configuration with particles
aligned in each minimum of the periodic potential is obtained for V_0 larger
than some critical value which has a power law dependence on the density. The
phonon spectrum of different configurations were also calculated. A
localization of the modes into a small frequency interval is observed for a
sufficient strength of the periodic potential. A tunable band-gap is found as a
function of . This model system can be viewed as a generalization of the
Frenkel and Kontorova model.Comment: Submmited to PR
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