13 research outputs found
A simple variational approach to the quantum Frenkel-Kontorova model
We present a simple and complete variational approach to the one-dimensional
quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle
is adopted together with a Hatree-type many-body trial wavefunction for the
atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We
obtain an effective classical Hamiltonian for the system which is simple enough
for a complete numerical solution for the static ground state of the model.
Numerical results show that our simple approach captures the essence of the
quantum effects first observed in quantum Monte Carlo studies.Comment: 12 pages, 2 figure
The antiferromagnetic phi4 Model, II. The one-loop renormalization
It is shown that the four dimensional antiferromagnetic lattice phi4 model
has the usual non-asymptotically free scaling law in the UV regime around the
chiral symmetrical critical point. The theory describes a scalar and a
pseudoscalar particle. A continuum effective theory is derived for low
energies. A possibility of constructing a model with a single chiral boson is
mentioned.Comment: To appear in Phys. Rev.
Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas
We study analytically and numerically the one-dimensional quantum
Frenkel-Kontorova chain in the regime when the classical model is located in
the pinned phase characterized by the gaped phonon excitations and devil's
staircase. By extensive quantum Monte Carlo simulations we show that for the
effective Planck constant smaller than the critical value the
quantum chain is in the pinned instanton glass phase. In this phase the
elementary excitations have two branches: phonons, separated from zero energy
by a finite gap, and instantons which have an exponentially small excitation
energy. At the quantum phase transition takes place and for
the pinned instanton glass is transformed into the sliding
phonon gas with gapless phonon excitations. This transition is accompanied by
the divergence of the spatial correlation length and appearence of sliding
modes at .Comment: revtex 16 pages, 18 figure
Avalanches in the Weakly Driven Frenkel-Kontorova Model
A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in
Phys. Rev.
Simulations of the Static Friction Due to Adsorbed Molecules
The static friction between crystalline surfaces separated by a molecularly
thin layer of adsorbed molecules is calculated using molecular dynamics
simulations. These molecules naturally lead to a finite static friction that is
consistent with macroscopic friction laws. Crystalline alignment, sliding
direction, and the number of adsorbed molecules are not controlled in most
experiments and are shown to have little effect on the friction. Temperature,
molecular geometry and interaction potentials can have larger effects on
friction. The observed trends in friction can be understood in terms of a
simple hard sphere model.Comment: 13 pages, 13 figure
The antiferromagnetic phi4 Model, I. The Mean-field Solution
Certain higher dimensional operators of the lagrangian may render the vacuum
inhomogeneous. A rather rich phase structure of the phi4 scalar model in four
dimensions is presented by means of the mean-field approximation. One finds
para- ferro- ferri- and antiferromagnetic phases and
commensurate-incommensurate transitions. There are several particles described
by the same quantum field in a manner similar to the species doubling of the
lattice fermions. It is pointed out that chiral bosons can be introduced in the
lattice regularized theory.Comment: To appear in Phys. Rev.