76 research outputs found
Mode entanglement of electrons in the one-dimensional Frenkel-Kontorova model
We study the mode entanglement in the one-dimensional Frenkel-Kontorova
model, and found that behaviors of quantum entanglement are distinct before and
after the transition by breaking of analyticity. We show that the more extended
the electron is, the more entangled the corresponding state. Finally, a
quantitative relation is given between the average square of the concurrence
quantifying the degree of entanglement and the participation ratio
characterizing the degree of localization.Comment: 4 pages, 4 figures. V
Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential
We study the phase diagram and the commensurate-incommensurate transitions in
a phase field model of a two-dimensional crystal lattice in the presence of an
external pinning potential. The model allows for both elastic and plastic
deformations and provides a continuum description of lattice systems, such as
for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a
mode expansion analysis is used to determine the ground states and the
commensurate-incommensurate transitions in the model as a function of the
strength of the pinning potential and the lattice mismatch parameter. Numerical
minimization of the corresponding free energy shows good agreement with the
analytical predictions and provides details on the topological defects in the
transition region. We find that for small mismatch the transition is of
first-order, and it remains so for the largest values of mismatch studied here.
Our results are consistent with results of simulations for atomistic models of
adsorbed overlayers
A gauge theoretic approach to elasticity with microrotations
We formulate elasticity theory with microrotations using the framework of
gauge theories, which has been developed and successfully applied in various
areas of gravitation and cosmology. Following this approach, we demonstrate the
existence of particle-like solutions. Mathematically this is due to the fact
that our equations of motion are of Sine-Gordon type and thus have soliton type
solutions. Similar to Skyrmions and Kinks in classical field theory, we can
show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page;
revised and extended versio
Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
We study numerically the phase diagram and the response under a driving force
of the phase field crystal model for pinned lattice systems introduced recently
for both one and two dimensional systems. The model describes the lattice
system as a continuous density field in the presence of a periodic pinning
potential, allowing for both elastic and plastic deformations of the lattice.
We first present results for phase diagrams of the model in the absence of a
driving force. The nonlinear response to a driving force on an initially pinned
commensurate phase is then studied via overdamped dynamic equations of motion
for different values of mismatch and pinning strengths. For large pinning
strength the driven depinning transitions are continuous, and the sliding
velocity varies with the force from the threshold with power-law exponents in
agreement with analytical predictions. Transverse depinning transitions in the
moving state are also found in two dimensions. Surprisingly, for sufficiently
weak pinning potential we find a discontinuous depinning transition with
hysteresis even in one dimension under overdamped dynamics. We also
characterize structural changes of the system in some detail close to the
depinning transition
Wavefronts may move upstream in doped semiconductor superlattices
In weakly coupled, current biased, doped semiconductor superlattices, domain
walls may move upstream against the flow of electrons. For appropriate doping
values, a domain wall separating two electric field domains moves downstream
below a first critical current, it remains stationary between this value and a
second critical current, and it moves upstream above. These conclusions are
reached by using a comparison principle to analyze a discrete drift-diffusion
model, and validated by numerical simulations. Possible experimental
realizations are suggested.Comment: 12 pages, 11 figures, 2-column RevTex, Phys. Rev. E 61, 1 May 200
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