1,134 research outputs found
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
Renormalization and Quantum Scaling of Frenkel-Kontorova Models
We generalise the classical Transition by Breaking of Analyticity for the
class of Frenkel-Kontorova models studied by Aubry and others to non-zero
Planck's constant and temperature. This analysis is based on the study of a
renormalization operator for the case of irrational mean spacing using
Feynman's functional integral approach. We show how existing classical results
extend to the quantum regime. In particular we extend MacKay's renormalization
approach for the classical statistical mechanics to deduce scaling of low
frequency effects and quantum effects. Our approach extends the phenomenon of
hierarchical melting studied by Vallet, Schilling and Aubry to the quantum
regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy
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
Transient Dynamics in Magnetic Force Microscopy for a Single-Spin Measurement
We analyze a single-spin measurement using a transient process in magnetic
force microscopy (MFM) which could increase the maximum operating temperature
by a factor of Q (the quality factor of the cantilever) in comparison with the
static Stern-Gerlach effect. We obtain an exact solution of the master
equation, which confirms this result. We also discuss the conditions required
to create a macroscopic Schrodinger cat state in the cantilever.Comment: 22 pages 2 figure
Spin Diffusion and Relaxation in Solid State Spin Quantum Computer
The processes of spin diffusion and relaxation are studied theoretically and
numerically for quantum computation applications. Two possible realizations of
a spin quantum computer (SQC) are analyzed: (i) a boundary spin chain in a 2D
spin array and (ii) an isolated spin chain. In both cases, spin diffusion and
relaxation are caused by a fast relaxing spin located outside the SQC. We have
shown that in both cases the relaxation can be suppressed by an external
non-uniform magnetic field. In the second case, our computer simulations have
revealed various types of relaxation processes including the excitation of a
random distribution of magnetic moments and the formation of stationary and
moving domain walls. The region of optimal parameters for suppression of rapid
spin relaxation is discussed.Comment: 15 pages uncluding 23 figure
Realistic simulations of single-spin nondemolition measurement by magnetic resonance force microscopy
A requirement for many quantum computation schemes is the ability to measure
single spins. This paper examines one proposed scheme: magnetic resonance force
microscopy, including the effects of thermal noise and back-action from
monitoring. We derive a simplified equation using the adiabatic approximation,
and produce a stochastic pure state unraveling which is useful for numerical
simulations.Comment: 33 pages LaTeX, 9 figure files in EPS format. Submitted to Physical
Review
Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals
The equations for the three-dimensional incompressible flow of liquid
crystals are considered in a smooth bounded domain. The existence and
uniqueness of the global strong solution with small initial data are
established. It is also proved that when the strong solution exists, all the
global weak solutions constructed in [16] must be equal to the unique strong
solution
Heat conduction in 1D lattices with on-site potential
The process of heat conduction in one-dimensional lattice with on-site
potential is studied by means of numerical simulation. Using discrete
Frenkel-Kontorova, --4 and sinh-Gordon we demonstrate that contrary to
previously expressed opinions the sole anharmonicity of the on-site potential
is insufficient to ensure the normal heat conductivity in these systems. The
character of the heat conduction is determined by the spectrum of nonlinear
excitations peculiar for every given model and therefore depends on the
concrete potential shape and temperature of the lattice. The reason is that the
peculiarities of the nonlinear excitations and their interactions prescribe the
energy scattering mechanism in each model. For models sin-Gordon and --4
phonons are scattered at thermalized lattice of topological solitons; for
sinh-Gordon and --4 - models the phonons are scattered at localized
high-frequency breathers (in the case of --4 the scattering mechanism
switches with the growth of the temperature).Comment: 26 pages, 18 figure
Reionization: Characteristic Scales, Topology and Observability
Recently the numerical simulations of the process of reionization of the
universe at z>6 have made a qualitative leap forward, reaching sufficient sizes
and dynamic range to determine the characteristic scales of this process. This
allowed making the first realistic predictions for a variety of observational
signatures. We discuss recent results from large-scale radiative transfer and
structure formation simulations on the observability of high-redshift Ly-alpha
sources. We also briefly discuss the dependence of the characteristic scales
and topology of the ionized and neutral patches on the reionization parameters.Comment: 4 pages, 5 figures (4 in color), to appear in Astronomy and Space
Science special issue "Space Astronomy: The UV window to the Universe",
proceedings of 1st NUVA Conference ``Space Astronomy: The UV window to the
Universe'' in El Escorial (Spain
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