14,268 research outputs found
Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings
Get PDFWe show that a Hopf term exists in the effective action of long-wavelength
skyrmions in quantum Hall systems for both odd integer and fractional filling
factors , where is an integer. We evaluate the prefactor
of the Hopf term using Green function method in the limit of strong external
magnetic field using model of local interaction. The prefactor () of the
Hopf term is found to be equal to . The spin and charge densities and
hence the total spin and charge of the skyrmion are computed from the effective
action. The total spin is found to have a dominant contribution from the Berry
term in the effective action and to increase with the size of the skyrmion. The
charge and the statistics of the skyrmion, on the other hand, are completely
determined by the prefactor of the Hopf term. Consequently, the skyrmions have
charge and are Fermions (anyons) for odd integer (fractional) fillings.
We also obtain the effective action of the skyrmions at finite temperature. It
is shown that at finite temperature, the value of the prefactor of the Hopf
term depends on the order in which the zero-momentum and zero-frequency limits
are taken.Comment: Replaced with revised versio
Quantitative modeling and data analysis of SELEX experiments
Full text linkSELEX (Systematic Evolution of Ligands by Exponential Enrichment) is an
experimental procedure that allows extracting, from an initially random pool of
DNA, those oligomers with high affinity for a given DNA-binding protein. We
address what is a suitable experimental and computational procedure to infer
parameters of transcription factor-DNA interaction from SELEX experiments. To
answer this, we use a biophysical model of transcription factor-DNA
interactions to quantitatively model SELEX. We show that a standard procedure
is unsuitable for obtaining accurate interaction parameters. However, we
theoretically show that a modified experiment in which chemical potential is
fixed through different rounds of the experiment allows robust generation of an
appropriate data set. Based on our quantitative model, we propose a novel
bioinformatic method of data analysis for such modified experiment and apply it
to extract the interaction parameters for a mammalian transcription factor
CTF/NFI. From a practical point of view, our method results in a significantly
improved false positive/false negative trade-off, as compared to both the
standard information theory based method and a widely used empirically
formulated procedure.Comment: 29 pages, 8 figures, to appear in Physical Biolog
Theory of phonon dynamics in an ion trap
We develop a theory to address the non-equilibrium dynamics of phonons in a
one-dimensional trapped ion system. We elaborate our earlier results obtained
in Phys. Rev. Lett. {\bf 111}, 170406 (2013) to chart out the mechanism of
dynamics-induced cooling and entanglement generation between phonons in these
systems when subjected to a linear ramp protocol inducing site-specific tuning
of on-site interactions between the phonons. We further extend these studies to
non-linear ramps and periodic drive protocols and identify the optimal ramp
protocol for minimal cooling and entanglement generation time. We qualitatively
address the effect of noise arising out of fluctuation of the intensity of the
laser used to generate entanglement and provide a detailed discussion of a
realistic experimental setup which may serve as a test bed for our theory.Comment: 10 pages and 11 figure
Non-equilibrium phonon dynamics in trapped ion systems
We propose a concrete experiment to probe the non-equilibrium local dynamics
of the one-dimensional Bose-Hubbard model using a trapped ion system consisting
of a linear chain of few Ba^+ ions prepared in a state of transverse motional
mode which corresponds to a fixed number of phonons per ion. These phonons are
well-known to be described by an effective Bose-Hubbard model. We propose a
protocol which leads to a sudden local sign reversal of the on-site interaction
strength of this Hubbard model at one of the sites and demonstrate that the
subsequent non-equilibrium dynamics of the model can be experimentally probed
by measuring the time-dependent phonon number in a specific motional state of
the Ba+ ions. We back our experimental proposal with exact numerical
calculation of the dynamics of a Bose-Hubbard model subsequent to a local
quench.Comment: The submission contains 5 pages and 4 figure
Simulation of Vortex-Antivortex Pair Production in a Phase Transition with Explicit Symettry Breaking
Full text linkWe carry out numerical simulation of the formation of U(1) global vortices in
a first order phase transition in 2+1 dimensions in the presence of small
explicit symmetry breaking. Bubbles of broken symmetry phase are randomly
nucleated, which grow and coalesce. Vortices form at junctions of bubbles via
standard Kibble mechanism as well as due to a new mechanism, recently proposed
by us, where defect-antidefect pairs are produced due to field oscillations. In
a simulation involving nucleation of 63 bubbles, with bias in phase
distribution inside bubbles arising from explicit symmetry breaking, we find
that not a single vortex/antivortex is produced via the Kibble mechanism, while
the new mechanism leads to production of 104 vortices and antivortices. Even
without biasing the phase distribution inside bubbles, the vortex production is
completely dominated by this new mechanism, which accounts for the production
of about 80% of the vortices and antivortices, remaining 20% being produced via
the Kibble mechanism. We study the dependence of the effectiveness of the new
mechanism on the magnitude of explicit symmetry breaking, as well as on the
nucleation rate of bubbles. We also study the effect of damping on this
mechanism and show that damping suppresses this mode of vortex production.Comment: 15 pages, 13 figures(1 new figure added). A new section on the effect
of bias in phases of nucleating bubbles, due to the presence of explicit
symmetry breaking, has been adde
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