50,851 research outputs found
Infrared Behaviour and Running Couplings in Interpolating Gauges in QCD
We consider the class of gauges that interpolates between Landau- and
Coulomb-gauge QCD, and show the non-renormalisation of the two independent
ghost-gluon vertices. This implies the existence of two RG-invariant running
couplings, one of which is interpreted as an RG-invariant gauge parameter. We
also present the asymptotic infrared limit of solutions of the Dyson-Schwinger
equations in interpolating gauges. The infrared critical exponents of these
solutions as well as the resulting infrared fixed point of one of the couplings
are independent of the gauge parameter. This coupling also has a fixed point in
the Coulomb gauge limit and constitutes a second invariant charge besides the
well known colour-Coulomb potential.Comment: 8 pages, 2 figures; v2: minor changes, version published in PR
Robust Quantum Error Correction via Convex Optimization
We present a semidefinite program optimization approach to quantum error
correction that yields codes and recovery procedures that are robust against
significant variations in the noise channel. Our approach allows us to optimize
the encoding, recovery, or both, and is amenable to approximations that
significantly improve computational cost while retaining fidelity. We
illustrate our theory numerically for optimized 5-qubit codes, using the
standard [5,1,3] code as a benchmark. Our optimized encoding and recovery
yields fidelities that are uniformly higher by 1-2 orders of magnitude against
random unitary weight-2 errors compared to the [5,1,3] code with standard
recovery. We observe similar improvement for a 4-qubit decoherence-free
subspace code.Comment: 4 pages, including 3 figures. v2: new example
Interferometric differentiation between resonant Coherent Anti-Stokes Raman Scattering and nonresonant four-wave-mixing processes
A major impediment of using Coherent Anti-Stokes Raman Scattering to identify
biological molecules is that the illumination levels required to produce a
measurable signal often also produce significant nonresonant background from
the medium, especially from water, that is not specific to the resonance being
investigated. We present a method of using nonlinear interferometry to measure
the temporal shape of the anti-Stokes signal to differentiate which components
are resonant and nonresonant. This method is easily adaptable to most existing
pulsed CARS illumination methods and should allow for distinguishing resonant
CARS when using higher energy pulses. By examining the differences between
signals produced by acetone and water, we show that the resonant and
nonresonant signals can be clearly differentiated.Comment: 8 pages, 4 figure
Order and Disorder in AKLT Antiferromagnets in Three Dimensions
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a
family of quantum antiferromagnets on arbitrary lattices, where the local spin
S is an integer multiple M of half the lattice coordination number. The equal
time quantum correlations in their ground states may be computed as finite
temperature correlations of a classical O(3) model on the same lattice, where
the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping
implies that all AKLT states are quantum disordered. We consider AKLT states in
d=3 where the nature of the AKLT states is now a question of detail depending
upon the choice of lattice and spin; for sufficiently large S some form of Neel
order is almost inevitable. On the unfrustrated cubic lattice, we find that all
AKLT states are ordered while for the unfrustrated diamond lattice the minimal
S=2 state is disordered while all other states are ordered. On the frustrated
pyrochlore lattice, we find (conservatively) that several states starting with
the minimal S=3 state are disordered. The disordered AKLT models we report here
are a significant addition to the catalog of magnetic Hamiltonians in d=3 with
ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure
Composite Majorana Fermion Wavefunctions in Nanowires
We consider Majorana fermions (MFs) in quasi-one-dimensional nanowire systems
containing normal and superconducting sections where the topological phase
based on Rashba spin orbit interaction can be tuned by magnetic fields. We
derive explicit analytic solutions of the MF wavefunction in the weak and
strong spin orbit interaction regimes. We find that the wavefunction for one
single MF is a composite object formed by superpositions of different MF
wavefunctions which have nearly disjoint supports in momentum space. These
contributions are coming from the extrema of the spectrum, one centered around
zero momentum and the other around the two Fermi points. As a result, the
various MF wavefunctions have different localization lengths in real space and
interference among them leads to pronounced oscillations of the MF probability
density. For a transparent normal-superconducting junction we find that in the
topological phase the MF leaks out from the superconducting into the normal
section of the wire and is delocalized over the entire normal section, in
agreement with recent numerical results by Chevallier et al. (arXiv:1203.2643)
Combined Error Correction Techniques for Quantum Computing Architectures
Proposals for quantum computing devices are many and varied. They each have
unique noise processes that make none of them fully reliable at this time.
There are several error correction/avoidance techniques which are valuable for
reducing or eliminating errors, but not one, alone, will serve as a panacea.
One must therefore take advantage of the strength of each of these techniques
so that we may extend the coherence times of the quantum systems and create
more reliable computing devices. To this end we give a general strategy for
using dynamical decoupling operations on encoded subspaces. These encodings may
be of any form; of particular importance are decoherence-free subspaces and
quantum error correction codes. We then give means for empirically determining
an appropriate set of dynamical decoupling operations for a given experiment.
Using these techniques, we then propose a comprehensive encoding solution to
many of the problems of quantum computing proposals which use exchange-type
interactions. This uses a decoherence-free subspace and an efficient set of
dynamical decoupling operations. It also addresses the problems of
controllability in solid state quantum dot devices.Comment: Contribution to Proceedings of the 2002 Physics of Quantum
Electronics Conference", to be published in J. Mod. Optics. This paper
provides a summary and review of quant-ph/0205156 and quant-ph/0112054, and
some new result
Multipartite fully-nonlocal quantum states
We present a general method to characterize the quantum correlations obtained
after local measurements on multipartite systems. Sufficient conditions for a
quantum system to be fully-nonlocal according to a given partition, as well as
being (genuinely) multipartite fully-nonlocal, are derived. These conditions
allow us to identify all completely-connected graph states as multipartite
fully-nonlocal quantum states. Moreover, we show that this feature can also be
observed in mixed states: the tensor product of five copies of the Smolin
state, a biseparable and bound entangled state, is multipartite fully-nonlocal.Comment: 5 pages, 1 figure. Version published in PRA. Note that it does not
contain all the results from the previous version; these will be included in
a later, more general, pape
The plasmonic eigenvalue problem
A plasmon of a bounded domain is a non-trivial
bounded harmonic function on which is
continuous at and whose exterior and interior normal
derivatives at have a constant ratio. We call this ratio a
plasmonic eigenvalue of . Plasmons arise in the description of
electromagnetic waves hitting a metallic particle . We investigate
these eigenvalues and prove that they form a sequence of numbers converging to
one. Also, we prove regularity of plasmons, derive a variational
characterization, and prove a second order perturbation formula. The problem
can be reformulated in terms of Dirichlet-Neumann operators, and as a side
result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in
Review in Mathematical Physic
Base pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium
We study the nonlinear dynamics of a protein-DNA molecular system by treating
DNA as a set of two coupled linear chains and protein in the form of a single
linear chain sliding along the DNA at the physiological temperature in a
viscous medium. The nonlinear dynamics of the above molecular system in general
is governed by a perturbed nonlinear Schr\"{o}dinger equation. In the
non-viscous limit, the equation reduces to the completely integrable nonlinear
Schr\"{o}dinger (NLS) equation which admits N-soliton solutions. The soliton
excitations of the DNA bases make localized base pair opening and travel along
the DNA chain in the form of a bubble. This may represent the bubble generated
during the transcription process when an RNA-polymerase binds to a promoter
site in the DNA double helical chain. The perturbed NLS equation is solved
using a perturbation theory by treating the viscous effect due to surrounding
as a weak perturbation and the results show that the viscosity of the solvent
in the surrounding damps out the amplitude of the soliton.Comment: 4. Submitted to Phys. Rev.
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