6,626 research outputs found
First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy
We analyze in detail the fermionic self-energy \Sigma(\omega, T) in a Fermi
liquid (FL) at finite temperature T and frequency \omega. We consider both
canonical FLs -- systems in spatial dimension D >2, where the leading term in
the fermionic self-energy is analytic [the retarded Im\Sigma^R(\omega,T) =
C(\omega^2 +\pi^2 T^2)], and non-canonical FLs in 1<D <2, where the leading
term in Im\Sigma^R(\omega,T) scales as T^D or \omega^D. We relate the \omega^2
+ \pi^2 T^2 form to a special property of the self-energy -"the
first-Matsubara-frequency rule", which stipulates that \Sigma^R(i\pi T,T) in a
canonical FL contains an O(T) but no T^2 term. We show that in any D >1 the
next term after O(T) in \Sigma^R(i\pi T,T) is of order T^D (T^3\ln T in D=3).
This T^D term comes from only forward- and backward scattering, and is
expressed in terms of fully renormalized amplitudes for these processes. The
overall prefactor of the T^D term vanishes in the "local approximation", when
the interaction can be approximated by its value for the initial and final
fermionic states right on the Fermi surface. The local approximation is
justified near a Pomeranchuk instability, even if the vertex corrections are
non-negligible. We show that the strength of the first-Matsubara-frequency rule
is amplified in the local approximation, where it states that not only the T^D
term vanishes but also that \Sigma^R(i\pi T,T) does not contain any terms
beyond O(T). This rule imposes two constraints on the scaling form of the
self-energy: upon replacing \omega by i\pi T, Im\Sigma^R(\omega,T) must vanish
and Re\Sigma^R (\omega, T) must reduce to O(T). These two constraints should be
taken into consideration in extracting scaling forms of \Sigma^R(\omega,T) from
experimental and numerical data.Comment: 22 pages, 3 figure
A scalable, high-speed measurement-based quantum computer using trapped ions
We describe a scalable, high-speed, and robust architecture for
measurement-based quantum-computing with trapped ions. Measurement-based
architectures offer a way to speed-up operation of a quantum computer
significantly by parallelizing the slow entangling operations and transferring
the speed requirement to fast measurement of qubits. We show that a 3D cluster
state suitable for fault-tolerant measurement-based quantum computing can be
implemented on a 2D array of ion traps. We propose the projective measurement
of ions via multi-photon photoionization for nanosecond operation and discuss
the viability of such a scheme for Ca ions.Comment: 4 pages, 3 figure
Fluctuations in the level density of a Fermi gas
We present a theory that accurately describes the counting of excited states
of a noninteracting fermionic gas. At high excitation energies the results
reproduce Bethe's theory. At low energies oscillatory corrections to the
many--body density of states, related to shell effects, are obtained. The
fluctuations depend non-trivially on energy and particle number. Universality
and connections with Poisson statistics and random matrix theory are
established for regular and chaotic single--particle motion.Comment: 4 pages, 1 figur
Weak Field Hall Resistance and Effective Carrier Density Through Metal-Insulator Transition in Si-MOS Structures
We studied the weak field Hall voltage in 2D electron layers in Si-MOS
structures with different mobilities, through the metal-insulator transition.
In the vicinity of the critical density on the metallic side of the transition,
we have found weak deviations (about 6-20 %) of the Hall voltage from its
classical value. The deviations do not correlate with the strong temperature
dependence of the diagonal resistivity rho_{xx}(T). The smallest deviation in
R_{xy} was found in the highest mobility sample exhibiting the largest
variation in the diagonal resistivity \rho_{xx} with temperature (by a factor
of 5).Comment: 4 pages, 4 figures, RevTe
Particle size segregation in granular flow in silos
Segregation and layering of alumina in storage silos are investigated, with a view to predicting output quality versus time, given known variations in input quality on emplacement. A variety of experiments were conducted, existing relevant publications were reviewed, and the basis for an algorithm for predicting the effect of withdrawing from a central flowing region, in combination with variations in quality due to geometric, layering and segregation effects, is described in this report
Hierarchical Model for the Evolution of Cloud Complexes
The structure of cloud complexes appears to be well described by a "tree
structure" representation when the image is partitioned into "clouds". In this
representation, the parent-child relationships are assigned according to
containment. Based on this picture, a hierarchical model for the evolution of
Cloud Complexes, including star formation, is constructed, that follows the
mass evolution of each sub-structure by computing its mass exchange
(evaporation or condensation) with its parent and children, which depends on
the radiation density at the interphase. For the set of parameters used as a
reference model, the system produces IMFs with a maximum at too high mass (~2
M_sun) and the characteristic times for evolution seem too long. We show that
these properties can be improved by adjusting model parameters. However, the
emphasis here is to illustrate some general properties of this nonlinear model
for the star formation process. Notwithstanding the simplifications involved,
the model reveals an essential feature that will likely remain if additional
physical processes are included. That is: the detailed behavior of the system
is very sensitive to variations on the initial and external conditions,
suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs
corresponding to a variety of initial or external conditions is examined, the
slope of the IMF at high masses shows variations comparable to the range
derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap
Remote sensing applications to resource problems in South Dakota
There are no author-identified significant results in this report
Surface code quantum computing by lattice surgery
In recent years, surface codes have become a leading method for quantum error
correction in theoretical large scale computational and communications
architecture designs. Their comparatively high fault-tolerant thresholds and
their natural 2-dimensional nearest neighbour (2DNN) structure make them an
obvious choice for large scale designs in experimentally realistic systems.
While fundamentally based on the toric code of Kitaev, there are many variants,
two of which are the planar- and defect- based codes. Planar codes require
fewer qubits to implement (for the same strength of error correction), but are
restricted to encoding a single qubit of information. Interactions between
encoded qubits are achieved via transversal operations, thus destroying the
inherent 2DNN nature of the code. In this paper we introduce a new technique
enabling the coupling of two planar codes without transversal operations,
maintaining the 2DNN of the encoded computer. Our lattice surgery technique
comprises splitting and merging planar code surfaces, and enables us to perform
universal quantum computation (including magic state injection) while removing
the need for braided logic in a strictly 2DNN design, and hence reduces the
overall qubit resources for logic operations. Those resources are further
reduced by the use of a rotated lattice for the planar encoding. We show how
lattice surgery allows us to distribute encoded GHZ states in a more direct
(and overhead friendly) manner, and how a demonstration of an encoded CNOT
between two distance 3 logical states is possible with 53 physical qubits, half
of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure
Enhanced Optical Cooling of Ion Beams for LHC
The possibility of the enhanced optical cooling (EOC) of Lead ions in LHC is
investigated. Non-exponential feature of cooling and requirements to the ring
lattice, optical and laser systems are discussed. Comparison with optical
stochastic cooling (OSC) is represented.Comment: 4 page
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