55,472 research outputs found
Quantitative Description of by the Hubbard Model in Infinite Dimensions
We show that the analytic single-particle density of states and the optical
conductivity for the half-filled Hubbard model on the Bethe lattice in infinite
dimensions describe quantitatively the behavior of the gap and the kinetic
energy ratio of the correlated insulator . The form of the optical
conductivity shows rising and is quite similar to the
experimental data, and the density of states shows behavior near
the band edges.Comment: 9 pages, revtex, 4 figures upon reques
Provable Deterministic Leverage Score Sampling
We explain theoretically a curious empirical phenomenon: "Approximating a
matrix by deterministically selecting a subset of its columns with the
corresponding largest leverage scores results in a good low-rank matrix
surrogate". To obtain provable guarantees, previous work requires randomized
sampling of the columns with probabilities proportional to their leverage
scores.
In this work, we provide a novel theoretical analysis of deterministic
leverage score sampling. We show that such deterministic sampling can be
provably as accurate as its randomized counterparts, if the leverage scores
follow a moderately steep power-law decay. We support this power-law assumption
by providing empirical evidence that such decay laws are abundant in real-world
data sets. We then demonstrate empirically the performance of deterministic
leverage score sampling, which many times matches or outperforms the
state-of-the-art techniques.Comment: 20th ACM SIGKDD Conference on Knowledge Discovery and Data Minin
Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian
Based on the technique of integration within an ordered product (IWOP) of
operators we introduce the Fresnel operator for converting Caldirola-Kanai
Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel
operator with the parameters A,B,C,D corresponds to classical optical Fresnel
transformation, these parameters are the solution to a set of partial
differential equations set up in the above mentioned converting process. In
this way the exact wavefunction solution of the Schr\"odinger equation governed
by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed
number state. The corresponding Wigner function is derived by virtue of the
Weyl ordered form of the Wigner operator and the order-invariance of Weyl
ordered operators under similar transformations. The method used here can be
suitable for solving Schr\"odinger equation of other time-dependent
oscillators.Comment: 6 pages, 2 figure
A fluctuation-induced plasma transport diagnostic based upon fast-Fourier transform spectral analysis
A diagnostic, based on fast Fourier-transform spectral analysis techniques, that provides experimental insight into the relationship between the experimentally observable spectral characteristics of the fluctuations and the fluctuation-induced plasma transport is described. The model upon which the diagnostic technique is based and its experimental implementation is discussed. Some characteristic results obtained during the course of an experimental study of fluctuation-induced transport in the electric field dominated NASA Lewis bumpy torus plasma are presented
Topological current of point defects and its bifurcation
From the topological properties of a three dimensional vector order
parameter, the topological current of point defects is obtained. One shows that
the charge of point defects is determined by Hopf indices and Brouwer degrees.
The evolution of point defects is also studied. One concludes that there exist
crucial cases of branch processes in the evolution of point defects when the
Jacobian .Comment: revtex,14 pages,no figur
Fully gapped superconducting state in Au2Pb: a natural candidate for topological superconductor
We measured the ultra-low-temperature specific heat and thermal conductivity
of AuPb single crystal, a possible three-dimensional Dirac semimetal with a
superconducting transition temperature 1.05 K. The electronic
specific heat can be fitted by a two-band s-wave model, which gives the gap
amplitudes (0)/ = 1.38 and (0)/ = 5.25.
From the thermal conductivity measurements, a negligible residual linear term
in zero field and a slow field dependence of at low
field are obtained. These results suggest that AuPb has a fully gapped
superconducting state in the bulk, which is a necessary condition for
topological superconductor if AuPb is indeed one.Comment: 6 pages, 4 figure
Goos-H\"{a}nchen-Like Shifts in Atom Optics
We consider the propagation of a matter wavepacket of two-level atoms through
a square potential created by a super-Gaussian laser beam. We explore the
matter wave analog of Goos-H\"{a}nchen shift within the framework of atom
optics where the roles of atom and light is exchanged with respect to
conventional optics. Using a vector theory, where atoms are treated as
particles possessing two internal spin components, we show that not only large
negative but also large positive Goos-H\"{a}nchen shifts can occur in the
reflected atomic beam.Comment: 7 pages, 4 figure
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