266,574 research outputs found
On the Cauchy problem for Gross-Pitaevskii hierarchies
The purpose of this paper is to investigate the Cauchy problem for the
Gross-Pitaevskii infinite linear hierarchy of equations on We prove local existence and uniqueness of solutions in certain
Sobolev type spaces of sequences of marginal
density operators with In particular, we give a clear
discussion of all cases which covers the local well-posedness
problem for Gross-Pitaevskii hierarchy in this situation.Comment: 17 pages. The referee's comments and suggestions have been
incorporated into this version of the pape
Renormalization group approach to symmetry protected topological phases
A defining feature of a symmetry protected topological phase (SPT) in
one-dimension is the degeneracy of the Schmidt values for any given
bipartition. For the system to go through a topological phase transition
separating two SPTs, the Schmidt values must either split or cross at the
critical point in order to change their degeneracies. A renormalization group
(RG) approach based on this splitting or crossing is proposed, through which we
obtain an RG flow that identifies the topological phase transitions in the
parameter space. Our approach can be implemented numerically in an efficient
manner, for example, using the matrix product state formalism, since only the
largest first few Schmidt values need to be calculated with sufficient
accuracy. Using several concrete models, we demonstrate that the critical
points and fixed points of the RG flow coincide with the maxima and minima of
the entanglement entropy, respectively, and the method can serve as a
numerically efficient tool to analyze interacting SPTs in the parameter space.Comment: 5 pages, 3 figure
The 3D inelastic analysis methods for hot section components
Advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate and yet more cost-effective analysis of combustors, turbine blades, and vanes are being developed. The approach is to develop four different theories, one linear and three higher order with increasing complexities including embedded singularities. Progress in each area is reported
Width-amplitude relation of Bernstein-Greene-Kruskal solitary waves
Inequality width-amplitude relations for three-dimensional
Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas.
Criteria for neglecting effects of nonzero cyclotron radius are obtained. We
emphasize that the form of the solitary potential is not tightly constrained,
and the amplitude and widths of the potential are constrained by inequalities.
The existence of a continuous range of allowed sizes and shapes for these waves
makes them easily accessible. We propose that these solitary waves can be
spontaneously generated in turbulence or thermal fluctuations. We expect that
the high excitation probability of these waves should alter the bulk properties
of the plasma medium such as electrical resistivity and thermal conductivity.Comment: 5 pages, 2 figure
A model of a dual-core matter-wave soliton laser
We propose a system which can generate a periodic array of solitary-wave
pulses from a finite reservoir of coherent Bose-Einstein condensate (BEC). The
system is built as a set of two parallel quasi-one-dimensional traps (the
reservoir proper and a pulse-generating cavity), which are linearly coupled by
the tunneling of atoms. The scattering length is tuned to be negative and small
in the absolute value in the cavity, and still smaller but positive in the
reservoir. Additionally, a parabolic potential profile is created around the
center of the cavity. Both edges of the reservoir and one edge of the cavity
are impenetrable. Solitons are released through the other cavity's edge, which
is semi-transparent. Two different regimes of the intrinsic operation of the
laser are identified: circulations of a narrow wave-function pulse in the
cavity, and oscillations of a broad standing pulse. The latter regime is
stable, readily providing for the generation of an array containing up to
10,000 permanent-shape pulses. The circulation regime provides for no more than
40 cycles, and then it transforms into the oscillation mode. The dependence of
the dynamical regime on parameters of the system is investigated in detail.Comment: Journal of Physics B, in pres
Model choice versus model criticism
The new perspectives on ABC and Bayesian model criticisms presented in
Ratmann et al.(2009) are challenging standard approaches to Bayesian model
choice. We discuss here some issues arising from the authors' approach,
including prior influence, model assessment and criticism, and the meaning of
error in ABC.Comment: This is a comment on the recent paper by Ratmann, Andrieu, Wiuf, and
Richardson (PNAS, 106), submitted too late for PNAS to consider i
Equation-free dynamic renormalization in a glassy compaction model
Combining dynamic renormalization with equation-free computational tools, we
study the apparently self-similar evolution of void distribution dynamics in
the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev.
Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches,
forward as well as backward in time.Comment: 4 pages, 4 figures (Minor Modifications; Submitted Version
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Lateral shearing interferometry for high-NA EUV wavefront metrology
We present a lateral shearing interferometer suitable for high-NA EUV wavefront metrology. In this interferometer, a geometric model is used to accurately characterize and predict systematic errors that come from performing interferometry at high NA. This interferometer is compatible with various optical geometries, including systems where the image plane is tilted with respect to the optical axis, as in the Berkeley MET5. Simulation results show that the systematic errors in tilted geometries can be reduced by aligning the shearing interferometer grating and detector parallel to the image plane. Subsequent residual errors can be removed by linear fitting
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