13,862 research outputs found
Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian
The spin Hamiltonian that describes the molecular magnet Fe has biaxial
symmetry with mutually perpendicular easy, medium, and hard magnetic axes.
Previous calculations of the ground state tunnel splittings in the presence of
a magnetic field along the hard axis are extended, and the meaning of the
previously discovered oscillation of this splitting is further clarified
Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach
Certain spin Hamiltonians that give rise to tunnel splittings that are viewed
in terms of interfering instanton trajectories, are restudied using a discrete
WKB method, that is more elementary, and also yields wavefunctions and
preexponential factors for the splittings. A novel turning point inside the
classically forbidden region is analysed, and a general formula is obtained for
the splittings. The result is appled to the \Fe8 system. A previous result for
the oscillation of the ground state splitting with external magnetic field is
extended to higher levels.Comment: RevTex, one ps figur
Efficient algorithms for tensor scaling, quantum marginals and moment polytopes
We present a polynomial time algorithm to approximately scale tensors of any
format to arbitrary prescribed marginals (whenever possible). This unifies and
generalizes a sequence of past works on matrix, operator and tensor scaling.
Our algorithm provides an efficient weak membership oracle for the associated
moment polytopes, an important family of implicitly-defined convex polytopes
with exponentially many facets and a wide range of applications. These include
the entanglement polytopes from quantum information theory (in particular, we
obtain an efficient solution to the notorious one-body quantum marginal
problem) and the Kronecker polytopes from representation theory (which capture
the asymptotic support of Kronecker coefficients). Our algorithm can be applied
to succinct descriptions of the input tensor whenever the marginals can be
efficiently computed, as in the important case of matrix product states or
tensor-train decompositions, widely used in computational physics and numerical
mathematics.
We strengthen and generalize the alternating minimization approach of
previous papers by introducing the theory of highest weight vectors from
representation theory into the numerical optimization framework. We show that
highest weight vectors are natural potential functions for scaling algorithms
and prove new bounds on their evaluations to obtain polynomial-time
convergence. Our techniques are general and we believe that they will be
instrumental to obtain efficient algorithms for moment polytopes beyond the
ones consider here, and more broadly, for other optimization problems
possessing natural symmetries
Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric Configurations
The perfect quenching of spin tunneling first predicted for a model with
biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is
further studied using the discrete phase integral (or
Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is
extended to the case where the magnetic field has both hard and easy
components, so that the Hamiltonian has no obvious symmetry. Herring's formula
is now inapplicable, so the problem is solved by finding the wavefunction and
using connection formulas at every turning point. A general formula for the
energy surface in the vicinity of the diabolo is obtained in this way. This
formula gives the tunneling apmplitude between two wells unrelated by symmetry
in terms of a small number of action integrals, and appears to be generally
valid, even for problems where the recursion contains more than five terms.
Explicit results are obtained for the diabolical points in the model for Fe_8.
These results exactly parallel the experimental observations. It is found that
the leading semiclassical results for the diabolical points appear to be exact,
and the points themselves lie on a perfect centered rectangular lattice in the
magnetic field space. A variety of evidence in favor of this perfect lattice
hypothesis is presented.Comment: Revtex; 4 ps figures; follow up to cond-mat/000311
Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons
Spin coherent state path integrals with discontinuous semiclassical paths are
investigated with special reference to a realistic model for the magnetic
degrees of freedom in the Fe8 molecular solid. It is shown that such paths are
essential to a proper understanding of the phenomenon of quenched spin
tunneling in these molecules. In the Fe8 problem, such paths are shown to arise
as soon as a fourth order anisotropy term in the energy is turned on, making
this term a singular perturbation from the semiclassical point of view. The
instanton approximation is shown to quantitatively explain the magnetic field
dependence of the tunnel splitting, as well as agree with general rules for the
number of quenching points allowed for a given value of spin. An accurate
approximate formula for the spacing between quenching points is derived
Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps
{\em Verifiable computation} (VC) allows a computationally weak client to
outsource the evaluation of a function on many inputs to a powerful but
untrusted server. The client invests a large amount of off-line computation and
gives an encoding of its function to the server. The server returns both an
evaluation of the function on the client's input and a proof such that the
client can verify the evaluation using substantially less effort than doing the
evaluation on its own. We consider how to privately outsource computations
using {\em privacy preserving} VC schemes whose executions reveal no
information on the client's input or function to the server. We construct VC
schemes with {\em input privacy} for univariate polynomial evaluation and
matrix multiplication and then extend them such that the {\em function privacy}
is also achieved. Our tool is the recently developed {mutilinear maps}. The
proposed VC schemes can be used in outsourcing {private information retrieval
(PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International
Conference on Cryptology and Network Security (CANS 2013
Optical fiber interferometer for the study of ultrasonic waves in composite materials
The possibility of acoustic emission detection in composites using embedded optical fibers as sensing elements was investigated. Optical fiber interferometry, fiber acoustic sensitivity, fiber interferometer calibration, and acoustic emission detection are reported. Adhesive bond layer dynamical properties using ultrasonic interface waves, the design and construction of an ultrasonic transducer with a two dimensional Gaussian pressure profile, and the development of an optical differential technique for the measurement of surface acoustic wave particle displacements and propagation direction are also examined
Achieving Good Angular Resolution in 3D Arc Diagrams
We study a three-dimensional analogue to the well-known graph visualization
approach known as arc diagrams. We provide several algorithms that achieve good
angular resolution for 3D arc diagrams, even for cases when the arcs must
project to a given 2D straight-line drawing of the input graph. Our methods
make use of various graph coloring algorithms, including an algorithm for a new
coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on
Graph Drawing (GD 2013
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