13,025 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
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
Macroscopic Quantum Tunneling of a Domain Wall in a Ferromagnetic Metal
The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic
metal is studied based on the Hubbard model. It is found that the ohmic
dissipation is present even at zero temperature due to the gapless Stoner
excitation, which is the crucial difference from the case of the insulating
magnet. The dissipative effect is calculated as a function of width of the wall
and is shown to be effective in a thin wall and in a weak ferromagnet. The
results are discussed in the light of recent experiments on ferromagnets with
strong anisotropy. PACS numbers:75.60.Ch, 03.65.Sq, 75.10.LpComment: 13page
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
Bohr-Sommerfeld quantization of spin Hamiltonians
The Bohr-Sommerfeld rule for a spin system is obtained, including the first
quantum corrections. The rule applies to both integer and half-integer spin,
and respects Kramers degeneracy for time-reversal invariant systems. It is
tested for various models, in particular the Lipkin-Meshkov-Glick model, and
found to agree very well with exact results.Comment: Revtex 4, no figures, 1 tabl
Quantum Lightning Never Strikes the Same State Twice
Public key quantum money can be seen as a version of the quantum no-cloning
theorem that holds even when the quantum states can be verified by the
adversary. In this work, investigate quantum lightning, a formalization of
"collision-free quantum money" defined by Lutomirski et al. [ICS'10], where
no-cloning holds even when the adversary herself generates the quantum state to
be cloned. We then study quantum money and quantum lightning, showing the
following results:
- We demonstrate the usefulness of quantum lightning by showing several
potential applications, such as generating random strings with a proof of
entropy, to completely decentralized cryptocurrency without a block-chain,
where transactions is instant and local.
- We give win-win results for quantum money/lightning, showing that either
signatures/hash functions/commitment schemes meet very strong recently proposed
notions of security, or they yield quantum money or lightning.
- We construct quantum lightning under the assumed multi-collision resistance
of random degree-2 systems of polynomials.
- We show that instantiating the quantum money scheme of Aaronson and
Christiano [STOC'12] with indistinguishability obfuscation that is secure
against quantum computers yields a secure quantum money schem
- …