3,988 research outputs found
Spin Chains as Perfect Quantum State Mirrors
Quantum information transfer is an important part of quantum information
processing. Several proposals for quantum information transfer along linear
arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect
transfer was shown to exist in two models with specifically designed strongly
inhomogeneous couplings. We show that perfect transfer occurs in an entire
class of chains, including systems whose nearest-neighbor couplings vary only
weakly along the chain. The key to these observations is the Jordan-Wigner
mapping of spins to noninteracting lattice fermions which display perfectly
periodic dynamics if the single-particle energy spectrum is appropriate. After
a half-period of that dynamics any state is transformed into its mirror image
with respect to the center of the chain. The absence of fermion interactions
preserves these features at arbitrary temperature and allows for the transfer
of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the
text, one new reference. Accepted by Phys. Rev. A (Rapid Communications
Average persistence in random walks
We study the first passage time properties of an integrated Brownian curve
both in homogeneous and disordered environments. In a disordered medium we
relate the scaling properties of this center of mass persistence of a random
walker to the average persistence, the latter being the probability P_pr(t)
that the expectation value of the walker's position after time t has not
returned to the initial value. The average persistence is then connected to the
statistics of extreme events of homogeneous random walks which can be computed
exactly for moderate system sizes. As a result we obtain a logarithmic
dependence P_pr(t)~{ln(t)}^theta' with a new exponent theta'=0.191+/-0.002. We
note on a complete correspondence between the average persistence of random
walks and the magnetization autocorrelation function of the transverse-field
Ising chain, in the homogeneous and disordered case.Comment: 6 pages LaTeX, 3 postscript figures include
Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in and evolving by
a class of constrained surface diffusion flows. Our result, similar to earlier
results for the Willmore flow, gives both a positive lower bound on the time
for which a smooth solution exists, and a small upper bound on a power of the
total curvature during this time. By phrasing the theorem in terms of the
concentration of curvature in the initial surface, our result holds for very
general initial data and has applications to further development in asymptotic
analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1201.657
Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study
singular quantities in the Griffiths phase of random quantum spin chains. For
the random transverse-field Ising spin chain we have extended Fisher's
analytical solution to the off-critical region and calculated the dynamical
exponent exactly. Concerning other random chains we argue by scaling
considerations that the RG method generally becomes asymptotically exact for
large times, both at the critical point and in the whole Griffiths phase. This
statement is checked via numerical calculations on the random Heisenberg and
quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include
Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder
The Random Transverse Field Ising Chain is the simplest disordered model
presenting a quantum phase transition at T=0. We compare analytically its
finite-size scaling properties in two different ensembles for the disorder (i)
the canonical ensemble, where the disorder variables are independent (ii) the
microcanonical ensemble, where there exists a global constraint on the disorder
variables. The observables under study are the surface magnetization, the
correlation of the two surface magnetizations, the gap and the end-to-end
spin-spin correlation for a chain of length . At criticality, each
observable decays typically as in both ensembles, but the
probability distributions of the rescaled variable are different in the two
ensembles, in particular in their asymptotic behaviors. As a consequence, the
dependence in of averaged observables differ in the two ensembles. For
instance, the correlation decays algebraically as 1/L in the canonical
ensemble, but sub-exponentially as in the microcanonical
ensemble. Off criticality, probability distributions of rescaled variables are
governed by the critical exponent in both ensembles, but the following
observables are governed by the exponent in the microcanonical
ensemble, instead of the exponent in the canonical ensemble (a) in the
disordered phase : the averaged surface magnetization, the averaged correlation
of the two surface magnetizations and the averaged end-to-end spin-spin
correlation (b) in the ordered phase : the averaged gap. In conclusion, the
measure of the rare events that dominate various averaged observables can be
very sensitive to the microcanonical constraint.Comment: 24 page
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