4,710 research outputs found
Improved numerical methods for infinite spin chains with long-range interactions
We present several improvements of the infinite matrix product state (iMPS)
algorithm for finding ground states of one-dimensional quantum systems with
long-range interactions. As a main new ingredient we introduce the superposed
multi-optimization (SMO) method, which allows an efficient optimization of
exponentially many MPS of different length at different sites all in one step.
Hereby the algorithm becomes protected against position dependent effects as
caused by spontaneously broken translational invariance. So far, these have
been a major obstacle to convergence for the iMPS algorithm if no prior
knowledge of the systems translational symmetry was accessible. Further, we
investigate some more general methods to speed up calculations and improve
convergence, which might be partially interesting in a much broader context,
too. As a more special problem, we also look into translational invariant
states close to an invariance braking phase transition and show how to avoid
convergence into wrong local minima for such systems. Finally, we apply the new
methods to polar bosons with long-range interactions. We calculate several
detailed Devil's Staircases with the corresponding phase diagrams and
investigate some supersolid properties.Comment: Main text: 17 pages plus references, 8 figures. Supplementary info: 6
pages. v2: improved presentation and more results adde
On the Shapley-like Payoff Mechanisms in Peer-Assisted Services with Multiple Content Providers
This paper studies an incentive structure for cooperation and its stability
in peer-assisted services when there exist multiple content providers, using a
coalition game theoretic approach. We first consider a generalized coalition
structure consisting of multiple providers with many assisting peers, where
peers assist providers to reduce the operational cost in content distribution.
To distribute the profit from cost reduction to players (i.e., providers and
peers), we then establish a generalized formula for individual payoffs when a
"Shapley-like" payoff mechanism is adopted. We show that the grand coalition is
unstable, even when the operational cost functions are concave, which is in
sharp contrast to the recently studied case of a single provider where the
grand coalition is stable. We also show that irrespective of stability of the
grand coalition, there always exist coalition structures which are not
convergent to the grand coalition. Our results give us an important insight
that a provider does not tend to cooperate with other providers in
peer-assisted services, and be separated from them. To further study the case
of the separated providers, three examples are presented; (i) underpaid peers,
(ii) service monopoly, and (iii) oscillatory coalition structure. Our study
opens many new questions such as realistic and efficient incentive structures
and the tradeoffs between fairness and individual providers' competition in
peer-assisted services.Comment: 13 pages, 4 figures, an extended version of the paper to be presented
in ICST GameNets 2011, Shanghai, China, April 201
Dynamics of Learning with Restricted Training Sets I: General Theory
We study the dynamics of supervised learning in layered neural networks, in
the regime where the size of the training set is proportional to the number
of inputs. Here the local fields are no longer described by Gaussian
probability distributions and the learning dynamics is of a spin-glass nature,
with the composition of the training set playing the role of quenched disorder.
We show how dynamical replica theory can be used to predict the evolution of
macroscopic observables, including the two relevant performance measures
(training error and generalization error), incorporating the old formalism
developed for complete training sets in the limit as a
special case. For simplicity we restrict ourselves in this paper to
single-layer networks and realizable tasks.Comment: 39 pages, LaTe
Solvable Systems of Linear Differential Equations
The asymptotic iteration method (AIM) is an iterative technique used to find
exact and approximate solutions to second-order linear differential equations.
In this work, we employed AIM to solve systems of two first-order linear
differential equations. The termination criteria of AIM will be re-examined and
the whole theory is re-worked in order to fit this new application. As a result
of our investigation, an interesting connection between the solution of linear
systems and the solution of Riccati equations is established. Further, new
classes of exactly solvable systems of linear differential equations with
variable coefficients are obtained. The method discussed allow to construct
many solvable classes through a simple procedure.Comment: 13 page
On the renormalized scalar density in quenched QCD
We present a non-perturbative determination of the renormalization factor Z_S
of the scalar density in quenched QCD with overlap fermions. Results are
obtained at four values of the lattice spacing. By combining Z_S with results
for the low-energy constant Sigma we are able to compute the renormalization
group invariant scalar condensate in the continuum limit with a total accuracy
of 7%, excluding dynamical quark effects. Our result translates to
Sigma_msbar(2 GeV)=(285+/-9 MeV)^3 if the scale is set by the kaon decay
constant. We have also performed scaling studies of the pseudoscalar decay
constant and the vector mass. Our results indicate that quantities computed
using overlap quarks exhibit excellent scaling behaviour, with small residual
lattice artifacts.Comment: 15 pages, 7 figure
Two-photon ionization of Helium studied with the multiconfigurational time-dependent Hartree-Fock method
The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is
applied for simulations of the two-photon ionization of Helium. We present
results for the single- and double ionization from the groundstate for photon
energies in the non-sequential regime, and compare them to direct solutions of
the Schr\"odinger equation using the time-dependent (full) Configuration
Interaction method (TDCI). We find that the single-ionization is accurately
reproduced by MCTDHF, whereas the double ionization results correctly capture
the main trends of TDCI
Quantum Circulant Preconditioner for Linear System of Equations
We consider the quantum linear solver for with the circulant
preconditioner . The main technique is the singular value estimation (SVE)
introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in
ITCS 2017]. However, some modifications of SVE should be made to solve the
preconditioned linear system . Moreover, different from
the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C.
R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett.,
2013], the circulant preconditioner is easy to construct and can be directly
applied to general dense non-Hermitian cases. The time complexity depends on
the condition numbers of and , as well as the Frobenius norm
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