230,162 research outputs found
Dissipative Time Evolution of Observables in Non-equilibrium Statistical Quantum Systems
We discuss differential-- versus integral--equation based methods describing
out--of thermal equilibrium systems and emphasize the importance of a well
defined reduction to statistical observables. Applying the projection operator
approach, we investigate on the time evolution of expectation values of linear
and quadratic polynomials in position and momentum for a statistical anharmonic
oscillator with quartic potential. Based on the exact integro-differential
equations of motion, we study the first and naive second order approximation
which breaks down at secular time-scales. A method is proposed to improve the
expansion by a non--perturbative resummation of all quadratic operator
correlators consistent with energy conservation for all times. Motion cannot be
described by an effective Hamiltonian local in time reflecting non-unitarity of
the dissipative entropy generating evolution. We numerically integrate the
consistently improved equations of motion for large times. We relate entropy to
the uncertainty product, both being expressible in terms of the observables
under consideration.Comment: 20 pages, 6 Figure
How to simulate a quantum computer using negative probabilities
The concept of negative probabilities can be used to decompose the
interaction of two qubits mediated by a quantum controlled-NOT into three
operations that require only classical interactions (that is, local operations
and classical communication) between the qubits. For a single gate, the
probabilities of the three operations are 1, 1, and -1. This decomposition can
be applied in a probabilistic simulation of quantum computation by randomly
choosing one of the three operations for each gate and assigning a negative
statistical weight to the outcomes of sequences with an odd number of negative
probability operations. The exponential speed-up of a quantum computer can then
be evaluated in terms of the increase in the number of sequences needed to
simulate a single operation of the quantum circuit.Comment: 11 pages, including one figure and one table. Full paper version for
publication in Journal of Physics A. Clarifications of basic concepts and
discussions of possible implications have been adde
An Information-Theoretic Test for Dependence with an Application to the Temporal Structure of Stock Returns
Information theory provides ideas for conceptualising information and
measuring relationships between objects. It has found wide application in the
sciences, but economics and finance have made surprisingly little use of it. We
show that time series data can usefully be studied as information -- by noting
the relationship between statistical redundancy and dependence, we are able to
use the results of information theory to construct a test for joint dependence
of random variables. The test is in the same spirit of those developed by
Ryabko and Astola (2005, 2006b,a), but differs from these in that we add extra
randomness to the original stochatic process. It uses data compression to
estimate the entropy rate of a stochastic process, which allows it to measure
dependence among sets of random variables, as opposed to the existing
econometric literature that uses entropy and finds itself restricted to
pairwise tests of dependence. We show how serial dependence may be detected in
S&P500 and PSI20 stock returns over different sample periods and frequencies.
We apply the test to synthetic data to judge its ability to recover known
temporal dependence structures.Comment: 22 pages, 7 figure
The organisation of sociality: a manifesto for a new science of multi-agent systems
In this paper, we pose and motivate a challenge, namely the need for a new science of multi-agent systems. We propose that this new science should be grounded, theoretically on a richer conception of sociality, and methodologically on the extensive use of computational modelling for real-world applications and social simulations. Here, the steps we set forth towards meeting that challenge are mainly theoretical. In this respect, we provide a new model of multi-agent systems that reflects a fully explicated conception of cognition, both at the individual and the collective level. Finally, the mechanisms and principles underpinning the model will be examined with particular emphasis on the contributions provided by contemporary organisation theory
A Monte Carlo method for critical systems in infinite volume: the planar Ising model
In this paper we propose a Monte Carlo method for generating finite-domain
marginals of critical distributions of statistical models in infinite volume.
The algorithm corrects the problem of the long-range effects of boundaries
associated to generating critical distributions on finite lattices. It uses the
advantage of scale invariance combined with ideas of the renormalization group
in order to construct a type of "holographic" boundary condition that encodes
the presence of an infinite volume beyond it. We check the quality of the
distribution obtained in the case of the planar Ising model by comparing
various observables with their infinite-plane prediction. We accurately
reproduce planar two-, three- and four-point functions of spin and energy
operators. We also define a lattice stress-energy tensor, and numerically
obtain the associated conformal Ward identities and the Ising central charge.Comment: 43 pages, 21 figure
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