of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in perturbation theory at study. We analyze two spin chain toy models which might shed some light on the physics behind these wrapping effects. One of them, the Hubbard model, is known to be closely related to N

A number of writers have been attracted to the idea that some of the puzzling features of quantum mechanics might be manifestations of ‘reverse ’ or ‘retro ’ causality, at a level underlying that of the usual quantum description. The main motivation for this view stems from EPR/Bell phenomena, where it offers two virtues. First, as was noted by its earliest proponent, 1 it has the potential to provide a timelike decomposition of the nonlocal correlations revealed in EPR cases – i.e., as we would now put it, 2 for the violation of the Bell inequalities in the quantum world. Second, Bell’s derivation of his famous inequality depends explicitly on the assumption that hidden states do not depend on future measurement settings – so that its violation simply invites a retrocausal explanation, at least from the point of view of anyone who has already been bitten by the retrocausal bug. Most people working in the foundations of quantum mechanics remain resolutely unbitten, however. It is common for the retrocausal option to be ignored altogether, or, as in this rather careful recent survey article, relegated to the footnotes with other unmemorabilia: To be scrupulous,

We have designed a toy brain and have written computer code that simulates it. This toy brain is flexible, modular, has hierarchical learning and recognition, has short and long term memory, is distributed (i.e. has no central control), is asynchronous, and includes parallel and series processing

homogenization for an energy conserving

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights

A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current is explicitly calculated as a function of the rate

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Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions of higher-dimensional gauge theory models with fluxes