Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between different elements of the interaction matrix, we obtain its TAP free energy explicitly, which consists of a series of terms exhibiting the cluster effect. Nature of the spin-glass transition in the model is also examined and compared with those given by the replica method as well as the cavity method.Comment: 12 pages, LaTex, 1 PostScript figur

Comments on Proposed Gravitational Modifications of Schrodinger Dynamics and their Experimental Implications

We discuss aspects of gravitational modifications of Schrodinger dynamics proposed by Diosi and Penrose. We consider first the Diosi-Penrose criterion for gravitationally induced state vector reduction, and compute the reduction time expected for a superposition of a uniform density cubical solid in two positions displaced by a small fraction of the cube side. We show that the predicted effect is much smaller than would be observable in the proposed Marshall et al. mirror experiment. We then consider the ``Schrodinger -Newton'' equation for an N-particle system. We show that in the independent particle approximation, it differs from the usual Hartree approximation applied to the Newtonian potential by self-interaction terms, which do not have a consistent Born rule interpretation. This raises doubts about the use of the Schrodinger-Newton equation to calculate gravitational effects on molecular interference experiments. When the effects of Newtonian gravitation on molecular diffraction are calculated using the standard many-body Schrodinger equation, no washing out of the interference pattern is predicted.Comment: Tex, 17

Interaction-free measurement and forward scattering

Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the forward-scattered wave is locked both in amplitude and in phase. For an imperfect one it has a nontrivial phase of dynamical origin (``colored silhouette"), measurable by interferometry. Other examples of quantum silhouettes, all controlled by unitarity, are briefly discussed.Comment: 4 pages in RevTex + 1 figure in eps; submitted to Phys. Rev. A since 09Jan98; now update

High-efficiency quantum interrogation measurements via the quantum Zeno effect

The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, demonstrating efficiencies exceeding the 50% theoretical-maximum of the original ``interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss; efficiencies of up to 73% were observed and the feasibility of efficiencies up to 85% was demonstrated.Comment: 4 pages, 3 postscript figures. To appear in Phys. Rev. Lett; submitted June 11, 199

Are Interaction-free Measurements Interaction Free?

In 1993 Elitzur and Vaidman introduced the concept of interaction-free measurements which allowed finding objects without ``touching'' them. In the proposed method, since the objects were not touched even by photons, thus, the interaction-free measurements can be called as ``seeing in the dark''. Since then several experiments have been successfully performed and various modifications were suggested. Recently, however, the validity of the term ``interaction-free'' has been questioned. The criticism of the name is briefly reviewed and the meaning of the interaction-free measurements is clarified.Comment: 11 pages, 3 eps figures. Contribution to the ICQO 2000, Raubichi, Belaru

Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence

Both the additional non-linear term in the Schr\"odinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian interaction potential formally. We discuss certain aspects that are common for both equations. In particular, we calculate the enhancement of the proposed localisation and/or decoherence effects, which would take place if one could lower the conventional length-cutoff and resolve the mass density on the interatomic scale.Comment: 8pp LaTex, Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirard

On the interpretative essence of the term "interaction-free measurement": The role of entanglement

The polemical term "interaction-free measurement" (IFM) is analyzed in its interpretative nature. Two seminal works proposing the term are revisited and their underlying interpretations are assessed. The role played by nonlocal quantum correlations (entanglement) is formally discussed and some controversial conceptions in the original treatments are identified. As a result the term IFM is shown to be consistent neither with the standard interpretation of quantum mechanics nor with the lessons provided by the EPR debate.Comment: accepted in Found. Phy