51 research outputs found
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
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