4,398 research outputs found
Imaging geometry through dynamics: the observable representation
For many stochastic processes there is an underlying coordinate space, ,
with the process moving from point to point in or on variables (such as
spin configurations) defined with respect to . There is a matrix of
transition probabilities (whether between points in or between variables
defined on ) and we focus on its ``slow'' eigenvectors, those with
eigenvalues closest to that of the stationary eigenvector. These eigenvectors
are the ``observables,'' and they can be used to recover geometrical features
of
Opposite Thermodynamic Arrows of Time
A model in which two weakly coupled systems maintain opposite running
thermodynamic arrows of time is exhibited. Each experiences its own retarded
electromagnetic interaction and can be seen by the other. The possibility of
opposite-arrow systems at stellar distances is explored and a relation to dark
matter suggested.Comment: To appear in Phys. Rev. Let
Quantum algorithms for hidden nonlinear structures
Attempts to find new quantum algorithms that outperform classical computation
have focused primarily on the nonabelian hidden subgroup problem, which
generalizes the central problem solved by Shor's factoring algorithm. We
suggest an alternative generalization, namely to problems of finding hidden
nonlinear structures over finite fields. We give examples of two such problems
that can be solved efficiently by a quantum computer, but not by a classical
computer. We also give some positive results on the quantum query complexity of
finding hidden nonlinear structures.Comment: 13 page
Space Station Spartan study
The required extension, enhancement, and upgrading of the present Spartan concept are described to conduct operations from the space station using the station's unique facilities and operational features. The space station Spartan (3S), the free flyer will be deployed from and returned to the space station and will conduct scientific missions of much longer duration than possible with the current Spartan. The potential benefits of a space station Spartan are enumerated. The objectives of the study are: (1) to develop a credible concept for a space station Spartan; and (2) to determine the associated requirements and interfaces with the space station to help ensure that the 3S can be properly accommodated
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
We compare pseudopure state ensemble implementations, quantified by their
initial polarization and ensemble size, of Grover's search algorithm to
probabilistic classical sequential search algorithms in terms of their success
and failure probabilities. We propose a criterion for quantifying the resources
used by the ensemble implementation via the aggregate number of oracle
invocations across the entire ensemble and use this as a basis for comparison
with classical search algorithms. We determine bounds for a critical
polarization such that the ensemble algorithm succeeds with a greater
probability than the probabilistic classical sequential search. Our results
indicate that the critical polarization scales as N^(-1/4) where N is the
database size and that for typical room temperature solution state NMR, the
polarization is such that the ensemble implementation of Grover's algorithm
would be advantageous for N > 10^2
Sharing Polarization within Quantum Subspaces
Given an ensemble of n spins, at least some of which are partially polarized,
we investigate the sharing of this polarization within a subspace of k spins.
We assume that the sharing results in a pseudopure state, characterized by a
single purity parameter which we call the bias. As a concrete example we
consider ensembles of spin-1/2 nuclei in liquid-state nuclear magnetic
resonance (NMR) systems. The shared bias levels are compared with some current
entanglement bounds to determine whether the reduced subspaces can give rise to
entangled states.Comment: 7 pages, 3 figure
Analysis of a three-component model phase diagram by Catastrophe Theory
We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We find
the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential, the
canonical form Wigwam or , constitutes the adequate starting point to
study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.
Closed Path Integrals and Renormalisation in Quantum Mechanics
We suggest a closed form expression for the path integral of quantum
transition amplitudes. We introduce a quantum action with renormalized
parameters. We present numerical results for the potential. The
renormalized action is relevant for quantum chaos and quantum instantons.Comment: Revised text, 1 figure added; Text (LaTeX file), 1 Figure (ps file
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