9,437 research outputs found
ON THE SMARANDACHE FUNCTION AND THE FIXED - POINT THEORY OF NUMBERS
This brief note points out several basic connections between the Smarandache
function, fixed-point theory and prime-number theory. First recall that fixed-point theory in function spaces provides elegent, if not short, proofs of the existence of solutions to many kinds of differential equations, integral equations, optimization problems and game-theoretic problems
Quantum Statistics: Is there an effective fermion repulsion or boson attraction?
Physicists often claim that there is an effective repulsion between fermions,
implied by the Pauli principle, and a corresponding effective attraction
between bosons. We examine the origins of such exchange force ideas, the
validity for them, and the areas where they are highly misleading. We propose
that future explanations of quantum statistics should avoid the idea of a
effective force completely and replace it with more appropriate physical
insights, some of which are suggested here.Comment: 26 pages, 3 figures. Submitted to American Journal of Physic
Angular momentum conservation in measurements on spin Bose-Einstein condensates
We discuss a thought experiment where two operators, Alice and Bob, perform
transverse spin measurements on a quantum system; this system is initially in a
double Fock spin state, which extends over a large distance in space so that
the two operators are far away from each other. Standard quantum mechanics
predicts that, when Alice makes a few measurements, a large transverse
component of the spin angular momentum may appear in Bob's laboratory. A
paradox then arises since local angular momentum conservation seems to be
violated. It has been suggested that this angular momentum may be provided by
the interaction with the measurement apparatuses. We show that this solution of
the paradox is not appropriate, so that another explanation must be sought. The
general question is the retroaction of a quantum system onto a measurement
apparatus. For instance, when the measured system is entangled with another
quantum system, can its reaction on a measurement apparatus be completely
changed? Is angular momentum conserved only on average over several
measurements, but not during one realization of the experiment?Comment: 11 pages, 3 figure
Quantum properties of a single beam splitter
When a single beam-splitter receives two beams of bosons described by Fock
states (Bose-Einstein condensates at very low temperatures), interesting
generalizations of the two-photon Hong-Ou-Mandel effect take place for larger
number of particles. The distributions of particles at two detectors behind the
beam splitter can be understood as resulting from the combination of two
effects, the spontaneous phase appearing during quantum measurement, and the
quantum angle. The latter introduces quantum "population oscillations", which
can be seen as a generalized Hong-Ou-Mandel effect, although they do not always
correspond to even-odd oscillations.Comment: 14 pages, 11 figure
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