43,769 research outputs found
Commutation Relations in Mesoscopic Electric Circuits
In the talk, I briefly demonstrate the quantum theory for mesoscopic electric
circuits and its applications. In the theory, the importance of the charge
discreteness in a mesoscopic electric circuit is addressed. As a result, a new
kind of commutation relation for electric charge and current occurred
inevitably. The charge representation, canonical current representation and
pseudo-current representation are discussed extensively. It not only provides a
concrete realization of mathematical models which discuss the space
quantization in high energy physics and quantum gravity but also presents a
sequence of applications in condensed matter physics from a different point of
view. A possible generalization to coupled circuits is also proposed.Comment: 7 pages, talk at ``Spin-Statistics Connection and Commutation
Relations'' Capri 200
Random Attractor for Stochastic Wave Equation with Arbitrary Exponent and Additive Noise on
Asymptotic random dynamics of weak solutions for a damped stochastic wave
equation with the nonlinearity of arbitrarily large exponent and the additive
noise on is investigated. The existence of a pullback random
attractor is proved in a parameter region with a breakthrough in proving the
pullback asymptotic compactness of the cocycle with the quasi-trajectories
defined on the integrable function space of arbitrary exponent and on the
unbounded domain of arbitrary dimension
The effects of optically induced non-Abelian gauge field in cold atoms
We show that degenerate dark states can be generated by coupling
-fold degenerate ground states and a common excited state with laser
fields. Interferences between light waves with different frequencies can
produce laser fields with time-dependent amplitudes, which can induce not only
U(N) non-Abelian vector fields but also the scalar ones for the adiabatic
motion of atoms in such laser fields. As an example, a time-periodic gauge
potential is produced by applying specific laser fields to a tripod system.
Some features of the Landau levels and the ground-state phase diagram of a
rotating Bose-Einstein condensate for a concrete gauge field are also
discussed.Comment: Revtex 6 pages, 2 figures, version to be published in PR
Infinite Volume of Noncommutative Black Hole Wrapped by Finite Surface
The volume of a black hole under noncommutative spacetime background is found
to be infinite, in contradiction with the surface area of a black hole, or its
Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result
rules out the possibility of interpreting the entropy of a black hole by
counting the number of modes wrapped inside its surface if the final
evaporation stage can be properly treated. It implies the statistical
interpretation for the BH entropy can be independent of the volume, provided
spacetime is noncommutative. The effect of radiation back reaction is found to
be small and doesn't influence the above conclusion
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