793 research outputs found
On -functions with bounded spectrum
We consider the class of functions in ,
whose Fourier transform has bounded support. We obtain a description of
continuous maps such that
for every function .
Only injective affine maps have this property
Conductance Phases in Aharonov-Bohm Ring Quantum Dots
The regimes of growing phases (for electron numbers N~0-8) that pass into
regions of self-returning phases (for N>8), found recently in quantum dot
conductances by the Weizmann group are accounted for by an elementary Green
function formalism, appropriate to an equi-spaced ladder structure (with at
least three rungs) of electronic levels in the quantum dot. The key features of
the theory are physically a dissipation rate that increases linearly with the
level number (and tentatively linked to coupling to longitudinal optical
phonons) and a set of Fano-like meta-stable levels, which disturb the
unitarity, and mathematically the change over of the position of the complex
transmission amplitude-zeros from the upper-half in the complex gap-voltage
plane to the lower half of that plane. The two regimes are identified with
(respectively) the Blaschke-term and the Kramers-Kronig integral term in the
theory of complex variables.Comment: 20 pages, 4 figure
Photon wave mechanics and position eigenvectors
One and two photon wave functions are derived by projecting the quantum state
vector onto simultaneous eigenvectors of the number operator and a recently
constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples
spin and orbital angular momentum. While only the Landau-Peierls wave function
defines a positive definite photon density, a similarity transformation to a
biorthogonal field-potential pair of positive frequency solutions of Maxwell's
equations preserves eigenvalues and expectation values. We show that this real
space description of photons is compatible with all of the usual rules of
quantum mechanics and provides a framework for understanding the relationships
amongst different forms of the photon wave function in the literature. It also
gives a quantum picture of the optical angular momentum of beams that applies
to both one photon and coherent states. According to the rules of qunatum
mechanics, this wave function gives the probability to count a photon at any
position in space.Comment: 14 pages, to be published in Phys. Rev.
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604.
Discussion expanded to include the case of Hamiltonians with an infinitely
degenerate spectru
On the nonlinearity interpretation of q- and f-deformation and some applications
q-oscillators are associated to the simplest non-commutative example of Hopf
algebra and may be considered to be the basic building blocks for the symmetry
algebras of completely integrable theories. They may also be interpreted as a
special type of spectral nonlinearity, which may be generalized to a wider
class of f-oscillator algebras. In the framework of this nonlinear
interpretation, we discuss the structure of the stochastic process associated
to q-deformation, the role of the q-oscillator as a spectrum-generating algebra
for fast growing point spectrum, the deformation of fermion operators in
solid-state models and the charge-dependent mass of excitations in f-deformed
relativistic quantum fields.Comment: 11 pages Late
Momentum transport in TCV across sawteeth events
Abstract only
Observation of seasonal variation of atmospheric multiple-muon events in the MINOS Near and Far Detectors
We report the first observation of seasonal modulations in the rates of cosmic ray multiple-muon events at two underground sites, the MINOS Near Detector with an overburden of 225 mwe, and the MINOS Far Detector site at 2100 mwe. At the deeper site, multiple-muon events with muons separated by more than 8 m exhibit a seasonal rate that peaks during the summer, similar to that of single-muon events. In contrast and unexpectedly, the rate of multiple-muon events with muons separated by less than 5-8 m, and the rate of multiple-muon events in the smaller, shallower Near Detector, exhibit a seasonal rate modulation that peaks in the winter
Precision measurement of the speed of propagation of neutrinos using the MINOS detectors
We report a two-detector measurement of the propagation speed of neutrinos over a baseline of 734 km. The measurement was made with the NuMI beam at Fermilab between the near and far MINOS detectors. The fractional difference between the neutrino speed and the speed of light is determined to be (v/c - 1) = (1.0 +/- 1.1) x 10(-6), consistent with relativistic neutrinos
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