820 research outputs found
Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"
It is shown by examples that the position uncertainty on a circle, proposed
recently by Kowalski and Rembieli\'nski [J. Phys. A 35 (2002) 1405] is not
consistent with the state localization. We argue that the relevant
uncertainties and uncertainty relations (UR's) on a circle are that based on
the Gram-Robertson matrix. Several of these generalized UR's are displayed and
related criterions for squeezed states are discussed.Comment: 5 pages, LaTex2e, 3 figures.ep
Remarks on the Extended Characteristic Uncertainty Relations
Three remarks concerning the form and the range of validity of the
state-extended characteristic uncertainty relations (URs) are presented. A more
general definition of the uncertainty matrix for pure and mixed states is
suggested. Some new URs are provided.Comment: LaTex, 4 pages, no figure
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some
formulas. To appear in J. Phys. A, v. 3
Uncertainty Relations in Deformation Quantization
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian
forms are generalized to an arbitrary ordered field. These results are then
applied to the case of formal power series fields, and the
Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations
in deformation quantization are found. Some conditions under which the
uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte
On misspecifications in regularity and properties of estimators
The problem of parameter estimation by the continuous time observations of a deterministic signal in white Gaussian noise is considered. The asymptotic properties of the maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter
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