27,908 research outputs found
Physical properties of the Schur complement of local covariance matrices
General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state described by a covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a -partite Gaussian state is given and it is demonstrated that the
system state conditioned to a partial parity projection is given by a
covariance matrix such as its block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Three-dimensional Dirac oscillator in a thermal bath
The thermal properties of the three-dimensional Dirac oscillator are
considered. The canonical partition function is determined, and the
high-temperature limit is assessed. The degeneracy of energy levels and their
physical implications on the main thermodynamic functions are analyzed,
revealing that these functions assume values greater than the one-dimensional
case. So that at high temperatures, the limit value of the specific heat is
three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match
accepted version in Europhysics Letters
The Casimir effect for the scalar and Elko fields in a Lifshitz-like field theory
In this work, we obtain the Casimir energy for the real scalar field and the
Elko neutral spinor field in a field theory at a Lifshitz fixed point (LP). We
analyze the massless and the massive case for both fields using dimensional
regularization. We obtain the Casimir energy in terms of the dimensional
parameter and the LP parameter. Particularizing our result, we can recover the
usual results without LP parameter in (3+1) dimensions presented in the
literature. Moreover, we compute the effects of the LP parameter in the thermal
corrections for the massless scalar field.Comment: 20 pages, 2 figures, some results have been modified and other
changes to the text have been made to match the accepted version in Eur.
Phys. J.
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