33,538 research outputs found

### Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field

### 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

### 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

### 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 $\rho_{12}$ described by a $4\times 4$ covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix $\textbf{V}_1$ 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 $n$-partite Gaussian state is given and it is demonstrated that the $n-1$
system state conditioned to a partial parity projection is given by a
covariance matrix such as its $2 \times 2$ block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio

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