370 research outputs found
q-thermostatistics and the analytical treatment of the ideal Fermi gas
We discuss relevant aspects of the exact q-thermostatistical treatment for an
ideal Fermi system. The grand canonical exact generalized partition function is
given for arbitrary values of the nonextensivity index q, and the ensuing
statistics is derived. Special attention is paid to the mean occupation numbers
of single-particle levels. Limiting instances of interest are discussed in some
detail, namely, the thermodynamic limit, considering in particular both the
high- and low-temperature regimes, and the approximate results pertaining to
the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1).
We compare our findings with previous Tsallis' literature.Comment: v2: comparison with conventional results and validity of
approximations clarified, typos corrected; accepted for publication in
Physica
Equipartition and Virial theorems in a nonextensive optimal Lagrange multipliers scenario
We revisit some topics of classical thermostatistics from the perspective of
the nonextensive optimal Lagrange multipliers (OLM), a recently introduced
technique for dealing with the maximization of Tsallis' information measure. It
is shown that Equipartition and Virial theorems can be reproduced by Tsallis'
nonextensive formalism independently of the value of the nonextensivity index.Comment: 13 pages, no figure
Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential
A novel realization of the classical SU(2) algebra is introduced for the
Dirac relativistic hydrogen atom defining a set of operators that, besides,
allow the factorization of the problem. An extra phase is needed as a new
variable in order to define the algebra. We take advantage of the operators to
solve the Dirac equation using algebraic methods. To acomplish this, a similar
path to the one used in the angular momentum case is employed; hence, the
radial eigenfuntions calculated comprise non unitary representations of the
algebra. One of the interesting properties of such non unitary representations
is that they are not labeled by integer nor by half-integer numbers as happens
in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math.
Phy
Nonextensive thermodynamic relations
The generalized zeroth law of thermodynamics indicates that the physical
temperature in nonextensive statistical mechanics is different from the inverse
of the Lagrange multiplier, beta. This leads to modifications of some of
thermodynamic relations for nonextensive systems. Here, taking the first law of
thermodynamics and the Legendre transform structure as the basic premises, it
is found that Clausius definition of the thermodynamic entropy has to be
appropriately modified, and accordingly the thermodynamic relations proposed by
Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be
rectified. It is shown that the definition of specific heat and the equation of
state remain form invariant. As an application, the classical gas model is
reexamined and, in marked contrast with the previous result obtained by Abe
[Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical
temperature and the unphysical pressure, the specific heat and the equation of
state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is
modified and some additional comments are mad
Ideal gas in nonextensive optimal Lagrange multipliers formalism
Based on the prescription termed the optimal Lagrange multipliers formalism
for extremizing the Tsallis entropy indexed by q, it is shown that key aspects
of the treatment of the ideal gas problem are identical in both the
nonextensive and extensive cases.Comment: 5 pages, no figure
Tsallis' entropy maximization procedure revisited
The proper way of averaging is an important question with regards to Tsallis'
Thermostatistics. Three different procedures have been thus far employed in the
pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP)
normalization procedure, exhibits clear advantages with respect to earlier
ones. In this work, we advance a distinct (from the TMP-one) way of handling
the Lagrange multipliers involved in the extremization process that leads to
Tsallis' statistical operator. It is seen that the new approach considerably
simplifies the pertinent analysis without losing the beautiful properties of
the Tsallis-Mendes-Plastino formalism.Comment: 17 pages, no figure
Thermodynamics' 0-th-Law in a nonextensive scenario
Tsallis' thermostatistics is by now recognized as a new paradigm for
statistical mechanical considerations. However, it is still affected by a
serious hindrance: the generalization of thermodynamics' zero-th law to a
nonextensive scenario is plagued by difficulties. Here we show how to overcome
this problem.Comment: 4 pages, latex; added references for section
Gauge Independence and Relativistic Electron Dispersion Equation in Dense Media
We discuss the gauge parameter dependence of particle spectra in statistical
quantum electrodynamics and conclude that the electron spectrum is
gauge-parameter dependent. The physical spectrum being obtained in the Landau
gauge, which leads to gauge invariance in a restricted class of gauge
transformations.Comment: Style corrections 16 pages, three figures, RevTe
Lie algebroid structures on a class of affine bundles
We introduce the notion of a Lie algebroid structure on an affine bundle
whose base manifold is fibred over the real numbers. It is argued that this is
the framework which one needs for coming to a time-dependent generalization of
the theory of Lagrangian systems on Lie algebroids. An extensive discussion is
given of a way one can think of forms acting on sections of the affine bundle.
It is further shown that the affine Lie algebroid structure gives rise to a
coboundary operator on such forms. The concept of admissible curves and
dynamical systems whose integral curves are admissible, brings an associated
affine bundle into the picture, on which one can define in a natural way a
prolongation of the original affine Lie algebroid structure.Comment: 28 page
A control problem arising in the process of waste water purification
AbstractIn this paper we state and solve an optimal control problem arisen from the management of the sewage disposal which is dumped into the sea through submarine outfalls. Firstly, we fix oxygen and amount of organic matter as water quality indicators and we state a partial differential equations model to simulate them in a domain occupied by shallow waters. Constraints about water quality and economic objectives lead us to a pointwise optimal control problem with state and control constraints. (The theoretical analysis of the problem has been developed by the authors in (Martinez et al., C. R. Acad. Sci. Paris, Serie I 328 (1999) 35.) (Martinez et al., Preprint, Dept. Matematica Aplicada, Univ. Santiago de Compostela, Spain, 1998.)). We deal with the problem by using time and space discretizations and we propose two algorithms for the numerical resolution of the discretized problem. Finally, we give numerical results obtained by applying the described techniques for a realistic problem posed in the rı́a of Vigo (Spain)
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