José Noronha | Universidades Lusíada (original) (raw)
Papers by José Noronha
Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap, Jan 2016
We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperat... more We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.
Representations for the derivative at zero and finite parts of the Barnes zeta function, Mar 2017
We provide new representations for the finite parts at the poles and the derivative at zero of th... more We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an integral representation for the finite parts at the poles. Similar results are derived for an associated function, which we term homogeneous Barnes zeta function. Our expressions immediately yield analogous representations for the logarithm of the Barnes Gamma function, including the particular case also known as multiple Gamma function.
We study the finite size effects on ideal Bose gas thermodynamics (and where applicable Bose-Eins... more We study the finite size effects on ideal Bose gas thermodynamics (and where applicable Bose-Einstein condensation) in several systems with quadratic particle energy levels, namely the Einstein Universe, the one-dimensional box and the three-dimensional flat box (1D box cross infinite plane). The Mellin-Barnes transform technique is used to obtain analytical approximations to thermodynamic quantities, providing an analytical description of the
Bose-Einstein condensation in the three-sphere and in the infinite slab: Analytical results, Sep 2013
We study the finite size effects on Bose-Einstein condensation (BEC) of an ideal non-relativisti... more We study the finite size effects on Bose-Einstein condensation (BEC) of an ideal
non-relativistic Bose gas in the three-sphere (spatial section of the Einstein
universe) and in a partially finite box which is infinite in two of the spatial
directions (infinite slab). Using the framework of grand-canonical statistics, we
consider the number of particles, the condensate fraction and the specific heat.
After obtaining asymptotic expansions for large system size, which are valid
throughout the BEC regime, we describe analytically how the thermodynamic
limit behaviour is approached. In particular, in the critical region of the BEC
transition, we express the chemical potential and the specific heat as simple
explicit functions of the temperature, highlighting the effects of finite size. These
effects are seen to be different for the two different geometries. We also consider
the Bose gas in a one-dimensional box, a system which does not possess BEC
in the sense of a phase transition even in the infinite volume limit.
The specific heat of a trapped Fermi gas: an analytical approach, Mar 2000
We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a ... more We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kBT≳ℏwx,y,z and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.
Comment on “Bose-Einstein condensation with a finite number of particles in a power-law trap”, Jul 2015
In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an analytical finite-size e... more In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an analytical finite-size expansion for the Bose-Einstein condensation critical temperature of an ideal Bose gas in a generic power-law trap. In the case of a harmonic trap, this expansion adds higher-order terms to the well-known first-order correction. We point out a delicate point in connection to these results, showing that the claims of Jaouadi et al. should be treated with caution. In particular, for a harmonic trap, the given expansion yields results that, depending on what is considered to be the critical temperature of the finite system, do not generally improve on the established first-order correction. For some nonharmonic traps, the results differ at first order from other results in the literature.
Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap, Jan 2016
We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperat... more We obtain second and higher order corrections to the shift of the Bose-Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.
Representations for the derivative at zero and finite parts of the Barnes zeta function, Mar 2017
We provide new representations for the finite parts at the poles and the derivative at zero of th... more We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an integral representation for the finite parts at the poles. Similar results are derived for an associated function, which we term homogeneous Barnes zeta function. Our expressions immediately yield analogous representations for the logarithm of the Barnes Gamma function, including the particular case also known as multiple Gamma function.
We study the finite size effects on ideal Bose gas thermodynamics (and where applicable Bose-Eins... more We study the finite size effects on ideal Bose gas thermodynamics (and where applicable Bose-Einstein condensation) in several systems with quadratic particle energy levels, namely the Einstein Universe, the one-dimensional box and the three-dimensional flat box (1D box cross infinite plane). The Mellin-Barnes transform technique is used to obtain analytical approximations to thermodynamic quantities, providing an analytical description of the
Bose-Einstein condensation in the three-sphere and in the infinite slab: Analytical results, Sep 2013
We study the finite size effects on Bose-Einstein condensation (BEC) of an ideal non-relativisti... more We study the finite size effects on Bose-Einstein condensation (BEC) of an ideal
non-relativistic Bose gas in the three-sphere (spatial section of the Einstein
universe) and in a partially finite box which is infinite in two of the spatial
directions (infinite slab). Using the framework of grand-canonical statistics, we
consider the number of particles, the condensate fraction and the specific heat.
After obtaining asymptotic expansions for large system size, which are valid
throughout the BEC regime, we describe analytically how the thermodynamic
limit behaviour is approached. In particular, in the critical region of the BEC
transition, we express the chemical potential and the specific heat as simple
explicit functions of the temperature, highlighting the effects of finite size. These
effects are seen to be different for the two different geometries. We also consider
the Bose gas in a one-dimensional box, a system which does not possess BEC
in the sense of a phase transition even in the infinite volume limit.
The specific heat of a trapped Fermi gas: an analytical approach, Mar 2000
We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a ... more We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kBT≳ℏwx,y,z and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.
Comment on “Bose-Einstein condensation with a finite number of particles in a power-law trap”, Jul 2015
In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an analytical finite-size e... more In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an analytical finite-size expansion for the Bose-Einstein condensation critical temperature of an ideal Bose gas in a generic power-law trap. In the case of a harmonic trap, this expansion adds higher-order terms to the well-known first-order correction. We point out a delicate point in connection to these results, showing that the claims of Jaouadi et al. should be treated with caution. In particular, for a harmonic trap, the given expansion yields results that, depending on what is considered to be the critical temperature of the finite system, do not generally improve on the established first-order correction. For some nonharmonic traps, the results differ at first order from other results in the literature.