Chemical potential and internal energy of the noninteracting Fermi gas in fractional-dimensional space

Panda, Subhashree; Panda, B. K.

doi:10.1007/s12043-010-0125-5

Cited by 7 publications

(2 citation statements)

References 24 publications

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“…We have derived the conditions for the extremum of the figure of merit µ is an important thermodynamic variable that describes both classical and quantum mechanical states of a system [35]. Our analysis is applicable to the case where * µ , the argument z , and the index r of the polylog can be complex [36].…”

Section: Discussionmentioning

confidence: 99%

The polylogarithm and the Lambert W functions in thermoelectrics

2011

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In this work, we determine the conditions for the extremum of the figure of merit 2 θ , in a degenerate semiconductor for thermoelectric (TE) applications. We study the variation of the function 2 θ with respect to the reduced chemical potential * µ using relations involving polylogarithms of both integral and non-integral orders. We present the relevant equations for the thermopower, thermal, and electrical conductivities that result in optimizing  2 and obtaining the extremum equations. We discuss the different cases that arise for various values of r, which depends on the type of carrier scattering mechanism present in the semiconductor. We also present the important extremum conditions for  2 obtained by extremizing the TE power factor and the thermal conductivity separately. In this case, simple functional equations, which lead to solutions in terms of the Lambert W function, result. We also present some solutions for the zeros of the polylogarithms. Our analysis allows for the possibility of considering the reduced chemical potential and the index r of the polylogarithm as complex variables.

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Section: Discussionmentioning

confidence: 99%

The polylogarithm and the Lambert W functions in thermoelectrics

2011

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“…Truly, the significance of µ has motivated the discussion of its meaning and/or importance at different levels and contexts [41][42][43][44][45][46][47][48][49][50][51][52]. For the widely discussedtextbook-case, namely the three-dimensional IFG confined by a impenetrable box potential, the chemical potential results to be a monotonic decreasing function of the temperature, diminishing from the Fermi energy, E F , at zero temperature, to the values of the ideal classical gas for temperatures much larger than k −1 B ( 2 /mλ 2 T ), where k B is the Boltzmann's constant, is the Planck's constant divided by 2π, m the mass of the particle and λ T = 2π 2 /mk B T is the thermal wavelength of de Broglie, where T denotes the system's absolute temperature.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of Low-Dimensional Trapped Fermi Gases

Sevilla

2017

Journal of Thermodynamics

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The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.

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