The BCS Critical Temperature for Potentials with Negative Scattering Length

AbstractWe show that the energy gap for the BCS gap equation is $$\begin{aligned} \varXi = \mu \left( 8 {\mathrm{e}}^{-2} + o(1)\right) \exp \left( \frac{\pi }{2\sqrt{\mu } a}\right) \end{aligned}$$ Ξ = μ 8 e - 2 + o ( 1 ) exp π 2 μ a in the low density limit $$\mu \rightarrow 0$$ μ → 0 . Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.

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A systematic neutron reflectometry study on hydrogen absorption in thin Mg1-xAlx alloy films Special issue on Neutron Scattering in Canada.

Canadian Journal of Physics ◽

10.1139/p09-085 ◽

2010 ◽

Vol 88 (10) ◽

pp. 723-728 ◽

Cited By ~ 3

Author(s):

H. Fritzsche ◽

E. Poirier ◽

J. Haagsma ◽

C. Ophus ◽

E. Luber ◽

...

Keyword(s):

Hydrogen Absorption ◽

Scattering Length ◽

Catalyst Layer ◽

Neutron Reflectometry ◽

Hydrogen Distribution ◽

Hydrogen Atoms ◽

Alloy Films ◽

Negative Scattering Length ◽

Insight Into ◽

Optimum Alloy

In this article, we show how neutron reflectometry (NR) can provide deep insight into the absorption and desorption properties of commercially promising hydrogen storage materials. NR benefits from the large negative scattering length of hydrogen atoms, which changes the reflectivity curve substantially, so that NR can determine not only the total amount of stored hydrogen but also the hydrogen distribution along the film normal, with nanometer resolution. To use NR, the samples must have smooth surfaces, and the film thickness should range between 10 and 200 nm. We performed a systematic study on thin Mg1–xAlx alloy films (x = 0.2, 0.3, 0.4, 0.67) capped with a Pd catalyst layer. Our NR experiments showed that Mg0.7Al0.3 is the optimum alloy composition with the highest amount of stored hydrogen and the lowest desorption temperature. All the thin films expand by about 20% because of hydrogen absorption, and the hydrogen is stored only in the MgAl layer with no hydrogen content in the Pd layer.

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BOSE-EINSTEIN CONDENSATION OF ATOMS WITH ATTRACTIVE INTERACTION

International Journal of Modern Physics B ◽

10.1142/s0217979299000515 ◽

1999 ◽

Vol 13 (05n06) ◽

pp. 625-631 ◽

Cited By ~ 42

Author(s):

N. AKHMEDIEV ◽

M. P. DAS ◽

A. V. VAGOV

Keyword(s):

Statistical Physics ◽

Scattering Length ◽

Stationary Solutions ◽

Attractive Potential ◽

Einstein Condensation ◽

Pitaevskii Equation ◽

Bose Einstein Condensation ◽

Three Body ◽

Negative Scattering Length ◽

Bose Einstein

We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.

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Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

Applied Physics Research ◽

10.5539/apr.v9n5p96 ◽

2017 ◽

Vol 9 (5) ◽

pp. 96

Author(s):

M. Serhan

Keyword(s):

Low Temperatures ◽

Chemical Potential ◽

Scattering Length ◽

Einstein Condensation ◽

Pitaevskii Equation ◽

Atomic Gases ◽

Bose Einstein Condensation ◽

Gaussian Type ◽

Negative Scattering Length ◽

Bose Einstein

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

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CRITICAL TEMPERATURE OF AN INTERACTING BOSE GAS IN A GENERIC POWER-LAW POTENTIAL

International Journal of Modern Physics B ◽

10.1142/s0217979202010348 ◽

2002 ◽

Vol 16 (16) ◽

pp. 2185-2190 ◽

Cited By ~ 10

Author(s):

LUCA SALASNICH

Keyword(s):

Critical Temperature ◽

Power Law ◽

Size Effects ◽

Scattering Length ◽

Analytical Formula ◽

Finite Size ◽

Bose Gas ◽

Finite Size Effects ◽

First Order ◽

Power Law Exponent

We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as Nn/3(n+2), where N is the number of Bosons and n is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent n. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as N-2n/3(n+2).

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