On the Dispersion Law of the Form $\varepsilon(p)=\hbar^2p^2/2m+\widetilde V(p)-\widetilde V(0)$ for Elementary Excitations of a Nonideal Fermi Gas in the Pair Interaction Approximation $(i\leftrightarrow j)$, $V(|x_i-x_j|)$
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 690-708.

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We give a derivation of the dispersion law $\varepsilon(p)=\hbar^2p^2/2m+\widetilde V(p)-\widetilde V(0)$, where $\widetilde V(p)$ is the Fourier transform of the pair interaction potential $V(r)$. (The interaction between particles $x_i$ and $x_j$ is $V(|x_i-x_j|)$.)
Keywords: dispersion law, elementary excitation, pair interaction
Mots-clés : Fermi gas.
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V. P. Maslov. On the Dispersion Law of the Form $\varepsilon(p)=\hbar^2p^2/2m+\widetilde V(p)-\widetilde V(0)$ for Elementary Excitations of a Nonideal Fermi Gas in the Pair Interaction Approximation $(i\leftrightarrow j)$, $V(|x_i-x_j|)$. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 690-708. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a4/

[1] N. N. Bogolyubov, “K teorii sverkhtekuchesti”, Izbrannye trudy v trekh tomakh. Tom vtoroi, Naukova Dumka, Kiev, 1970, 210–224 ; “On the theory of superfluidity”, Acad. Sci. USSR. J. Phys., 11 (1947), 23–32 | MR | Zbl | MR

[2] L. D. Landau, “K teorii sverkhtekuchesti”, Sobranie trudov, t. 2, Nauka, M., 1969, 42–46 | MR

[3] J. M. Vogels, K. Xu, C. Raman, J. R. Abo-Shaeer, W. Ketterle, “Experimental Observation of the Bogoliubov Transformation for a Bose–Einstein Condensed Gas”, preprint No 060402, Phys. Rev. Lett., 88:6 (2002) | DOI

[4] B. P. Maslov, Kvantovanie termodinamiki i ultravtorichnoe kvantovanie, In-t kompyuternykh issledovanii, M., 2001

[5] V. P. Maslov, “Kvantovanie Boltsmanovskoi entropii, pary i korrelyatsionnaya funktsiya”, TMF, 131:2 (2002), 261–277 | MR | Zbl

[6] V. P. Maslov, “O sposobe osredneniya dlya bolshogo chisla klasterov. Fazovye perekhody”, TMF, 125:2 (2000), 297–314 | MR | Zbl

[7] V. P. Maslov, “Ultravtorichnoe kvantovanie i “dukhi” v kvantovannoi entropii”, TMF, 129:3 (2001), 464–490 | MR | Zbl

[8] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1987 | MR | Zbl

[9] V. P. Maslov, O. Yu. Shvedov, Metod kompleksnogo rostka v zadache mnogikh chastits i v kvantovoi teorii polya, Editorial URSS, M., 2000

[10] V. P. Maslov, Operatornye metody, Nauka, M., 1973 | MR | Zbl