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29 results on '"Crouzeix, M."'

1. Two-Cooper-pair problem and the Pauli exclusion principle

Author

Pogosov, W. V., Combescot, M., and Crouzeix, M.

Subjects
Condensed Matter - Superconductivity, Condensed Matter - Quantum Gases
Abstract

While the one-Cooper pair problem is now a textbook exercise, the energy of two pairs of electrons with opposite spins and zero total momentum has not been derived yet, the exact handling of Pauli blocking between bound pairs being not that easy for N=2 already. The two-Cooper pair problem however is quite enlightening to understand the very peculiar role played by the Pauli exclusion principle in superconductivity. Pauli blocking is known to drive the change from 1 to $N$ pairs, but no precise description of this continuous change has been given so far. Using Richardson procedure, we here show that Pauli blocking increases the free part of the two-pair ground state energy, but decreases the binding part when compared to two isolated pairs - the excitation gap to break a pair however increasing from one to two pairs. When extrapolated to the dense BCS regime, the decrease of the pair binding while the gap increases strongly indicates that, at odd with common belief, the average pair binding energy cannot be of the order of the gap., Comment: 9 pages, no figures, final version

Published
2009
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14. THE NUMERICAL RANGE IS A (1 + √2)-SPECTRAL SET.

Author

CROUZEIX, M. and PALENCIA, C.

Subjects
*NUMERICAL range, *LINEAR operators, *MATRICES (Mathematics), *HILBERT space, *BANACH spaces
Abstract

It is shown that the numerical range of a linear operator on a Hilbert space is a (complete) (1+√2)-spectral set. The proof relies, among other things, on the behavior of the Cauchy transform of the conjugates of holomorphic functions. [ABSTRACT FROM AUTHOR]

Published
2017
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15. BIT Numerical Mathematics: Editorial

Author

Åhlander, K., Allen, E., Aptekarev, A. I., Arioli, M., Arnold, M., Asadzadeh, M., Baglama, J., Bailly, C., Baker, C., Bartels, S., Bendali, A., Benzi, M., Berntsson, F., Breda, D., Brunner, H., SERRA CAPIZZANO, Stefano, Cash, J., Chan, R., Chandrasekaran, S., Chang, X. W., Chern, I. L., Crouzeix, M., Van Daele, M., Damhaug, A. C., Davis, T., Davydov, O., Dieci, L., Eriksson, J., Eriksson, L. E., Espelid, T., Estep, D., Fontich, E., Ford, N., Fornberg, B., Foster, L., Frank, J., Gander, W., Garća Palomares, U. M., Giraud, L., Greenbaum, A., Gripenberg, G., Gulliksson, M., Gustafsson, B., Gustafsson, N., Hairer, E., Hanke, M., Heggernes, P., Van Emden Henson, N., Hesthaven, J., Sanz, I. H., Hochbruck, M., Hochstenbach, M., Huckle, T., Kamvar, S., Kaps, P., Karlsen, K. H., Klarbring, A., Knizhnerman, L., Kopotum, K., Korotov, S., Kuijlaars, A., Kværnø, A., Langtangen, H. P., Larsson, E., Lenarduzzi, L., Lewalle, J., R. C., Li, Lin, P., Malyshev, A., Marletta, M., Mazzia, F., Mehl, C., Moore, P., Müller, B., Mørken, K., Neytcheva, M., Niederman, L., Olver, S., Ostrouchov, G., Pareschi, L., Parlett, B. N., Pralet, S., Raghavan, P., Rannacher, R., Runborg, O., Ruuth, S., Sand, J., Saunders, M., Sauter, S., Savaré, G., Shen, W. Z., Sidi, A., Spiteri, R., Steihaug, T., Stenger, F., Stoer, J., Strakoš, Z., and Tang, T.

Subjects
Computational Mathematics, Applied Mathematics, Computer Graphics and Computer-Aided Design, Software
Published
2005

22. Structure Microscopique d'un Melange Binaire de Cristaux Liquides Etude par Resonance Paramagnetique Electronique

Author

Barbarin, F., Chausse, J. P., Crouzeix, M., and Germain, J. P.

Abstract

The microscopic structure of thermotropic liquid crystals is experimentally investigated. The behavior of aromatic cores and aliphatic chains are analysed when defects are introduced in the mesophase as follows: to a liquid crystal having long aliphatic chains (40.8) is added one having shorter chains (40.2). An E.S.R. study is performed using two nitroxide probes: in smectic phases the first one is localized close to the aromatic cores while the other remains in the vicinity of aliphatic chains. In the nematic phases, when concentration in 40.2 varies, the orientational potential is found to be homogeneous because of the molecular translation diffusion. For high ordered smectic phases (SB) the potential does not depend on the concentration of 40.2 while introducing defects close to the aliphatic chains make the corresponding potential vary in a significant manner. In the SB phase die effect observed by E.S.R. (decrease of the order parameter of probe II) is more significant than the splitting variation previously observed by D.M.R. These results are consistent with a "partial rigidity" of aliphatic chains (interpenetrating structure of layers, intrinsic rigidity, etc.), limiting the new possible conformations in the mixture and with a localization of the probes corresponding to a low orientational potential (the "aliphatic density defects").

Published
1983
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29. Energy of N Cooper pairs by analytically solving the Richardson-Gaudin equations for conventional superconductors.

Author

Crouzeix M and Combescot M

Abstract

This Letter provides the solution to a yet unsolved basic problem of solid state physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the N-pair energy depends on N as N(N-1) only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.

Published
2011
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