On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current
Confluentes Mathematici, Tome 3 (2011) no. 2, pp. 237-251.
Publié le :
DOI : 10.1142/S1793744211000308
@article{CML_2011__3_2_237_0,
     author = {Helffer, Bernard},
     title = {On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current},
     journal = {Confluentes Mathematici},
     pages = {237--251},
     publisher = {World Scientific Publishing Co Pte Ltd},
     volume = {3},
     number = {2},
     year = {2011},
     doi = {10.1142/S1793744211000308},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1142/S1793744211000308/}
}
TY  - JOUR
AU  - Helffer, Bernard
TI  - On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current
JO  - Confluentes Mathematici
PY  - 2011
SP  - 237
EP  - 251
VL  - 3
IS  - 2
PB  - World Scientific Publishing Co Pte Ltd
UR  - http://archive.numdam.org/articles/10.1142/S1793744211000308/
DO  - 10.1142/S1793744211000308
LA  - en
ID  - CML_2011__3_2_237_0
ER  - 
%0 Journal Article
%A Helffer, Bernard
%T On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current
%J Confluentes Mathematici
%D 2011
%P 237-251
%V 3
%N 2
%I World Scientific Publishing Co Pte Ltd
%U http://archive.numdam.org/articles/10.1142/S1793744211000308/
%R 10.1142/S1793744211000308
%G en
%F CML_2011__3_2_237_0
Helffer, Bernard. On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current. Confluentes Mathematici, Tome 3 (2011) no. 2, pp. 237-251. doi : 10.1142/S1793744211000308. http://archive.numdam.org/articles/10.1142/S1793744211000308/

[1] Y. Almog, The motion of vortices in superconductors under the action of electric currents, talk at the CRM in Montreal (2008).

[2] Y. Almog, The stability of the normal state of superconductors in the presence of electric currents, Siam J. Math. Anal. 40 (2008) 824–850.

[3] Y. Almog, B. Helffer and X. Pan, Superconductivity near the normal state under the action of electric currents and induced magnetic field in R2 , Commun. Math. Phys. 300 (2010) 147–184.

[4] Y. Almog, B. Helffer and X. Pan, Superconductivity near the normal state in a half- plane under the action of a perpendicular electric current and an induced magnetic field, to appear in Trans. AMS.

[5] P. Bauman, H. Jadallah and D. Phillips, Classical solutions to the time-dependent Ginzburg–Landau equations for a bounded superconducting body in a vacuum, J. Math. Phys. 46 (2005) 095104.

[6] W. Bordeaux-Montrieux, Estimation de résolvante et construction de quasi-modes près du bord du pseudospectre, preprint 2010.

[7] L. Boulton, Non-self-adjoint harmonic oscillator, compact semigroups and pseudo- spectra, J. Operator Theory 47 (2002) 413–429.

[8] B. Davies, Linear Operators and Their Spectra, Cambridge Studies in Advanced Mathematics (Cambridge Univ. Press, 2007).

[9] B. Davies, Wild spectral behaviour of anharmonic oscillators, Bull. London Math. Soc. 32 (2000) 432–438.

[10] E. B. Davies and A. B. J. Kuijlaars, Spectral asymptotics of the non-self-adjoint harmonic oscillator, J. London Math. Soc. 70 (2004) 420–426.

[11] N. Dencker, J. Sjöstrand and M. Zworski, Pseudospectra of semiclassical (pseudo)differential operators, Comm. Pure Appl. Math. 57 (2004) 384–415.

[12] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations (Springer-Verlag, 2000).

[13] S. Fournais and B. Helffer, Spectral Methods in Surface Superconductivity, Progress in non linear PDE 77 (Birkhäuser, 2010).

[14] B. Helffer, Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, No. 1336 (Springer, 1988).

[15] B. Helffer, The montgomery model revisited, Colloq. Math. 118 (2010) 391–400.

[16] B. Helffer, On spectral problems related to a time dependent model in superconduc- tivity with electric current, Proc. Evian Conference (June, 2009), preprint.

[17] B. Helffer and F. Nier, Hypoelliptic Estimates and Spectral Theory for Fokker–Planck Operators and Witten Laplacians, Lecture Notes in Mathematics, No. 1862 (Springer- Verlag, 2004).

[18] B. Helffer and J. Sjöstrand, From resolvent bounds to semi-groups bounds, in [23].

[19] R. Henry, Analyse spectrale pour l’opérateur de Airy complexe et applications, Master Thesis, Université Paris-Sud (September, 2010).

[20] B. I. Ivlev and N. B. Kopnin, Electric currents and resistive states in thin supercon- ductors, Adv. Phys. 33 (1984) 47–114.

[21] J. Martinet, Sur les propriétés spectrales d’opérateurs non-autoadjoints provenant de la mécanique des fluides. Thèse de doctorat de l’Université Paris-Sud, December, 2009.

[22] J. Sjöstrand, Resolvent estimates for non-self-adjoint operators via semigroups, arXiv: 0906.0094.

[23] J. Sjöstrand, Spectral properties for non self-adjoint differential operators, Lecture notes for Evian, 2009, arXiv:1002.4844v1.

[24] L. N. Trefethen, Pseudospectra of linear operators, SIAM Rev. 39 (1997) 383–406.

[25] L. N. Trefethen and M. Embree, Spectra and Pseudospectra, A course in three volumes (Princeton Univ. Press, 2005).

[26] C. Villani, Hypocoercivity, Memoirs of the AMS 202 (Amer. Math. Soc., 2009), No. 950.

Cité par Sources :