Exponential of a hamiltonian in large subsets of a lattice and applications
Nourrigat, J.
Journées équations aux dérivées partielles, (2005), p. 1-9 / Harvested from Numdam
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Publié le : 2005-01-01
DOI : https://doi.org/10.5802/jedp.21 
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     author = {Nourrigat, J.},
     title = {Exponential of a hamiltonian in large subsets of a lattice and applications},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2005},
     pages = {1-9},
     doi = {10.5802/jedp.21},
     mrnumber = {2352777},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2005____A9_0}
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Nourrigat, J. Exponential of a hamiltonian in large subsets of a lattice and applications. Journées équations aux dérivées partielles,  (2005), pp. 1-9. doi : 10.5802/jedp.21. http://gdmltest.u-ga.fr/item/JEDP_2005____A9_0/

[1] S. ALBEVERIO, Y. KONDRATIEV, T. PASUREK, M. RÖCKNER, Euclidean Gibbs states of quantum crystals. Moscow Math. Journal. 1, No 3, (2001), p. 307-313. | MR 1877595 | Zbl 0993.82006

[2] L. AMOUR, M. BEN-ARTZI, Global existence and decay for viscous Hamilton-Jacobi equations, Nonlinear Analysis: Theory, Methods and Applications, 31, 5-6, (1998), 621-628. | MR 1487850 | Zbl 1023.35049

[3] L. AMOUR, C. CANCELIER, P. LEVY-BRUHL and J. NOURRIGAT, Thermodynamic limits for a quantum crystal by heat kernel methods. Université de Reims, 2003, and mp-arc 03.541.

[4] L. AMOUR, C. CANCELIER, P. LEVY-BRUHL and J. NOURRIGAT, States of a one dimensional quantum crystal. C. R. Math. Acad. Sci. Paris, 336 (2003), no. 12, 981-984. | MR 1993966 | Zbl 1052.82004

[5] L. AMOUR, Ph. KERDELHUE, J. NOURRIGAT. Calcul pseudodifférentiel en grande dimension. Asymptot. Anal. 26 (2001), no. 2, 135-161. | MR 1832582 | Zbl 0981.35108

[6] N. ASHCROFT, D. MERMIN, Solid State Physics. Saunders College . Fort Worth, 1976.

[7] V. BACH, J.S. MÖLLER, Correlation at low temperature. I. Exponential decay. J. Funct. Anal., 203 (2003), no. 1, 93-148. | MR 1996869 | Zbl 1031.82003

[8] J. BELLISSARD, R. HOEGH-KROHN, Compactness and the maximal Gibbs state for random Gibbs fields on a lattice. Comm. Math. Phys, 84 (1982), no. 3, 297-327. | MR 667405 | Zbl 0495.60057

[9] O. BRATTELI, D.W. ROBINSON, Operator algebras and quantum statistical mechanics. 2. Equilibrium states. Models in quantum statistical mechanics. Second edition. Texts and Monographs in Physics. Springer-Verlag, Berlin, 1997. | MR 1441540 | Zbl 0903.46066

[10] L. GROSS, Decay of correlations in classical lattice models at high temperature. Comm. in Math. Phys, 68 (1979), 1, 9-27. | MR 539733 | Zbl 0442.60097

[11] B. HELFFER, Semiclassical analysis, Witten Laplacians, and statistical mechanics. Series on Partial Differential Equations and Applications, 1. World Scientific Publishing Co., Inc., River Edge, NJ, 2002. | MR 1936110 | Zbl 1046.82001

[12] B. HELFFER, Remarks on the decay of correlations and Witten Laplacians, Brascamp-Lieb inequalities and semi-classical limit, J. Funct. Analysis, 155, (2), (1998), p.571-586. | MR 1624506 | Zbl 0921.35141

[13] B. HELFFER, Remarks on the decay of correlations and Witten Laplacians, II. Analysis of the dependence of the interaction. Rev. Math. Phys. 11 (3), (1999), p.321-336. | MR 1688446 | Zbl 1054.82002

[14] B. HELFFER, Remarks on the decay of correlations and Witten Laplacians, III. Applications to the logarithmic Sobolev inequalities. Ann. I.H.P. Proba. Stat, 35, (4), (1999), p.483-508. | Numdam | MR 1702239 | Zbl 1055.82004

[15] B. HELFFER, J. SJÖSTRAND, On the correlation for Kac like models in the convex case, J. Stat. Physics, 74 (1, 2), (1994), p.349-409. | MR 1257821 | Zbl 0946.35508

[16] R. A. MINLOS, Introduction to Mathematical Statistical Physics. University Lecture Series 19, American Mathematical Society, Providence, 2000. | MR 1727910 | Zbl 0998.82501

[17] R. A. MINLOS, E.A. PECHERSKY, V. A. ZAGREBNOV, Analyticity of the Gibbs states for a quantum anharmonic crystal: no order parameter. Ann. Henri Poincaré 3 (2002), p. 921-938. | MR 1937608 | Zbl 1016.82005

[18] J. NOURRIGAT, Ch. ROYER, Thermodynamic limits for Hamiltonians defined as pseudo-differential operators. Comm. Partial Differential Equations, 29 (2004), no. 3-4, 383-417. | MR 2041601 | Zbl 1072.35212

[19] D. ROBERT, Autour de l’approximation semiclassique. Progress in Mathematics, 68. Birkhauser Boston, Inc., Boston, MA, 1987. | MR 897108 | Zbl 0621.35001

[20] Ch. ROYER, Formes quadratiques et calcul pseudodifférentiel en grande dimension. Prépublication 00.05. Reims, 2000.

[21] D. RUELLE, Statistical Mechanics: rigorous results. Addison-Wesley, 1969. | MR 289084 | Zbl 0177.57301

[22] B. SIMON, The statistical Mechanics of lattice gases. Vol. I. Princeton Series in Physics. Princeton, 1993. | MR 1239893 | Zbl 0804.60093

[23] J. SJÖSTRAND, Evolution equations in a large number of variables, Math. Nachr. 166 (1994), 17-53. | MR 1273320 | Zbl 0837.35061

[24] J. SJÖSTRAND, Correlation asymptotics and Witten Laplacians, Algebra i Analiz, 8 (1996), 1, 160-191. Translation in St Petersburg Math. Journal, 8 (1997), 1, 123-147. | MR 1392018 | Zbl 0877.35084

[25] J. SJÖSTRAND, Complete asymptotics for correlations of Laplace integrals in the semiclassical limit. Memoires S.M.F., 83, (2000). | Numdam | Zbl 1044.81046