Exponential of a hamiltonian in large subsets of a lattice and applications
Nourrigat, J.1
1 Département de Mathématiques, UMR CNRS 6056, Université de Reims. B.P. 1039. 51687 Reims Cedex 2. France
Journées équations aux dérivées partielles (2005), article no. 9, 9 p.
DOI : 10.5802/jedp.21
Nourrigat, J. 1

1 Département de Mathématiques, UMR CNRS 6056, Université de Reims. B.P. 1039. 51687 Reims Cedex 2. France 
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Nourrigat, J. Exponential of a hamiltonian in large subsets of a lattice and applications. Journées équations aux dérivées partielles (2005), article  no. 9, 9 p. doi : 10.5802/jedp.21. http://www.numdam.org/articles/10.5802/jedp.21/

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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