Exponential of a hamiltonian in large subsets of a lattice and applications
J. Nourrigat[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)
- page 1-9
- ISSN: 0752-0360
Access Full Article
topHow to cite
topNourrigat, J.. "Exponential of a hamiltonian in large subsets of a lattice and applications." Journées Équations aux dérivées partielles (2005): 1-9. <http://eudml.org/doc/10615>.
@article{Nourrigat2005,
affiliation = {Département de Mathématiques, UMR CNRS 6056, Université de Reims. B.P. 1039. 51687 Reims Cedex 2. France},
author = {Nourrigat, J.},
journal = {Journées Équations aux dérivées partielles},
keywords = {quantum Hamiltonian; large system of particles; lattice of particles; exponential and its properties},
language = {eng},
month = {6},
pages = {1-9},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Exponential of a hamiltonian in large subsets of a lattice and applications},
url = {http://eudml.org/doc/10615},
year = {2005},
}
TY - JOUR
AU - Nourrigat, J.
TI - Exponential of a hamiltonian in large subsets of a lattice and applications
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 9
LA - eng
KW - quantum Hamiltonian; large system of particles; lattice of particles; exponential and its properties
UR - http://eudml.org/doc/10615
ER -
References
top- S. ALBEVERIO, Y. KONDRATIEV, T. PASUREK, M. RÖCKNER, Euclidean Gibbs states of quantum crystals. Moscow Math. Journal.1, No 3, (2001), p. 307-313. Zbl0993.82006MR1877595
- 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. Zbl1023.35049MR1487850
- 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. Zbl1052.82004
- 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. Zbl1052.82004MR1993966
- L. AMOUR, Ph. KERDELHUE, J. NOURRIGAT. Calcul pseudodifférentiel en grande dimension. Asymptot. Anal. 26 (2001), no. 2, 135-161. Zbl0981.35108MR1832582
- N. ASHCROFT, D. MERMIN, Solid State Physics. Saunders College . Fort Worth, 1976.
- V. BACH, J.S. MÖLLER, Correlation at low temperature. I. Exponential decay. J. Funct. Anal., 203 (2003), no. 1, 93-148. Zbl1031.82003MR1996869
- 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. Zbl0495.60057MR667405
- 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. Zbl0903.46066MR1441540
- L. GROSS, Decay of correlations in classical lattice models at high temperature. Comm. in Math. Phys, 68 (1979), 1, 9-27. Zbl0442.60097MR539733
- 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. Zbl1046.82001MR1936110
- 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. Zbl0921.35141MR1624506
- 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. Zbl1054.82002MR1688446
- 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. Zbl1055.82004MR1702239
- 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. Zbl0946.35508MR1257821
- R. A. MINLOS, Introduction to Mathematical Statistical Physics. University Lecture Series 19, American Mathematical Society, Providence, 2000. Zbl0998.82501MR1727910
- R. A. MINLOS, E.A. PECHERSKY, V. A. ZAGREBNOV, Analyticity of the Gibbs states for a quantum anharmonic crystal: no order parameter. Ann. Henri Poincaré3 (2002), p. 921-938. Zbl1016.82005MR1937608
- J. NOURRIGAT, Ch. ROYER, Thermodynamic limits for Hamiltonians defined as pseudo-differential operators. Comm. Partial Differential Equations, 29 (2004), no. 3-4, 383-417. Zbl1072.35212MR2041601
- D. ROBERT, Autour de l’approximation semiclassique. Progress in Mathematics, 68. Birkhauser Boston, Inc., Boston, MA, 1987. Zbl0621.35001MR897108
- Ch. ROYER, Formes quadratiques et calcul pseudodifférentiel en grande dimension. Prépublication 00.05. Reims, 2000.
- D. RUELLE, Statistical Mechanics: rigorous results. Addison-Wesley, 1969. Zbl0177.57301MR289084
- B. SIMON, The statistical Mechanics of lattice gases. Vol. I. Princeton Series in Physics. Princeton, 1993. Zbl0804.60093MR1239893
- J. SJÖSTRAND, Evolution equations in a large number of variables, Math. Nachr.166 (1994), 17-53. Zbl0837.35061MR1273320
- 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. Zbl0877.35084MR1392018
- J. SJÖSTRAND, Complete asymptotics for correlations of Laplace integrals in the semiclassical limit. Memoires S.M.F., 83, (2000). Zbl1044.81046
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.