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Quantum mechanics. Quantumfield theory --- Differential geometry. Global analysis --- Schrodinger operator. --- Differential equations, Partial --- Spectral theory (Mathematics) --- Asymptotic theory. --- 530.145.6 --- Schrodinger operator --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation --- Wave mechanics. Corpuscular waves. Matrices --- Schrödinger operator --- Schrödinger operator. --- Spectral theory (Mathematics). --- 530.145.6 Wave mechanics. Corpuscular waves. Matrices --- Schrödinger operator --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Asymptotic theory in partial differential equations --- Asymptotic expansions --- Asymptotic theory --- Differential equations, Partial - Asymptotic theory.

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This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.
Contents:

• Witten Laplacians Approach
• Problems in Statistical Mechanics with Discrete Spins
• Laplace In

Statistical mechanics.

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There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities.

Operatoren. --- Laplace-operatoren. --- Spectraaltheorie. --- Hypoelliptic operators. --- Spectral theory (Mathematics) --- Spectre (Mathématiques) --- Mathematics. --- Global analysis. --- Differential equations, partial. --- Quantum theory. --- Statistics. --- Partial Differential Equations. --- Global Analysis and Analysis on Manifolds. --- Quantum Physics. --- Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences. --- Hypoelliptic operators --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Operators, Hypoelliptic --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Partial differential equations --- Math --- Global analysis (Mathematics) --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Geometry. --- Quantum physics. --- Thermodynamics. --- Heat engineering. --- Heat transfer. --- Mass transfer. --- Engineering Thermodynamics, Heat and Mass Transfer. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Econometrics --- Science --- Mass transport (Physics) --- Thermodynamics --- Transport theory --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Heat --- Mechanical engineering --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat-engines --- Quantum theory --- Euclid's Elements --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Engineering. --- Construction --- Industrial arts --- Technology --- Statistics . --- Partial differential operators --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics)