02821nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003200207245017800239260008200417300003400499336002600533337002600559338003600585347002400621490003900645506006600684520137900750650003302129650005202162650002902214700003102243700002902274700003202303856003202335856006802367100-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090708sz fot ||| 0|eng d a978303719570370a10.4171/0702doi ach0018173 7aPHDD2bicssc a82-xxa46-xx2msc1 aAlbeverio, Sergio,eauthor.10aThe Statistical Mechanics of Quantum Lattice Systemsh[electronic resource] :bA Path Integral Approach /cSergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Röckner3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (392 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v81 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aQuantum statistical mechanics plays a major role in many fields
such as, for instance, thermodynamics, plasma physics, solid-state
physics, and the study of stellar structure.
While the theory of quantum harmonic oscillators is relatively simple,
the case of anharmonic oscillators, a mathematical model of a localized quantum
particle, is more complex and challenging.
Moreover, infinite
systems of interacting quantum anharmonic oscillators possess
interesting ordering properties with respect to quantum
stabilization.
This book presents a rigorous approach to the
statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice.
The text is addressed to both mathematicians and physicists, especially those who are concerned with
the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here
a concise collection of facts, concepts, and tools relevant for the
application of path integrals and other methods based on measure and
integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum
anharmonic crystals. The methods developed in
the book are also applicable to other problems involving infinitely
many variables, for example, in biology and economics.07aAnalytical mechanics2bicssc07aStatistical mechanics, structure of matter2msc07aFunctional analysis2msc1 aKondratiev, Yuri,eauthor.1 aKozitsky, Yuri,eauthor.1 aRöckner, Michael,eauthor.40uhttps://doi.org/10.4171/070423cover imageuhttps://www.ems-ph.org/img/books/roeckner_mini.jpg