Elliott H. Lieb Livres

The first edition of „The Stability of Matter: From Atoms to Stars“ was sold out after a time unusually short for a selecta collection and we thought it ap propriate not just to make a reprinting but to include eight new contributionso They demonstrate that this field is still lively and keeps revealing unexpected featureso Of course, we restricted ourselves to developments in which Elliott Lieb participated and thus the heroic struggle in Thomas-Fermi theory where 7 3 5 3 the accuracy has been pushed from Z 1 to Z 1 is not includedo A rich landscape opened up after Jakob Yngvason's observation that atoms in magnetic fields also are described in suitable limits by a Thomas-Fermi-type theoryo Together with Elliott Lieb and Jan Philip Solovej it was eventually worked out that one has to distinguish 5 regionso If one takes as a dimensionless measure of the magnetic field strength B the ratio Larmor radius/Bohr radius one can compare it with N "' Z and for each of the domains 4 3 (i) B « N 1 , 4 3 (ii) B "' N 1 , 4 3 3 (iii) N 1« B « N , 3 (iv) B "' N , 3 (v) B » N a different version ofmagnetic Thomas-Fermi theory becomes exact in the limit N --+ ooo In two dimensions and a confining potential („quantum dots“) the situation is somewhat simpler, one has to distinguish only (i) B « N, (ii) B "'N,

"Have a Little Faith  is not merely a fan’s notes; this is a riveting book that tells the stories of one of our greatest roots musicians and the tenacity that’s grown out of his enduring passion for music." —  No DepressionA journey through an artist's quest for success, deep dive into substance abuse, family tragedy, and ultimate triumphBy the mid-1980s, singer-songwriter John Hiatt had been dropped from three record labels, burned through two marriages, and had fallen deep into substance abuse. It took a stint in rehab and a new marriage to inspire him, then a producer and an A&R man to have a little faith. By February 1987, he was back in the studio on a shoestring budget with a hand-picked supergroup consisting of Ry Cooder on guitar, Nick Lowe on bass, and Jim Keltner on drums, recording what would become his masterpiece, Bring the Family . Based on author Michael Elliott's multiple extensive and deeply personal interviews with Hiatt as well as his collaborators and contemporaries, including Rosanne Cash, Bonnie Raitt, Ry Cooder, and many others, Have a Little Faith is the journey through the musical landscape of the 1960s through today that places Hiatt’s long career in context with the glossy pop, college-alternative, mainstream country, and heartland rock of the last half-century.Hiatt’s life both pre- and post- Family will be revealed, as well as the music loved by critics, fellow musicians, and fans alike.

On a hot summer day in 1876, George Armstrong Custer led the Seventh Cavalry to the famous defeat in US military history. Outnumbered and exhausted, the Seventh Cavalry lost more than half of its four hundred men, and every soldier under Custer's direct command was killed. This title takes readers to each of the important places of Custer's life.

Elliott Lieb's influential works on Condensed Matter Physics are compiled in this selecta, showcasing his pivotal role in mathematical physics. Renowned as a founding figure in the field, Lieb has tackled complex problems, challenging the notion that rigorous formulation is unnecessary. His meticulous approach to defining and solving key questions has proven that many issues previously deemed intractable can indeed be addressed, although they often require decades to resolve. This collection highlights the depth and impact of his contributions.

The mathematical study of the Bose gas began in the early twentieth century with the advent of quantum mechanics. The term originates from Indian physicist S. N. Bose, who in 1924 recognized that the statistics governing photons, initially conceptualized by Max Planck in 1900, could be understood by restricting the physical Hilbert space to the symmetric tensor product of single photon states. Einstein later applied this concept to massive particles, leading to the discovery of Bose-Einstein condensation. Initially regarded as a mathematical curiosity, this phenomenon gained experimental relevance with the peculiar properties of liquid helium, first liquefied by Kammerlingh Onnes in 1908. However, a significant mathematical challenge arose: the atoms in liquid helium are not the non-interacting particles assumed in Einstein's theory. The critical question remains whether Bose-Einstein condensation occurs in strongly or even weakly interacting systems, a query that persists today. The first systematic mathematical approach to this issue was introduced by Bogoliubov in 1947. Although his theory was intuitively appealing and correct in many respects, it contained notable gaps and flaws. Renewed interest in the 1950s and 1960s advanced theoretical intuition, yet the mathematical framework did not see significant improvement.

In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors.

This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is „probably impossible and certainly unnecessary“. By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.