The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars)

by Elliott H. Lieb

Publisher: Birkhäuser Basel

Written in English
Cover of: The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) | Elliott H. Lieb
Published: Pages: 208 Downloads: 419
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Subjects:

  • States of matter,
  • Mathematical Physics,
  • Applied,
  • Mathematics,
  • Science,
  • Science/Mathematics,
  • Physics,
  • Bose Gas,
  • Mathematics / Applied,
  • Phase Transition,
  • Bose-Einstein condensation,
  • Bose-Einstein gas
The Physical Object
FormatPaperback
Number of Pages208
ID Numbers
Open LibraryOL9091015M
ISBN 103764373369
ISBN 109783764373368

In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the weakly interacting bosons, we study the reduction of GPE to lower dimensions, the ground states of BEC including the existence and uniqueness as well as Cited by: He also explores applications in the non-relativistic context, in particular applying the techniques to the Bose-Einstein condensation of an ideal Bose gas. Self-contained and clearly written, Spectral Functions in Mathematics and Physics offers a unique opportunity to acquire valuable new techniques, use them in a variety of applications, and. Download The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) Ebook Pdf. Download The Next Million Years. Ebook free Linux Networking Architecture book (Lecture Notes in Mathematics) Book Download Ebook The Roman Army: the . Bose-Einstein condensation is a phenomenon that theoretically happens for free Bose gases because Bose-Einstein distribution holds for free Bose gases. But in superconductors and superfluids, there.

Department of Mathematics, National University of Singapore, Singapore and Beijing Computational Science Research Center, Beijing , P. R. China Abstract. In this paper, we systematically review mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on Gross-Pitaevskii equation (GPE). Starting from the.   We focus, in particular, on the excitation spectrum of a Bose gas in the mean-field (Hartree) limit. A list of open problems will be discussed at the end. Bose gases, Bose–Einstein condensation, and the Bogoliubov approximation: Journal of Mathematical Physics: No 7Cited by: 4. Download Book Links Sites. Search this site. Home. Days: The Battle for Stalingrad Download Pdf and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics) Book. Download The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) Ebook Pdf. On Bose-Einstein Condensation - Volume 50 Issue 1 - P. T. Landsberg. We use cookies to distinguish you from other users and to provide you with a better experience on our by:

() Mathematical theory and numerical methods for Bose-Einstein condensation. Kinetic and Related Models , () Mean-field dynamics of rotating bosons in strongly anisotropic by:

The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) by Elliott H. Lieb Download PDF EPUB FB2

This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years. These topics are relevant to current experiments on ultra-cold gases; they are also mathematically rigorous, using many analytic techniques developed over the years to handle such problems.

Some of the topics treated are the ground state Cited by: The Mathematics of the Bose Gas and its Condensation. Authors but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers.

Book Title The Mathematics of the Bose. The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars Book 34) - Kindle edition by Lieb, Elliott H., Seiringer, Robert, Solovej, Jan Philip, Yngvason, Jakob. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading The Mathematics of the Bose Gas and its Condensation (Oberwolfach 1/5(1). The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.

Keywords Bose Gas Bose-Einstein Condensation Helium-Atom-Streuung Mathematical Physics PAS PED Phase Transition. The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) th Edition by Elliott H.

Lieb (Author) out of 5 stars 1 rating. ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: The Mathematics of the Bose Gas and its Condensation. This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the.

Get this from a library. The mathematics of the Bose gas and its condensation. [Elliott H Lieb;] -- "This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years.

It addresses. This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years.

These topics are relevant to current experiments on ultra-cold gases; they are also mathematically rigorous, using many analytic techniques developed over the years to handle such problems.

Some of the topics treated are the Cited by: The Mathematics of the Bose Gas and its Condensation Elliott H. Lieb, Jan Philip Solovej, Robert Seiringer, Jakob Yngvason (auth.) This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years.

Home» MAA Publications» MAA Reviews» The Mathematics of the Bose Gas and Its Condensation. The Mathematics of the Bose Gas and Its Condensation. Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej, and Jakob Yngvason 10 The Charged Bose Gas, the One- and Two-Component Cases The Mathematics of the Bose Gas and Its Condensation 作者: Solovej, Jan Philip 页数: 定价: $ ISBN: 豆瓣评分.

Shortly afterwards, Einstein applied this idea to massive particles, such as a gas of atoms, and discovered the phenomenon that we now call Bose-Einstein condensation.

At that time this was viewed as a mathematical curiosity with little experimental interest, : $ This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years.

An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal is composed of bosons, which have an integer value of spin, and obey Bose–Einstein statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a.

For an ideal Bose gas, the corresponding average occupancy becomes infinite for ε = 0 as λ → 1. However, for fermions, λ =e βμ can be any positive number, so 0 ≤ λ ≤ ∞.

In particular, one does not have to take the ground state into account explicitly, so conversion from. Some of the topics treated are the ground state energy, the Gross-Pitaevskii equation, Bose-Einstein condensation, superfluidity, one-dimensional gases, and rotating gases.

The book also provides a pedagogical entry into the field for graduate students and t: pages. The book is an introductory text to the physics of Bose-Einstein condensation. This phenomenon, first predicted by Einstein inhas been realized experimentally in in a remarkable series of experiments whose importance has been recognized by the award of the Nobel Prize in Physics.

The condensate is actually a new state of matter, where quantum-mechanical 5/5(1). The achievement of Bose– Einstein condensation of trapped atomic gases in was a watershed event in the history of many-body physics [2–5].Since then, an astounding number of phenomena, described in Chapter 2 of this volume, have been explored with atomic bosons.

Within just a few months of these first experiments, a proposal to use 6 Li to experimentally realize Cooper pairing in an. Cite this chapter as: () The Charged Bose Gas, the One- and Two-Component Cases. In: The Mathematics of the Bose Gas and its Condensation.

In Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose-Einstein condensate, was produced in the laboratory for the first time in and investigating such condensates has become one of the most active areas in contemporary physics.

The study of Bose-Einstein condensates in dilute gases encompasses a 5/5(3). Bose-Einstein Condensation of An Ideal Gas An ideal gas consisting of non-interacting Bose particles is a flctitious system since every realistic Bose gas shows some level of particle-particle interaction.

Nevertheless, such a mathematical model provides the simplest example for the realization of Bose-Einstein Size: KB. Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate Pages from Volume (), Issue 1 by László Erdős, Benjamin Schlein, Horng-Tzer Yau AbstractCited by: Satyendra Nath Bose, FRS (IPA: [ʃotːendronatʰ boʃu]; 1 January – 4 February ) was an Indian physicist specialising in theoretical is best known for his work on quantum mechanics in the early s, providing the foundation for Bose–Einstein statistics and the theory of the Bose–Einstein condensate.A Fellow of the Royal Society, he was awarded India's second Awards: Padma Vibhushan, Fellow of the Royal Society.

Bose-Einstein Condensation L. Pitaevskii and S. Stringari. A Clarendon Press Publication. International Series of Monographs on Physics. Bose-Einstein Condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the Nobel Prize.

Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. The Hartree and the nonlinear Schrodinger equation can be derived as the mean field limit of the dynamics of an interacting gas of Bosons exhibiting Bose-Einstein condensation; the nonlinear dispersive PDE describes the dynamics of the Bose-Einstein condensate.

The topic of this talk is an extension to the Hartree equation, which describes thermal fluctuations around the. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This book was first published by Birkhäuser Verlag (Basel-Boston-Berlin) in under the title “The Mathematics of the Bose Gas and its Condensation ” as number 34 of its “Oberwolfach Seminar ” series.

The present version differs from the originally published version in several respects. Mathematics and Politics. ; Mathematics as Problem Solving.

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; Mathématiques et Technologie. ; Mathématiques, Informatique, Physique. Au fil des TIPE. The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars) Elliott H.

Lieb, Robert Seiringer, Jan Philip Solovej, Jakob Yngvason, Year: Jakob Yngvason (born 23 November ) is an Icelandic/Austrian physicist and emeritus professor of mathematical physics at the University of has made important contributions to local quantum field theory, thermodynamics, and the quantum theory of many-body systems, in particular cold atomic gases and Bose–Einstein is co-author, together with Elliott H.

Lieb, Jan Doctoral advisor: Hans-Jürgen Borchers. This book covers the fundamentals of and new developments in gaseous Bose-Einstein condensation. It begins with a review of fundamental concepts and theorems, and introduces basic theories Author: Masahito Ueda.

Figure 6 shows the peak density of the gas as a function of the RF frequency used to excite the atoms into a non-confined state and to assist the cooling by evaporation). There is a sharp increase in density at a frequency of MHz. This indicates the appearance of Bose-Einstein condensation.Gas-liquid condensation (GLC) in an attractive Bose gas is studied on the basis of statistical mechanics.

Using some results in combinatorial mathematics, the following are derived. (1) With decreasing temperature, the Bose-statistical coherence grows in the many-body wave function, which gives rise to the divergence of the grand partition. As with most physical systems, we can describe the behaviour approximately, and Bose-Einstein condensates are no different.

The most tested means of describing condensate behaviour mathematically is using a non-linear form of the Schrödinger equat.