國立虎尾科技大學 |

Spectral analysis of N-body schrödinger operators at two-cluster thresholds

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spectral analysis of N-body schrödinger operators at two-cluster thresholds/ by Erik Skibsted, Xue Ping Wang.
作者:	Skibsted, Erik.
其他作者:	Wang, Xue Ping.
出版者:	Singapore :Springer Nature Singapore : : 2024.,
面頁冊數:	ix, 258 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Theoretical, Mathematical and Computational Physics. -
電子資源:	https://doi.org/10.1007/978-981-97-2624-0
ISBN:	9789819726240

Spectral analysis of N-body schrödinger operators at two-cluster thresholds
Skibsted, Erik.

Spectral analysis of N-body schrödinger operators at two-cluster thresholds[electronic resource] /by Erik Skibsted, Xue Ping Wang. - Singapore :Springer Nature Singapore :2024. - ix, 258 p. :ill., digital ;24 cm. - Mathematical physics studies,2352-3905. - Mathematical physics studies..

Introduction -- Many-Body Schrödinger Operators, Conditions and Notation -- Reduction to a One-Body Problem -- Spectral Analysis of H0 near 0 -- Rellich-Type Theorems -- Resolvent Asymptotics near a Two-Cluster Threshold -- Elastic Scattering at a Threshold -- Non-Transmission at a Threshold for Physical Models -- Threshold Behaviour of Cross-Sections in Atom-Ion Scattering.

This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors' analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors' principal tools are the Feshbach-Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.

ISBN: 9789819726240

Standard No.: 10.1007/978-981-97-2624-0doiSubjects--Topical Terms:

768900
Theoretical, Mathematical and Computational Physics.

LC Class. No.: QC174.17.S3

Dewey Class. No.: 530.124

Spectral analysis of N-body schrödinger operators at two-cluster thresholds
LDR:02965nam a2200337 a 4500 001 1134332
003 DE-He213
005 20240704125413.0
006 m d
007 cr nn 008maaau
008 241213s2024 si s 0 eng d
020 $a 9789819726240 $q (electronic bk.)
020 $a 9789819726233 $q (paper)
024 7 $a 10.1007/978-981-97-2624-0 $2 doi
035 $a 978-981-97-2624-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.S3
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.124 $2 23
090 $a QC174.17.S3 $b S628 2024
100 1 $a Skibsted, Erik. $3 1455733
245 1 0 $a Spectral analysis of N-body schrödinger operators at two-cluster thresholds $h [electronic resource] / $c by Erik Skibsted, Xue Ping Wang.
260 $a Singapore : $c 2024. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a ix, 258 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematical physics studies, $x 2352-3905
505 0 $a Introduction -- Many-Body Schrödinger Operators, Conditions and Notation -- Reduction to a One-Body Problem -- Spectral Analysis of H0 near 0 -- Rellich-Type Theorems -- Resolvent Asymptotics near a Two-Cluster Threshold -- Elastic Scattering at a Threshold -- Non-Transmission at a Threshold for Physical Models -- Threshold Behaviour of Cross-Sections in Atom-Ion Scattering.
520 $a This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors' analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors' principal tools are the Feshbach-Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 2 4 $a Functional Analysis. $3 672166
650 1 4 $a Mathematical Physics. $3 786661
650 0 $a Schrödinger operator. $3 1455735
700 1 $a Wang, Xue Ping. $3 1455734
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Mathematical physics studies. $3 1062361
856 4 0 $u https://doi.org/10.1007/978-981-97-2624-0
950 $a Physics and Astronomy (SpringerNature-11651)