國立虎尾科技大學 |

Bulk and Boundary Invariants for Complex Topological Insulators = From K-Theory to Physics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Bulk and Boundary Invariants for Complex Topological Insulators/ by Emil Prodan, Hermann Schulz-Baldes.
其他題名:	From K-Theory to Physics /
作者:	Prodan, Emil.
其他作者:	Schulz-Baldes, Hermann.
面頁冊數:	XXII, 204 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Physics. -
電子資源:	https://doi.org/10.1007/978-3-319-29351-6
ISBN:	9783319293516

Bulk and Boundary Invariants for Complex Topological Insulators = From K-Theory to Physics /
Prodan, Emil.

Bulk and Boundary Invariants for Complex Topological InsulatorsFrom K-Theory to Physics /[electronic resource] :by Emil Prodan, Hermann Schulz-Baldes. - 1st ed. 2016. - XXII, 204 p. 1 illus.online resource. - Mathematical Physics Studies,0921-3767. - Mathematical Physics Studies,.

Illustration of key concepts in dimension d = 1 -- Topological solid state systems: conjectures, experiments and models -- Observables algebras for solid state systems -- K-theory for topological solid state systems -- The topological invariants and their interrelations -- Index theorems for solid state systems -- Invariants as measurable quantities.

This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.

ISBN: 9783319293516

Standard No.: 10.1007/978-3-319-29351-6doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Bulk and Boundary Invariants for Complex Topological Insulators = From K-Theory to Physics /
LDR:03043nam a22004095i 4500 001 977701
003 DE-He213
005 20200629165941.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319293516 $9 978-3-319-29351-6
024 7 $a 10.1007/978-3-319-29351-6 $2 doi
035 $a 978-3-319-29351-6
050 4 $a QC5.53
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.15 $2 23
100 1 $a Prodan, Emil. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1106284
245 1 0 $a Bulk and Boundary Invariants for Complex Topological Insulators $h [electronic resource] : $b From K-Theory to Physics / $c by Emil Prodan, Hermann Schulz-Baldes.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XXII, 204 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Mathematical Physics Studies, $x 0921-3767
505 0 $a Illustration of key concepts in dimension d = 1 -- Topological solid state systems: conjectures, experiments and models -- Observables algebras for solid state systems -- K-theory for topological solid state systems -- The topological invariants and their interrelations -- Index theorems for solid state systems -- Invariants as measurable quantities.
520 $a This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.
650 0 $a Physics. $3 564049
650 0 $a K-theory. $3 672462
650 0 $a Mathematical physics. $3 527831
650 0 $a Solid state physics. $3 641431
650 1 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a K-Theory. $3 672463
650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Solid State Physics. $3 768851
700 1 $a Schulz-Baldes, Hermann. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1106285
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319293509
776 0 8 $i Printed edition: $z 9783319293523
776 0 8 $i Printed edition: $z 9783319805504
830 0 $a Mathematical Physics Studies, $x 0921-3767 $3 1262110
856 4 0 $u https://doi.org/10.1007/978-3-319-29351-6
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)