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Numerical methods in the study of nonequilibrium strongly interacting quantum many-body physics

Ulrich Schollwöck

in Strongly Interacting Quantum Systems out of Equilibrium: Lecture Notes of the Les Houches Summer School: Volume 99, August 2012

Published in print:
2016
Published Online:
August 2016
ISBN:
9780198768166
eISBN:
9780191821905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198768166.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter provides a detailed description of the numerical algorithms used to study open and closed quantum systems out of equilibrium. In a first step, the physical formulas to be evaluated ... More


Geodesics

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0008
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

Let M denote a smooth manifold. A metric on TM can be used to define a notion of the distance between any two points in M and the distance travelled along any given path in M. This chapter first ... More


Maps and vector bundles

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0005
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This discussion of maps and vector bundles covers the pull-back construction; pull-backs and Grassmannians; pull-back of differential forms and push-forward of vector fields; invariant forms and ... More


Vector-Valued Forms

Loring W. Tu

in Introductory Lectures on Equivariant Cohomology: (AMS-204)

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691191751
eISBN:
9780691197487
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691191751.003.0014
Subject:
Mathematics, Educational Mathematics

This chapter studies vector-valued forms. Ordinary differential forms have values in the field of real numbers. This chapter allows differential forms to take values in a vector space. When the ... More


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