physics

Gian Michele Graf

Gian Michele Graf is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gian Michele Graf rather than just read about it. In short: Gian Michele Graf (born 14 July 1962) is a Swiss mathematical physicist. Graf studied physics and mathematics at ETH Zurich, where he graduated in 1986 with Diplom thesis supervised by Jürg Fröhlich and received his doctorate in 1990 with thesis supervised by Walter Hunziker (1935–2012) .

Key takeaways

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Reference excerpt

Gian Michele Graf (born 14 July 1962) is a Swiss mathematical physicist. Graf studied physics and mathematics at ETH Zurich, where he graduated in 1986 with Diplom thesis supervised by Jürg Fröhlich and received his doctorate in 1990 with thesis supervised by Walter Hunziker (1935–2012) . From 1990 to 1992 Graf was an assistant professor of mathematics at Caltech. At ETH Zurich he was from 1992 to 1998 an assistant professor and from 1998 to 2001 an associate professor and is since 2001 a full professor. He was at the Institute for Advanced Study in 1996 and in 2002. He has been a visiting researcher in six different countries. Graf's research deals with fundamental thermodynamic properties of matter (especially questions related to the problem of the "stability of matter" mathematically investigated by Elliott Lieb and others), many-body scattering processes in quantum mechanics, quantum pumps and various problems of solid-state physics such as the quantum Hall effect and topological insulators. He was a plenary speaker at the 10th International Congress on Mathematical Physics (ICMP) in Leipzig in 1991 and an invited speaker at the 14th ICMP in Lisbon in 2003. In 1992 he was a Sloan Fellow. He was an invited speaker of the International Congress of Mathematicians (ICM) in 1998 in Berlin and of the ICM in 2006 in Madrid. Graf is a Swiss Bürger of Lugano and Rebstein.

Selected publications Graf, Gian Michele (1990). "Asymptotic completeness for N-body short-range quantum systems: A new proof". Communications in Mathematical Physics. 132 (1): 73–101. Bibcode:1990CMaPh.132...73G. doi:10.1007/BF02278000. S2CID 123376798. Graf, Gian Michele; Solovej, Jan Philip (1994). "A Correlation Estimate with Applications to Quantum Systems with Coulomb Interactions". Reviews in Mathematical Physics. 06 (5a): 977–997. Bibcode:1994RvMaP...6..977G. doi:10.1142/S0129055X94000328. Graf, Gian Michele (1994). "Anderson localization and the space-time characteristic of continuum states". Journal of Statistical Physics. 75 (1–2): 337–346. Bibcode:1994JSP....75..337G. doi:10.1007/BF02186292. ISSN 0022-4715. S2CID 122136518. Aizenman, M.; Graf, G. M. (1998). "Localization bounds for an electron gas". Journal of Physics A: Mathematical and General. 31 (32): 6783–6806. arXiv:cond-mat/9603116. Bibcode:1998JPhA...31.6783A. doi:10.1088/0305-4470/31/32/004. Avron, J. E.; Elgart, A.; Graf, G. M.; Sadun, L. (2000). "Geometry, statistics, and asymptotics of quantum pumps". Physical Review B. 62 (16): R10618–R10621. arXiv:cond-mat/0002194. Bibcode:2000PhRvB..6210618A. doi:10.1103/PhysRevB.62.R10618. Avron, J. E.; Elgart, A.; Graf, G. M.; Sadun, L. (2001). "Optimal Quantum Pumps". Physical Review Letters. 87 (23) 236601. arXiv:math-ph/0105011. Bibcode:2001PhRvL..87w6601A. doi:10.1103/PhysRevLett.87.236601. PMID 11736465. Elbau, P.; Graf, G. M. (2002). "Equality of Bulk and Edge Hall Conductance Revisited". Communications in Mathematical Physics. 229 (3): 415–432. arXiv:math-ph/0203019. Bibcode:2002CMaPh.229..415E. doi:10.1007/s00220-002-0698-z. Aschbacher, W. H.; Fröhlich, J.; Graf, G. M.; Schnee, K.; Troyer, M. (2002). "Symmetry breaking regime in the nonlinear Hartree equation". Journal of Mathematical Physics. 43 (8): 3879–3891. Bibcode:2002JMP....43.3879A. doi:10.1063/1.1488673. ISSN 0022-2488. Hassler, F.; Suslov, M. V.; Graf, G. M.; Lebedev, M. V.; Lesovik, G. B.; Blatter, G. (2008). "Wave-packet formalism of full counting statistics". Physical Review B. 78 (16) 165330. arXiv:0802.0143. Bibcode:2008PhRvB..78p5330H. doi:10.1103/PhysRevB.78.165330. Graf, Gian Michele; Porta, Marcello (2013). "Bulk-Edge Correspondence for Two-Dimensional Topological Insulators". Communications in Mathematical Physics. 324 (3): 851–895. arXiv:1207.5989. Bibcode:2013CMaPh.324..851G. doi:10.1007/s00220-013-1819-6. ISSN 0010-3616.

References

Illustrations

Worked examples

Example 1 — a first encounter with Gian Michele Graf

Start with the simplest possible case. Write down what Gian Michele Graf claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gian Michele Graf before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Gian Michele Graf ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Gian Michele Graf

In research: Gian Michele Graf appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Gian Michele Graf in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Gian Michele Graf is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1962 births, Academic staff of ETH Zurich, ETH Zurich alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Gian Michele Graf outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Gian Michele Graf in 20 minutes

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Close the page and write down what Gian Michele Graf means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Gian Michele Graf in simple terms?

Why does Gian Michele Graf matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Gian Michele Graf?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gian Michele Graf.