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Hajo Leschke (born 11 February 1945 in Wentorf bei Hamburg) is a German mathematical physicist and (semi-)retired professor of theoretical physics at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). He is probably best known for notable rigorous results on some model systems in quantum (statistical) mechanics obtained by functional-analytic and probabilistic techniques, jointly with his (former) students and other co-workers. His research topics include: Peierls Transition, Functional Formulations of Quantum and Stochastic Dynamics, Pekar–Fröhlich Polaron, Quantum Spin Chains, Feynman–Kac Formulas, (Random) Schrödinger Operators, Landau-Level Broadening, Lifschitz Tails, Anderson Localization, Fermionic Entanglement Entropies, Quantum Spin Glasses.

Academic education

Leschke studied physics and mathematics at the Universität Hamburg and graduated with a diploma in physics (1970). The underlying thesis was supervised by Wolfgang Kundt (born 1931). He received his doctorate in physics (1975) with dissertation supervisor Uwe Brandt (1944–1997) at the (Technische) Universität Dortmund, where he also earned the habilitation in physics (1981). His studies were supported by the prestigious Studienstiftung des deutschen Volkes (German Academic Scholarship Foundation) and the Kurt-Hartwig-Siemers–Wissenschaftspreis on the recommendation of Werner Döring (1911–2006) and of Pascual Jordan (1902–1980), respectively.

Professional experience (excerpt)

Leschke was a research (and teaching) assistant to Ludwig Tewordt (1926–2016) at the Universität Hamburg, to Uwe Brandt at the Universität Dortmund, to Herbert Wagner (born 1935) at the Forschungszentrum Jülich (then: KFA Jülich), and to Richard Bausch (born 1935) at the (Heinrich-Heine–)Universität Düsseldorf (HHU) before he became a professor there in 1982 and at the FAU in 1983. In 1987 he was a guest professor at the University of Georgia, Athens (UGA) with host David P. Landau (born 1941). In 2004 he organized the workshop "Mathematics and physics of disordered systems" jointly with Michael Baake, Werner Kirsch, and Leonid A. Pastur at the Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany. In 2017 he organized the workshop "Fisher–Hartwig asymptotics, Szegő expansions, and applications to statistical physics" jointly with Alexander V. Sobolev and Wolfgang Spitzer at the American Institute of Mathematics (AIM), San Jose, California. From 1998 to 2011 Leschke belonged to the advisory board of the legendary Annalen der Physik, then edited by Ulrich Eckern (born 1952) at the Universität Augsburg.

In academia internationally esteemed former students

Leschke's diploma and doctoral students Peter Müller (born 1967) and Simone Warzel (born 1973) are professors of mathematics in München/Garching at the Ludwig-Maximilians–Universität (LMU) and the Technische Universität (TUM), respectively. Also his diploma students Dirk Hundertmark (born 1965) and Bernhard G. Bodmann (born 1972) are professors of mathematics at the Karlsruher Institut für Technologie (KIT) and the University of Houston Texas (UH), respectively. These four careers indicate that Leschke's thorough and lucid teaching has attracted and inspired many talented students interested to learn how to convert physical arguments into mathematical ones and vice versa.

Selected research achievements

Leschke's achievements in research are well illustrated by his ten publications listed below. They all refer to properties of non-relativistic quantum systems which are modelled by some energy operator or Hamiltonian, possibly depending on random parameters representing disorder. In the publications from 2000 to 2017 the Hamiltonian is of Schrödinger type, that is, an operator for the sum of the kinetic and potential energy of "point-like" particles in Euclidean space. His publications from 2000 to 2004 extend previously known properties of its corresponding one-parameter semigroup (or Gibbs operator for different temperatures) to nonzero magnetic fields and to (random) potentials leading to unbounded semigroups; by suitably extending the Feynman–Kac formula. Moreover, in case of a single particle subject to a magnetic field and a (Gaussian) random potential without an underlying lattice structure they have provided the first proofs for the existence of the density of states and of Anderson localization in multi-dimensional continuous space. His publications in 2014 and 2017 refer to the case of non-interacting particles which obey Fermi–Dirac statistics. For the corresponding ideal Fermi gas in thermal equilibrium they have provided the first rigorous results on the asymptotic scaling of its Rényi entanglement entropies for all temperatures. They often serve as a sound standard of comparison for approximate arguments and/or numerical methods to better understand the correlations in many-fermion systems with interaction. His publications in 2021 are among the first ones providing rigorous results on quantum versions of the Sherrington–Kirkpatrick spin-glass model. In particular, they prove for the first time the existence of a phase transition (related to spontaneous replica-symmetry breaking) if the temperature and the "transverse" magnetic field are low enough. His publication in 2023 illuminates its relevance to the quantum-annealing algorithm in computer science.

Selected publications since 2000

• Chakrabarti, B.K.; Leschke, H.; Ray, P.; Shirai, T.; Tanaka, S. (2023). "Quantum annealing and computation: challenges and perspectives (Editors' introduction to the Theme Issue 2241)". Phil. Trans. R. Soc.(London) A. 381 (2241) 20210419: 5pp. doi:10.1098/rsta.2021.0419. PMC 9719792. PMID 36463926.
• Leschke, H.; Manai, C.; Ruder, R.; Warzel, S. (2021). "Existence of replica-symmetry breaking in quantum glasses". Phys. Rev. Lett. 127 (20) 207204: 6pp. arXiv:2106.00500. Bibcode:2021PhRvL.127t7204L. doi:10.1103/PhysRevLett.127.207204. PMID 34860058.
• Leschke, H.; Rothlauf, S.; Ruder, R.; Spitzer, W. (2021). "The free energy of a quantum spin-glass model for weak disorder". J. Stat. Phys. 182 55: 41pp. doi:10.1007/s10955-020-02689-8.
• Leschke, H.; Sobolev, A.V.; Spitzer, W. (2017). "Trace formulas for Wiener-Hopf operators with applications to entropies of free fermionic equilibrium states". J. Funct. Anal. 273 (3): 1049–1094. doi:10.1016/j.jfa.2017.04.005.
• Leschke, H.; Sobolev, A.V.; Spitzer, W. (2014). "Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof". Phys. Rev. Lett. 112 (16) 160403: 5pp. arXiv:1312.6828. Bibcode:2014PhRvL.112p0403L. doi:10.1103/PhysRevLett.112.160403. PMID 24815626.
• Broderix, K.; Leschke, H.; Müller, P. (2004). "Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections". J. Funct. Anal. 212 (2): 287–323. doi:10.1016/j.jfa.2004.01.009.
• Leschke, H.; Warzel, S. (2004). "Quantum-classical transitions in Lifshitz tails with magnetic fields". Phys. Rev. Lett. 92 (8) 086402: 4pp. arXiv:cond-mat/0310389. Bibcode:2004PhRvL..92h6402L. doi:10.1103/PhysRevLett.92.086402. PMID 14995799.
• Hupfer, T.; Leschke, H.; Müller, P.; Warzel, S. (2001). "The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials". Commun. Math. Phys. 221: 229–254. doi:10.1007/s002200100467.
• Fischer, W.; Leschke, H.; Müller, P. (2000). "Spectral localization by Gaussian random potentials in multi-dimensional continuous space". J. Stat. Phys. 101 (5/6): 935–985. arXiv:math-ph/9912025. Bibcode:2000JSP...101..935F. doi:10.1023/A:1026425621261.
• Broderix, K.; Hundertmark, D.; Leschke, H. (2000). "Continuity properties of Schrödinger semigroups with magnetic fields". Rev. Math. Phys. 12 (2): 181–225. arXiv:math-ph/9808004. Bibcode:2000RvMaP..12..181B. doi:10.1142/S0129055X00000083.

References

1. Dr. Hajo Leschke, University of Erlangen-Nuremberg, retrieved 2024-12-19
2. MacTudor-Biography: Pascual Jordan, retrieved 2024-12-19
3. ^ Curriculum Vitae, University of Erlangen-Nuremberg, retrieved 2024-12-19
4. Workshop "Fisher–Hartwig asymptotics, Szego expansions, and applications to statistical physics"
5. Advisory Board – Annalen der Physik, University of Augsburg, retrieved 2024-12-19
6. Homepage Peter Müller, retrieved 2024-12-19
7. Homepage Dirk Hundertmark, retrieved 2024-12-19
8. Homepage Bernhard G. Bodmann, retrieved 2024-12-19
9. Former members of the group of Hajo Leschke, University of Erlangen-Nuremberg, retrieved 2024-12-19
10. Mathematics Genealogy Project, retrieved 2024-12-19
11. Lőrinczi, J.; Hiroshima, F.; Betz, V. (2022). Feynman–Kac-Type Theorems and Gibbs Measures on Path Space – Volume 1 (2nd ed.). De Gruyter. p. 532. ISBN 978-3-11-033004-5.
12. Chulaevsky, V.; Suhov, Y. (2014). Multi-scale Analysis for Random Quantum Systems with Interaction. Birkhäuser. p. 249. ISBN 978-1-49-393952-7.
13. Leschke, H.; Sobolev, A. V.; Spitzer, W. (2016). "Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature". Journal of Physics A: Theoretical and Mathematical. 49 (30) 30LT04: 9 pp. arXiv:1501.03412. Bibcode:2016JPhA...49DLT04L. doi:10.1088/1751-8113/49/30/30LT04.
14. Leschke, H.; Sobolev, A. V.; Spitzer, W. (2022). "Rényi entropies of the free Fermi gas in multi-dimensional space at high temperature". In Basor, E.; Böttcher, A.; Erhardt, T.; Tracy, C. A. (eds.). Toeplitz Operators and Random Matrices – In Memory of Harold Widom. Cham: Birkhäuser/Springer Nature. doi:10.1007/978-3-031-13851-5_21.
15. Pan, G.; Da Liao, Y.; Jiang, W.; D'Emidio, J.; Qi, Y.; Yang Meng, Z. (2023). "Stable computation of entanglement entropy for two-dimensional interacting fermion systems". Phys. Rev. B. 108 (8) L081123: 6 pp. arXiv:2303.14326. Bibcode:2023PhRvB.108h1123P. doi:10.1103/PhysRevB.108.L081123.
16. Jiang, W.; Chen, B.-B.; Hong Liu, Z.; Rong, J.; Assaad, F.; Cheng, M.; Sun, K.; Yang Meng, Z. (2023). "Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter". SciPost Phys. 15 (3) 082: 38 pp. arXiv:2209.07103. Bibcode:2023ScPP...15...82J. doi:10.21468/SciPostPhys.15.3.082.
17. Physical Review Journals, December 6, 2021, retrieved 2024-12-23

External links

• Homepage at the FAU
• Hajo Leschke at the Mathematics Genealogy Project (MGP)
• Hajo Leschke at the Academic genealogy of theoretical physicists (HandWiki) via Arnold Sommerfeld (1868–1951) and Walter Franz (1911–1992)

• Living people
• 1945 births
• Studienstiftung alumni
• 20th-century German physicists
• 21st-century German physicists
• German theoretical physicists
• Mathematical physicists
• University of Hamburg alumni
• Technical University of Dortmund alumni
• Academic staff of the University of Erlangen-Nuremberg