Misplaced Pages

Hajo Leschke: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editContent deleted Content addedVisualWikitext
Revision as of 15:33, 6 January 2025 editCptcall (talk | contribs)102 editsm minor stylistic improvement in relation to the ideal Fermi gas← Previous edit Latest revision as of 12:30, 15 January 2025 edit undoCptcall (talk | contribs)102 editsm →Research achievements: "random parameters" replaced by "random variables" and linked to Misplaced Pages, also "random potential" linked 
(28 intermediate revisions by 11 users not shown)
Line 1: Line 1:
{{Short description|German mathematical physicist}} {{Short description|German mathematical physicist (born 1945)}}


{{Peacock|date=January 2025}}
]-straße]]
]
'''Hajo Leschke''' (born 11 February 1945 in ]) is a German mathematical physicist and (semi-)retired professor of ] at the Friedrich-Alexander-Universität Erlangen-Nürnberg (]).{{r|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. '''Hajo Leschke''' (born 11 February 1945 in ]) is a German ] and (semi-)retired professor of ] at the Friedrich-Alexander-Universität Erlangen-Nürnberg (]).{{r|fau}} He is known for rigorous results on model systems in ] obtained through ] and ], jointly with his (former) students and other co-workers. His research topics include: ], Functional Formulations of Quantum and Stochastic Dynamics, Pekar–Fröhlich ], Quantum ], ], (Random) ], Landau-Level Broadening, Lifschitz Tails, ], Fermionic Entanglement Entropies, Quantum ].


== Academic education == == Academic education ==
Leschke studied physics and mathematics at the ] and graduated with a ] in physics (1970). The underlying thesis was supervised by ] (born 1931). He received his ] in physics (1975) with dissertation supervisor ] (1944–1997) at the ], where he also earned the ] in physics (1981). His studies were supported by the ] des deutschen Volkes (German Academic Scholarship Foundation) and the ] on the recommendation of ] (1911–2006) and of ]{{r|PJ}} (1902–1980), respectively.{{r|cv}} Leschke studied physics and mathematics at the ] and graduated with a ] in physics (1970) with thesis advisor ] (born 1931). He received his ] in physics (1975) with dissertation advisor ] from the ], where he also earned the ] in physics (1981). His studies were supported by the ] des deutschen Volkes (German Academic Scholarship Foundation) and the ] on the recommendation of ] (1911–2006) and of ]{{r|PJ}} (1902–1980), respectively.{{r|cv}}


== Career ==
== 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 ] (born 1935) at the ] (then: KFA Jülich), and to Richard Bausch (born 1935) at the Universität Düsseldorf (]) 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 (]) with host ] (born 1941). In 2004 he organized the workshop "Mathematics and physics of disordered systems" jointly with Michael Baake, ], and ] at the Mathematisches Forschungsinstitut Oberwolfach (]), 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 (]), then located in San Jose, California.{{r|fha}} From 1998 to 2011 Leschke belonged to the advisory board of the legendary ]{{r|AdP}}, then edited by Ulrich Eckern (born 1952) at the Universität Augsburg.{{r|cv}} Leschke was a research (and teaching) assistant to Ludwig Tewordt (1926–2016) at the Universität Hamburg, to Uwe Brandt at the Universität Dortmund, to ] (born 1935) at the ] (then: KFA Jülich), and to Richard Bausch (born 1935) at the Universität Düsseldorf (]) 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 (]) with host ] (born 1941). In 2004, he organized the workshop "Mathematics and physics of disordered systems" jointly with Michael Baake, ], and ] at the Mathematisches Forschungsinstitut Oberwolfach (]), Germany.{{r|owr}} 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 (]), then located in San Jose, California.{{r|fha}} From 1998 to 2011 Leschke belonged to the advisory board of the ]{{r|AdP}}, then edited by Ulrich Eckern (born 1952) at the Universität Augsburg.{{r|cv}}


== In academia internationally esteemed former students == == Notable students ==
Leschke's diploma and doctoral students Peter Müller{{r|pm}} (born 1967) and ] (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{{r|dh}} (born 1965) and Bernhard G. Bodmann{{r|bb}} (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.{{r|former}}{{r|gen}}


Leschke's doctoral student Peter Müller (born 1967) is professor of mathematics at the Ludwig-Maximilians-Universität (]) in Munich and ] of the Faculty of Mathematics, Informatics, and Statistics (2021–2025).{{r|pm}} His student ] (born 1973) is professor of mathematics at the Technische Universität München (]) in Garching near Munich.{{r|mgp}}
⚫ == 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 Hamiltonian or ] on ] representing the energy of the system, possibly depending on random parameters representing disorder. In the publications from 2000 to 2017 the Hamiltonian is of ], that is, an operator for the sum of the kinetic and potential energy of "point-like" particles in ]. His publications from 2000 to 2004 extend previously known properties of its corresponding ] (or Gibbs operator for different temperatures) to rather general magnetic fields and to (random) potentials leading to unbounded semigroups; by suitably extending the ].{{r|LHB}} 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 ] in multi-dimensional continuous space.{{r|CS}} His publications in 2014 and 2017 refer to the case of non-interacting particles which obey ] statistics. For the corresponding ideal ] in thermal equilibrium they have provided the first rigorous results on the asymptotic growth of its local and entanglement Rényi entropies at arbitrary temperature.{{r|LSS}}{{r|LSS2}} 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.{{r|PL}}{{r|JC}} His publications in 2021 are among the first ones providing rigorous results on quantum versions of the ]. 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.{{r|LMRW}} His publication in 2023 illuminates its relevance to the ] algorithm in computer science.
⚫ == Research achievements ==
⚫ Leschke's research publications listed below refer to properties of non-relativistic quantum systems which are modeled by some ] or ] on ] representing the total energy of the system, possibly depending on ] representing disorder. In the publications from 2000 to 2017 the Hamiltonian is of ], that is, an operator for the sum of the kinetic and potential energy of "point-like" particles in ]. Leschke's publications from 2000 to 2004 extend previously known properties of its corresponding ] (or Gibbs operator for different temperatures) to rather general magnetic fields and to (random) potentials leading to unbounded semi-groups; by suitably extending the ].{{r|LHB}} In the case of a single particle subject to a constant magnetic field and a (Gaussian) ] without an underlying lattice structure Leschke provided the first proofs for the existence of the ] and of ] in multi-dimensional continuous space.{{r|CS}} Leschke's publications in 2014 and 2017 refer to the case of non-interacting particles which obey ]. For the corresponding ideal ] in thermal equilibrium he provided the first rigorous results on the asymptotic growth of its quantum Rényi ] at arbitrary temperature.{{r|LSS}}{{r|LSS2}} Leschke's results have served as a standard of comparison for approximate arguments and/or numerical methods to better understand the correlations in many-fermion systems with interaction.{{r|PL}}{{r|JC}} Leschke's publications in 2021 are among the first ones providing rigorous results on quantum versions of the classic(al) ]. In particular, they prove for the first time the existence of a phase transition (related to ]) if the temperature and the "transverse" magnetic field are low enough.{{r|LMRW}} Leschke's 2023 publication illuminates the phase transition's relevance to the ] algorithm in computer science.{{r|ach}}{{r|vczt}}{{r|kbpsmdd}}


== Selected publications since 2000 == == Selected publications since 2000 ==
Line 25: Line 27:
* {{cite journal | last1=Broderix | first1=K. | last2=Leschke | first2=H. | last3=Müller | first3=P. | title=Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections| journal=J. Funct. Anal. | volume=212 | pages=287–323 | year=2004 | issue=2 |doi=10.1016/j.jfa.2004.01.009| arxiv=math-ph/0209020 }} * {{cite journal | last1=Broderix | first1=K. | last2=Leschke | first2=H. | last3=Müller | first3=P. | title=Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections| journal=J. Funct. Anal. | volume=212 | pages=287–323 | year=2004 | issue=2 |doi=10.1016/j.jfa.2004.01.009| arxiv=math-ph/0209020 }}
* {{cite journal | last1=Leschke | first1=H. | last2=Warzel | first2=S. | title=Quantum-classical transitions in Lifshitz tails with magnetic fields | journal=Phys. Rev. Lett. | volume=92 | article-number=086402 | pages=4pp | year=2004 | issue=8 | doi=10.1103/PhysRevLett.92.086402| pmid=14995799 | arxiv=cond-mat/0310389 | bibcode=2004PhRvL..92h6402L }} * {{cite journal | last1=Leschke | first1=H. | last2=Warzel | first2=S. | title=Quantum-classical transitions in Lifshitz tails with magnetic fields | journal=Phys. Rev. Lett. | volume=92 | article-number=086402 | pages=4pp | year=2004 | issue=8 | doi=10.1103/PhysRevLett.92.086402| pmid=14995799 | arxiv=cond-mat/0310389 | bibcode=2004PhRvL..92h6402L }}
* {{cite journal | last1=Hupfer | first1=T. | last2=Leschke | first2=H.| last3=Müller | first3=P. | last4=Warzel | first4=S. | title=The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials | journal=Commun. Math. Phys. | volume=221 | pages=229–254 | year=2001 | doi=10.1007/s002200100467 }} * {{cite journal | last1=Hupfer | first1=T. | last2=Leschke | first2=H.| last3=Müller | first3=P. | last4=Warzel | first4=S. | title=The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials | journal=Commun. Math. Phys. | volume=221 | pages=229–254 | year=2001 | doi=10.1007/s002200100467 | arxiv=math-ph/0105046 }}
* {{cite journal | last1=Fischer | first1=W. | last2=Leschke | first2=H. | last3=Müller | first3=P. | title=Spectral localization by Gaussian random potentials in multi-dimensional continuous space | journal=J. Stat. Phys. | volume=101 | pages=935–985 | year=2000 | issue=5/6 | doi=10.1023/A:1026425621261| arxiv=math-ph/9912025 | bibcode=2000JSP...101..935F }} * {{cite journal | last1=Fischer | first1=W. | last2=Leschke | first2=H. | last3=Müller | first3=P. | title=Spectral localization by Gaussian random potentials in multi-dimensional continuous space | journal=J. Stat. Phys. | volume=101 | pages=935–985 | year=2000 | issue=5/6 | doi=10.1023/A:1026425621261| arxiv=math-ph/9912025 | bibcode=2000JSP...101..935F }}
* {{cite journal | last1=Broderix | first1=K. |last2=Hundertmark | first2=D. |last3= Leschke | first3=H. | title=Continuity properties of Schrödinger semigroups with magnetic fields | journal=Rev. Math. Phys. | volume=12 | pages=181–225 | year=2000 | issue=2 | doi=10.1142/S0129055X00000083| arxiv=math-ph/9808004 | bibcode=2000RvMaP..12..181B }} * {{cite journal | last1=Broderix | first1=K. |last2=Hundertmark | first2=D. |last3= Leschke | first3=H. | title=Continuity properties of Schrödinger semigroups with magnetic fields | journal=Rev. Math. Phys. | volume=12 | pages=181–225 | year=2000 | issue=2 | doi=10.1142/S0129055X00000083| arxiv=math-ph/9808004 | bibcode=2000RvMaP..12..181B }}
Line 35: Line 37:


<ref name=cv>{{citation|url=https://www.emergent.physics.nat.fau.de/dr-hajo-leschke/hajo-leschke-curriculum-vitae/|title=Curriculum Vitae|publisher=]|accessdate=2024-12-19}}</ref> <ref name=cv>{{citation|url=https://www.emergent.physics.nat.fau.de/dr-hajo-leschke/hajo-leschke-curriculum-vitae/|title=Curriculum Vitae|publisher=]|accessdate=2024-12-19}}</ref>

<ref name=former>{{citation|url=https://www.emergent.physics.nat.fau.de/dr-hajo-leschke/former-members-of-the-group-of-hajo-leschke/|title=Former members of the group of Hajo Leschke|publisher=]|accessdate=2024-12-19}}</ref>


<ref name=AdP>{{citation | url=https://myweb.rz.uni-augsburg.de/~eckern/adp/advisors.html|title=Advisory Board – Annalen der Physik|publisher=University of Augsburg|accessdate=2024-12-19}}</ref> <ref name=AdP>{{citation | url=https://myweb.rz.uni-augsburg.de/~eckern/adp/advisors.html|title=Advisory Board – Annalen der Physik|publisher=University of Augsburg|accessdate=2024-12-19}}</ref>

⚫ <ref name=gen>{{citation|url=https://www.mathgenealogy.org/id.php?id=80146|title=Mathematics Genealogy Project|accessdate=2024-12-19}}</ref>


<ref name=fha>{{citation|url=https://aimath.org/workshops/upcoming/fhszego/|title=Workshop "Fisher–Hartwig asymptotics, Szego expansions, and applications to statistical physics"}}</ref> <ref name=fha>{{citation|url=https://aimath.org/workshops/upcoming/fhszego/|title=Workshop "Fisher–Hartwig asymptotics, Szego expansions, and applications to statistical physics"}}</ref>


<ref name=PJ>{{citation | url=https://mathshistory.st-andrews.ac.uk/Biographies/Jordan_Pascual | title=MacTudor-Biography: Pascual Jordan|accessdate=2024-12-19}}</ref> <ref name=PJ>{{citation | url=https://mathshistory.st-andrews.ac.uk/Biographies/Jordan_Pascual | title=MacTudor-Biography: Pascual Jordan|accessdate=2024-12-19}}</ref>

⚫ <ref name=pm>{{citation|url=https://www.mathematik.uni-muenchen.de/~mueller/|title=Homepage Peter Müller|accessdate=2024-12-19}}</ref>

<ref name=bb>{{citation|url=https://www.math.uh.edu/~bgb/|title=Homepage Bernhard G. Bodmann|accessdate=2024-12-19}}</ref>

<ref name=dh>{{citation|url=https://www.math.kit.edu/iana1/~hundertmark/|title=Homepage Dirk Hundertmark|accessdate=2024-12-19}}</ref>


<ref name=LHB>{{cite book |last1=Lőrinczi |first1=J. | last2=Hiroshima | first2=F. | last3=Betz | first3=V. |date=2022 |title=Feynman–Kac-Type Theorems and Gibbs Measures on Path Space – Volume 1 |publisher=De Gruyter |page=532 |edition=2nd |isbn=978-3-11-033004-5}}</ref> <ref name=LHB>{{cite book |last1=Lőrinczi |first1=J. | last2=Hiroshima | first2=F. | last3=Betz | first3=V. |date=2022 |title=Feynman–Kac-Type Theorems and Gibbs Measures on Path Space – Volume 1 |publisher=De Gruyter |page=532 |edition=2nd |isbn=978-3-11-033004-5}}</ref>
Line 64: Line 56:


<ref name=JC>{{cite journal|first1=W.|last1=Jiang|first2=B.-B.|last2=Chen|first3=Z.|last3=Hong Liu|first4=J.|last4=Rong|first5=F.|last5=Assaad|first6=M.|last6=Cheng|first7=K.|last7=Sun|first8=Z.|last8=Yang Meng|title=Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter|journal=SciPost Phys.|volume=15|article-number=082|pages=38 pp|date=2023|issue=3 |doi=10.21468/SciPostPhys.15.3.082|doi-access=free |arxiv=2209.07103 |bibcode=2023ScPP...15...82J }}</ref> <ref name=JC>{{cite journal|first1=W.|last1=Jiang|first2=B.-B.|last2=Chen|first3=Z.|last3=Hong Liu|first4=J.|last4=Rong|first5=F.|last5=Assaad|first6=M.|last6=Cheng|first7=K.|last7=Sun|first8=Z.|last8=Yang Meng|title=Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter|journal=SciPost Phys.|volume=15|article-number=082|pages=38 pp|date=2023|issue=3 |doi=10.21468/SciPostPhys.15.3.082|doi-access=free |arxiv=2209.07103 |bibcode=2023ScPP...15...82J }}</ref>

<ref name=owr>{{cite journal|first1=M.|last1=Baake|first2=W.|last2=Kirsch|first3=H.|last3=Leschke|first4=L.|last4=Pastur|title=Mathematics and physics of disordered systems|journal=OWR|volume=1|pages=1167–1232|date=2004|issue=2|doi=10.4171/OWR/2004/22}}
</ref>

⚫ <ref name=pm>{{citation|url=https://www.mathematik.uni-muenchen.de/~mueller/|title=Homepage Peter Müller|accessdate=2025-01-14}}</ref>

⚫ <ref name=mgp>{{citation|url=https://www.mathgenealogy.org/id.php?id=80146|title=Mathematics Genealogy Project|accessdate=2025-01-14}}</ref>


<ref name=ach>{{cite journal | last1=Au-Yeung| first1=R. | last2=Chancellor | first2=N. | last3=Halffmann | first3=P. | title=NP-hard but no longer hard to solve? Using quantum computing to tackle optimization probems| journal=Front. Quantum Sci. Technol. | pages=9 pp | date=2023 |volume=2|article-number=1128576|doi=10.3389/frqst.2023.1128576| doi-access=free }}</ref>


<ref name=kbpsmdd>{{cite journal | last1=Kumar| first1=V.|last2=Baskaran | first2=N.|last3=Prasannaa | first3=V. S.|last4=Sugisaki | first4=K. |last5=Mukherjee | first5=D. |last6=Dyall | first6=K. G. |last7=Das | first7=B. P. |title=Computation of relativistic and many-body effects in atomic systems using quantum annealing| journal=Phys. Rev. A| volume=109| pages=10pp | date=2024 | issue=4|article-number=042808|doi= 10.1103/PhysRevA.109.042808| bibcode=2024PhRvA.109d2808K}}</ref>


<ref name=vczt>{{cite journal | last1=Volpe| first1=D.|last2=Cirillo | first2=G. A.|last3=Zamboni | first3=M.|last4=Turvani | first4=G. |title=Integration of simulated quantum annealing in parallel tempering and population annealing for heterogeneous-profile QUBO exploration| journal=IEEE Access| volume=11| pages=30390–30441|date=2023|doi=10.1109/ACCESS.2023.3260765| bibcode=2023IEEEA..1130390V}}</ref>




}} }}

Latest revision as of 12:30, 15 January 2025

German mathematical physicist (born 1945)
This article contains wording that promotes the subject in a subjective manner without imparting real information. Please remove or replace such wording and instead of making proclamations about a subject's importance, use facts and attribution to demonstrate that importance. (January 2025) (Learn how and when to remove this message)
Hajo Leschke in 2023

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 known for rigorous results on model systems in quantum (statistical) mechanics obtained through 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) with thesis advisor Wolfgang Kundt (born 1931). He received his doctorate in physics (1975) with dissertation advisor Uwe Brandt from the Universität Dortmund, where he also earned the habilitation in physics (1981). His studies were supported by the 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.

Career

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 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), then located in San Jose, California. From 1998 to 2011 Leschke belonged to the advisory board of the Annalen der Physik, then edited by Ulrich Eckern (born 1952) at the Universität Augsburg.

Notable students

Leschke's doctoral student Peter Müller (born 1967) is professor of mathematics at the Ludwig-Maximilians-Universität (LMU) in Munich and dean of the Faculty of Mathematics, Informatics, and Statistics (2021–2025). His student Simone Warzel (born 1973) is professor of mathematics at the Technische Universität München (TUM) in Garching near Munich.

Research achievements

Leschke's research publications listed below refer to properties of non-relativistic quantum systems which are modeled by some Hamiltonian or self-adjoint operator on Hilbert space representing the total energy of the system, possibly depending on random variables 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. Leschke's publications from 2000 to 2004 extend previously known properties of its corresponding one-parameter semi-group (or Gibbs operator for different temperatures) to rather general magnetic fields and to (random) potentials leading to unbounded semi-groups; by suitably extending the Feynman–Kac formula. In the case of a single particle subject to a constant magnetic field and a (Gaussian) random potential without an underlying lattice structure Leschke provided the first proofs for the existence of the density of states and of Anderson localization in multi-dimensional continuous space. Leschke's 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 he provided the first rigorous results on the asymptotic growth of its quantum Rényi entropies of (spatial) entanglement at arbitrary temperature. Leschke's results have served as a standard of comparison for approximate arguments and/or numerical methods to better understand the correlations in many-fermion systems with interaction. Leschke's publications in 2021 are among the first ones providing rigorous results on quantum versions of the classic(al) 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. Leschke's 2023 publication illuminates the phase transition's relevance to the quantum-annealing algorithm in computer science.

Selected publications since 2000

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. Baake, M.; Kirsch, W.; Leschke, H.; Pastur, L. (2004). "Mathematics and physics of disordered systems". OWR. 1 (2): 1167–1232. doi:10.4171/OWR/2004/22.
  5. Workshop "Fisher–Hartwig asymptotics, Szego expansions, and applications to statistical physics"
  6. Advisory Board – Annalen der Physik, University of Augsburg, retrieved 2024-12-19
  7. Homepage Peter Müller, retrieved 2025-01-14
  8. Mathematics Genealogy Project, retrieved 2025-01-14
  9. 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.
  10. Chulaevsky, V.; Suhov, Y. (2014). Multi-scale Analysis for Random Quantum Systems with Interaction. Birkhäuser. p. 249. ISBN 978-1-49-393952-7.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Physical Review Journals, December 6, 2021, retrieved 2024-12-23
  16. Au-Yeung, R.; Chancellor, N.; Halffmann, P. (2023). "NP-hard but no longer hard to solve? Using quantum computing to tackle optimization probems". Front. Quantum Sci. Technol. 2 1128576: 9 pp. doi:10.3389/frqst.2023.1128576.
  17. Volpe, D.; Cirillo, G. A.; Zamboni, M.; Turvani, G. (2023). "Integration of simulated quantum annealing in parallel tempering and population annealing for heterogeneous-profile QUBO exploration". IEEE Access. 11: 30390–30441. Bibcode:2023IEEEA..1130390V. doi:10.1109/ACCESS.2023.3260765.
  18. Kumar, V.; Baskaran, N.; Prasannaa, V. S.; Sugisaki, K.; Mukherjee, D.; Dyall, K. G.; Das, B. P. (2024). "Computation of relativistic and many-body effects in atomic systems using quantum annealing". Phys. Rev. A. 109 (4) 042808: 10pp. Bibcode:2024PhRvA.109d2808K. doi:10.1103/PhysRevA.109.042808.

External links

Categories: