Ergodicity (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Ergodicity" in English language version.

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Aaronson, Jon (1997). An introduction to infinite ergodic theory. Mathematical Surveys and Monographs. Vol. 50. Providence, Rhode Island: American Mathematical Society. p. 21. doi:10.1090/surv/050. ISBN 0-8218-0494-4. MR 1450400.

aps.org

link.aps.org

Heller, Eric J. (1984-10-15). "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits". Physical Review Letters. 53 (16): 1515–1518. Bibcode:1984PhRvL..53.1515H. doi:10.1103/PhysRevLett.53.1515.
Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.

archive.org

Walters 1982, §0.1, p. 2 Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 32. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 29. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 152. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 153. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 159. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.
Walters 1982, p. 42. Walters, Peter (1982). An Introduction to Ergodic Theory. Springer. ISBN 0-387-95152-0.

arxiv.org

Gallavotti, Giovanni (1995). "Ergodicity, ensembles, irreversibility in Boltzmann and beyond". Journal of Statistical Physics. 78 (5–6): 1571–1589. arXiv:chao-dyn/9403004. Bibcode:1995JSP....78.1571G. doi:10.1007/BF02180143. S2CID 17605281.
Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. S2CID 120635994.
Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.

books.google.com

Feller, William (1 August 2008). An Introduction to Probability Theory and Its Applications (2nd ed.). Wiley India Pvt. Limited. p. 271. ISBN 978-81-265-1806-7.

cambridge.org

Stöckmann, Hans-Jürgen (1999). Quantum Chaos: An Introduction. Cambridge: Cambridge University Press. doi:10.1017/cbo9780511524622. ISBN 978-0-521-02715-1.

degruyter.com

Heller, Eric Johnson (2018). The semiclassical way to dynamics and spectroscopy. Princeton: Princeton University Press. ISBN 978-1-4008-9029-3. OCLC 1034625177.

doi.org

Schöpf, H.‐G. (January 1970). "<scp>V. I. Arnold</scp> and<scp> A. Avez</scp>, Ergodic Problems of Classical Mechanics. (The Mathematical Physics Monograph Series) IX + 286 S. m. Fig. New York/Amsterdam 1968. W. A. Benjamin, Inc. Preis geb. $ 14.75, brosch. $ 6.95 ". ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 50 (7–9): 506–506. doi:10.1002/zamm.19700500721. ISSN 0044-2267.
Gallavotti, Giovanni (1995). "Ergodicity, ensembles, irreversibility in Boltzmann and beyond". Journal of Statistical Physics. 78 (5–6): 1571–1589. arXiv:chao-dyn/9403004. Bibcode:1995JSP....78.1571G. doi:10.1007/BF02180143. S2CID 17605281.
Plancherel, M. (1913). "Beweis der Unmöglichkeit ergodischer mechanischer Systeme". Annalen der Physik. 42: 1061–1063. doi:10.1002/andp.19133471509.
Stöckmann, Hans-Jürgen (1999). Quantum Chaos: An Introduction. Cambridge: Cambridge University Press. doi:10.1017/cbo9780511524622. ISBN 978-0-521-02715-1.
Heller, Eric J. (1984-10-15). "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits". Physical Review Letters. 53 (16): 1515–1518. Bibcode:1984PhRvL..53.1515H. doi:10.1103/PhysRevLett.53.1515.
Kaplan, L (1999-03-01). "Scars in quantum chaotic wavefunctions". Nonlinearity. 12 (2): R1 – R40. doi:10.1088/0951-7715/12/2/009. ISSN 0951-7715. S2CID 250793219.
Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. S2CID 120635994.
Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.
Aaronson, Jon (1997). An introduction to infinite ergodic theory. Mathematical Surveys and Monographs. Vol. 50. Providence, Rhode Island: American Mathematical Society. p. 21. doi:10.1090/surv/050. ISBN 0-8218-0494-4. MR 1450400.

dx.doi.org

Schöpf, H.‐G. (January 1970). "<scp>V. I. Arnold</scp> and<scp> A. Avez</scp>, Ergodic Problems of Classical Mechanics. (The Mathematical Physics Monograph Series) IX + 286 S. m. Fig. New York/Amsterdam 1968. W. A. Benjamin, Inc. Preis geb. $ 14.75, brosch. $ 6.95 ". ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 50 (7–9): 506–506. doi:10.1002/zamm.19700500721. ISSN 0044-2267.

elsevier.com

linkinghub.elsevier.com

Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. S2CID 120635994.

harvard.edu

ui.adsabs.harvard.edu

Gallavotti, Giovanni (1995). "Ergodicity, ensembles, irreversibility in Boltzmann and beyond". Journal of Statistical Physics. 78 (5–6): 1571–1589. arXiv:chao-dyn/9403004. Bibcode:1995JSP....78.1571G. doi:10.1007/BF02180143. S2CID 17605281.
Heller, Eric J. (1984-10-15). "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits". Physical Review Letters. 53 (16): 1515–1518. Bibcode:1984PhRvL..53.1515H. doi:10.1103/PhysRevLett.53.1515.
Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. S2CID 120635994.
Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.

iop.org

iopscience.iop.org

Kaplan, L (1999-03-01). "Scars in quantum chaotic wavefunctions". Nonlinearity. 12 (2): R1 – R40. doi:10.1088/0951-7715/12/2/009. ISSN 0951-7715. S2CID 250793219.

mathoverflow.net

"Example of a measure-preserving system with dense orbits that is not ergodic". MathOverflow. September 1, 2011. Retrieved May 16, 2020.
"Different uses of the word "ergodic"". MathOverflow. September 4, 2011. Retrieved May 16, 2020.

nature.com

Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.

nih.gov

pubmed.ncbi.nlm.nih.gov

Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.

ncbi.nlm.nih.gov

Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.

semanticscholar.org

api.semanticscholar.org

Gallavotti, Giovanni (1995). "Ergodicity, ensembles, irreversibility in Boltzmann and beyond". Journal of Statistical Physics. 78 (5–6): 1571–1589. arXiv:chao-dyn/9403004. Bibcode:1995JSP....78.1571G. doi:10.1007/BF02180143. S2CID 17605281.
Kaplan, L (1999-03-01). "Scars in quantum chaotic wavefunctions". Nonlinearity. 12 (2): R1 – R40. doi:10.1088/0951-7715/12/2/009. ISSN 0951-7715. S2CID 250793219.
Kaplan, L.; Heller, E.J. (April 1998). "Linear and Nonlinear Theory of Eigenfunction Scars". Annals of Physics. 264 (2): 171–206. arXiv:chao-dyn/9809011. Bibcode:1998AnPhy.264..171K. doi:10.1006/aphy.1997.5773. S2CID 120635994.
Keski-Rahkonen, J.; Ruhanen, A.; Heller, E. J.; Räsänen, E. (2019-11-21). "Quantum Lissajous Scars". Physical Review Letters. 123 (21): 214101. arXiv:1911.09729. Bibcode:2019PhRvL.123u4101K. doi:10.1103/PhysRevLett.123.214101. PMID 31809168. S2CID 208248295.
Keski-Rahkonen, J.; Luukko, P. J. J.; Kaplan, L.; Heller, E. J.; Räsänen, E. (2017-09-20). "Controllable quantum scars in semiconductor quantum dots". Physical Review B. 96 (9): 094204. arXiv:1710.00585. Bibcode:2017PhRvB..96i4204K. doi:10.1103/PhysRevB.96.094204. S2CID 119083672.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.

tuni.fi

trepo.tuni.fi

Keski-Rahkonen, Joonas (2020). Quantum Chaos in Disordered Two-Dimensional Nanostructures. Tampere University. ISBN 978-952-03-1699-0.

worldcat.org

search.worldcat.org

Schöpf, H.‐G. (January 1970). "<scp>V. I. Arnold</scp> and<scp> A. Avez</scp>, Ergodic Problems of Classical Mechanics. (The Mathematical Physics Monograph Series) IX + 286 S. m. Fig. New York/Amsterdam 1968. W. A. Benjamin, Inc. Preis geb. $ 14.75, brosch. $ 6.95 ". ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 50 (7–9): 506–506. doi:10.1002/zamm.19700500721. ISSN 0044-2267.
Kaplan, L (1999-03-01). "Scars in quantum chaotic wavefunctions". Nonlinearity. 12 (2): R1 – R40. doi:10.1088/0951-7715/12/2/009. ISSN 0951-7715. S2CID 250793219.
Heller, Eric Johnson (2018). The semiclassical way to dynamics and spectroscopy. Princeton: Princeton University Press. ISBN 978-1-4008-9029-3. OCLC 1034625177.
Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv:1511.04198. Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN 2045-2322. PMC 5124902. PMID 27892510.
Keski-Rahkonen, J; Luukko, P J J; Åberg, S; Räsänen, E (2019-01-21). "Effects of scarring on quantum chaos in disordered quantum wells". Journal of Physics: Condensed Matter. 31 (10): 105301. arXiv:1806.02598. Bibcode:2019JPCM...31j5301K. doi:10.1088/1361-648x/aaf9fb. ISSN 0953-8984. PMID 30566927. S2CID 51693305.
Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (July 2018). "Weak ergodicity breaking from quantum many-body scars". Nature Physics. 14 (7): 745–749. arXiv:1711.03528. Bibcode:2018NatPh..14..745T. doi:10.1038/s41567-018-0137-5. ISSN 1745-2481. S2CID 256706206.