메뉴 건너뛰기




Volumn 11, Issue 1, 2000, Pages 281-288

Fractal spectrum of periodic quantum systems in a magnetic field

Author keywords

[No Author keywords available]

Indexed keywords

MAGNETIC FLUX; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUMERICAL ANALYSIS; QUANTUM THEORY;

EID: 0033942922     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00296-3     Document Type: Article
Times cited : (8)

References (29)
  • 1
    • 0000653017 scopus 로고
    • Energy spectrum of a conductivity electron in a magnetic field
    • M.Ya. Azbel, Energy spectrum of a conductivity electron in a magnetic field, Sov. Phys. ZETP 46 (1964) 634-657.
    • (1964) Sov. Phys. ZETP , vol.46 , pp. 634-657
    • Azbel, M.Ya.1
  • 2
    • 0001032458 scopus 로고
    • Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
    • D.R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys.Rev. B 14 (1976) 2239-2249.
    • (1976) Phys.Rev. B , vol.14 , pp. 2239-2249
    • Hofstadter, D.R.1
  • 3
    • 84987157216 scopus 로고
    • A remark not dependent on rationality for Bloch electrons in a magnetic field
    • G.H. Wannier, A remark not dependent on rationality for Bloch electrons in a magnetic field, Phys. Stat. Sol. B 88 (1978) 757-765.
    • (1978) Phys. Stat. Sol. B , vol.88 , pp. 757-765
    • Wannier, G.H.1
  • 4
    • 84956131297 scopus 로고
    • Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential
    • D. Weiss, K. von Klitzing, K. Ploog, G. Weimann, Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential, Europhys. Lett. 8 (1989) 179-184.
    • (1989) Europhys. Lett. , vol.8 , pp. 179-184
    • Weiss, D.1    Von Klitzing, K.2    Ploog, K.3    Weimann, G.4
  • 5
    • 0000419240 scopus 로고
    • Magnetoresistance oscillations in a grid potential: Indication of a Hofstadter-type energy spectrum
    • R.R. Gerhardts, D. Weiss, U. Wulf, Magnetoresistance oscillations in a grid potential: Indication of a Hofstadter-type energy spectrum, Phys. Rev. B 43 (1991) 5192-5195.
    • (1991) Phys. Rev. B , vol.43 , pp. 5192-5195
    • Gerhardts, R.R.1    Weiss, D.2    Wulf, U.3
  • 6
    • 0001444468 scopus 로고    scopus 로고
    • Manifestation of the Hofstadter butterfly in far-infrared absorption
    • V. Gudmundsson, R.R. Gerhardts, Manifestation of the Hofstadter butterfly in far-infrared absorption, Phys. Rev. B 54 (1996) 5223-5227.
    • (1996) Phys. Rev. B , vol.54 , pp. 5223-5227
    • Gudmundsson, V.1    Gerhardts, R.R.2
  • 7
    • 0002330387 scopus 로고
    • Semi-classical analysis for Harper's equation III
    • B. Helffer, J. Sjöstrand, Semi-classical analysis for Harper's equation III, Memories Soc. Math. France 39 (1989) 1-124.
    • (1989) Memories Soc. Math. France , vol.39 , pp. 1-124
    • Helffer, B.1    Sjöstrand, J.2
  • 8
    • 0001539982 scopus 로고
    • On the measure of the spectrum for almost-Mathieu operator
    • J. Avron, P.H.M. van Mouche, B. Simon, On the measure of the spectrum for almost-Mathieu operator, Commun. Math. Phys. 132 (1990) 103-118.
    • (1990) Commun. Math. Phys. , vol.132 , pp. 103-118
    • Avron, J.1    Van Mouche, P.H.M.2    Simon, B.3
  • 9
    • 0001391870 scopus 로고
    • Gauss potentials and the rotation algebra
    • M.D. Choi, G.A. Elliot, N. Yui, Gauss potentials and the rotation algebra, Invent. Math. 99 (1990) 225-246.
    • (1990) Invent. Math. , vol.99 , pp. 225-246
    • Choi, M.D.1    Elliot, G.A.2    Yui, N.3
  • 10
    • 21844487920 scopus 로고
    • The noncommutative geometry and quantum Hall effect
    • J. Bellisard, A. vanElst, H. Schulz-Baldes, The noncommutative geometry and quantum Hall effect, J. Math. Phys. 35 (1994) 5373-5451.
    • (1994) J. Math. Phys. , vol.35 , pp. 5373-5451
    • Bellisard, J.1    VanElst, A.2    Schulz-Baldes, H.3
  • 11
    • 33646314353 scopus 로고
    • La papillon de Hofstadter
    • J. Bellissard, La papillon de Hofstadter, Astérisque 206 (1992) 7-39.
    • (1992) Astérisque , vol.206 , pp. 7-39
    • Bellissard, J.1
  • 14
    • 36149029662 scopus 로고
    • Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods
    • J. Bellisard, C. Kreft, R. Seiler, Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods, J. Phys. A 24 (1991) 2329-2353.
    • (1991) J. Phys. A , vol.24 , pp. 2329-2353
    • Bellisard, J.1    Kreft, C.2    Seiler, R.3
  • 15
    • 0030491042 scopus 로고    scopus 로고
    • Model of the Hofstadter-type
    • C. Kreft, R. Seiler, Model of the Hofstadter-type, J. Math. Phys. 37 (1996) 5207-5243.
    • (1996) J. Math. Phys. , vol.37 , pp. 5207-5243
    • Kreft, C.1    Seiler, R.2
  • 16
    • 0021757421 scopus 로고
    • Critical properties of electron eigenstates in incommensurate systems
    • A.M. Wilkinson, Critical properties of electron eigenstates in incommensurate systems, Proc. R. Soc. London, Ser. A 391 (1984) 305-350.
    • (1984) Proc. R. Soc. London, Ser. A , vol.391 , pp. 305-350
    • Wilkinson, A.M.1
  • 17
    • 0001615308 scopus 로고
    • Energy spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping
    • Y. Hatsugai, M. Kohmoto, Energy spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping, Phys. Rev. B 42 (1990) 8282-8294.
    • (1990) Phys. Rev. B , vol.42 , pp. 8282-8294
    • Hatsugai, Y.1    Kohmoto, M.2
  • 18
    • 4244101938 scopus 로고
    • Hofstadter spectra in two-dimensional superlattice with arbitrary modulation strength
    • M.A. Andrade Neto, P.A. Schulz, Hofstadter spectra in two-dimensional superlattice with arbitrary modulation strength, Phys. Rev. B 52 (1995) 14093-14097.
    • (1995) Phys. Rev. B , vol.52 , pp. 14093-14097
    • Andrade Neto, M.A.1    Schulz, P.A.2
  • 19
    • 0343680689 scopus 로고
    • Energy spectrum for two-dimensional periodic potentials in a magnetic field
    • O. Kühn, V. Fessatidis, H.L. Cui, P.E. Sellbmann, N.J.M. Horing, Energy spectrum for two-dimensional periodic potentials in a magnetic field, Phys. Rev. B 47 (1993) 13019-13022.
    • (1993) Phys. Rev. B , vol.47 , pp. 13019-13022
    • Kühn, O.1    Fessatidis, V.2    Cui, H.L.3    Sellbmann, P.E.4    Horing, N.J.M.5
  • 20
    • 4243184531 scopus 로고
    • Bloch electron in magnetic fields: Classical chaos and Hofstadter's butterfly
    • G. Petschel, T. Geisel, Bloch electron in magnetic fields: classical chaos and Hofstadter's butterfly, Phys. Rev. Lett. 71 (1993) 239-242.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 239-242
    • Petschel, G.1    Geisel, T.2
  • 21
    • 0030655465 scopus 로고    scopus 로고
    • Two-dimensional electron gas in a magnetical field and point potentials
    • S. Gredeskul, Ya. Avishai, M.Y. Azbel, Two-dimensional electron gas in a magnetical field and point potentials, Low-Temp. Physics 23 (1997) 21-33.
    • (1997) Low-Temp. Physics , vol.23 , pp. 21-33
    • Gredeskul, S.1    Avishai, Ya.2    Azbel, M.Y.3
  • 22
    • 0000782854 scopus 로고
    • The two-dimensional Schrödinger operator with a uniform magnetic field, and its perturbation by periodic zero-range potentials
    • V.A. Geyler, The two-dimensional Schrödinger operator with a uniform magnetic field, and its perturbation by periodic zero-range potentials, St. Petersburg Math. J. 3 (1992) 489-532.
    • (1992) St. Petersburg Math. J. , vol.3 , pp. 489-532
    • Geyler, V.A.1
  • 23
    • 4243079056 scopus 로고
    • The spectrum of a magneto-Bloch electron in a periodic array of quantum dots: Explicitly solvable model
    • V.A. Geyler, I.Yu. Popov, The spectrum of a magneto-Bloch electron in a periodic array of quantum dots: explicitly solvable model, Z. Phys. B 93 (1994) 437-439.
    • (1994) Z. Phys. B , vol.93 , pp. 437-439
    • Geyler, V.A.1    Popov, I.Yu.2
  • 24
    • 33744663636 scopus 로고
    • Periodic array of quantum dots in a magnetic field: Irrational flux; honeycomb lattice
    • V.A. Geyler, I.Yu. Popov, Periodic array of quantum dots in a magnetic field: irrational flux; honeycomb lattice, Z. Phys. B 98 (1995) 473-477.
    • (1995) Z. Phys. B , vol.98 , pp. 473-477
    • Geyler, V.A.1    Popov, I.Yu.2
  • 25
    • 0030502382 scopus 로고    scopus 로고
    • Spectral properties of a charged particle in antidot array: A limiting case of quantum billiard
    • V.A. Geyler, B.S. Pavlov, I.Yu. Popov, Spectral properties of a charged particle in antidot array: a limiting case of quantum billiard, J. Math. Phys. 37 (1996) 5171-5194.
    • (1996) J. Math. Phys. , vol.37 , pp. 5171-5194
    • Geyler, V.A.1    Pavlov, B.S.2    Popov, I.Yu.3
  • 28
    • 76549105667 scopus 로고
    • The theory of extensions and explicitly-solvable models
    • B.S. Pavlov, The theory of extensions and explicitly-solvable models, Russ. Math. Surv. 42 (1987) 127-168.
    • (1987) Russ. Math. Surv. , vol.42 , pp. 127-168
    • Pavlov, B.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.