메뉴 건너뛰기




Volumn 8, Issue 3, 2005, Pages 257-285

Lifshits tails caused by anisotropic decay: The emergence of a quantum-classical regime

Author keywords

Integrated density of states; Lifshits tails; Random Schr dinger operators

Indexed keywords


EID: 26644432948     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11040-005-0582-0     Document Type: Article
Times cited : (8)

References (45)
  • 5
    • 84980162898 scopus 로고
    • Asymptotics of the Wiener sausage
    • Errata: Ibid. p. 677
    • Donsker, M. D. and Varadhan, S.R. S.: Asymptotics of the Wiener sausage, Comm. Pure Appl. Math. 28 (1975), 525-565. Errata: Ibid. p. 677.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 525-565
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 8
    • 0032346360 scopus 로고    scopus 로고
    • Lifschitz tail in a magnetic field: The nonclassical regime
    • Erdos, L.: Lifschitz tail in a magnetic field: The nonclassical regime, Probab. Theory Related Fields 112 (1998), 321-371.
    • (1998) Probab. Theory Related Fields , vol.112 , pp. 321-371
    • Erdos, L.1
  • 9
    • 0035643283 scopus 로고    scopus 로고
    • Lifschitz tail in a magnetic field: Coexistence of the classical and quantum behavior in the borderline case
    • Erdos, L.: Lifschitz tail in a magnetic field: Coexistence of the classical and quantum behavior in the borderline case, Probab. Theory Related Fields 121 (2001), 219-236.
    • (2001) Probab. Theory Related Fields , vol.121 , pp. 219-236
    • Erdos, L.1
  • 10
    • 1842448921 scopus 로고    scopus 로고
    • Lifshits tails in three space dimensions: Impurity potentials with slow anisotropic decay
    • Hundertmark, D., Kirsch, W. and Warzel, S.: Lifshits tails in three space dimensions: Impurity potentials with slow anisotropic decay, Markov Process. Related Fields 9 (2003), 651-660.
    • (2003) Markov Process. Related Fields , vol.9 , pp. 651-660
    • Hundertmark, D.1    Kirsch, W.2    Warzel, S.3
  • 11
    • 0033235597 scopus 로고    scopus 로고
    • Poissonian obstacles with Gaussian walls discriminate between classical and quantum Lifshits tailing in magnetic fields
    • Hupfer, T., Leschke, H. and Warzel, S.: Poissonian obstacles with Gaussian walls discriminate between classical and quantum Lifshits tailing in magnetic fields, J. Statist. Phys. 97 (1999), 725-750.
    • (1999) J. Statist. Phys. , vol.97 , pp. 725-750
    • Hupfer, T.1    Leschke, H.2    Warzel, S.3
  • 12
    • 0040935939 scopus 로고    scopus 로고
    • The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity
    • Hupfer, T., Leschke, H. and Warzel, S.: The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity, AMS/IP Stud. Adv. Math. 16 (2000), 233-247.
    • (2000) AMS/IP Stud. Adv. Math. , vol.16 , pp. 233-247
    • Hupfer, T.1    Leschke, H.2    Warzel, S.3
  • 14
    • 0000818766 scopus 로고
    • Random Schrödinger operators: A course
    • H. Holden and A. Jensen (eds), Lecture Notes in Phys. 345, Springer, Berlin
    • Kirsch, W.: Random Schrödinger operators: A course, In: H. Holden and A. Jensen (eds), Schrödinger Operators, Lecture Notes in Phys. 345, Springer, Berlin, 1989, pp. 264-370.
    • (1989) Schrödinger Operators , pp. 264-370
    • Kirsch, W.1
  • 15
    • 0033148063 scopus 로고    scopus 로고
    • Internal Lifshits tails for random perturbations of periodic Schrödinger operators
    • Erratum: mp_arc 00-389
    • Klopp, F.: Internal Lifshits tails for random perturbations of periodic Schrödinger operators, Duke Math. J. 98 (1999), 335-369. Erratum: mp_arc 00-389.
    • (1999) Duke Math. J. , vol.98 , pp. 335-369
    • Klopp, F.1
  • 16
    • 0037715328 scopus 로고    scopus 로고
    • Une remarque á propos des asymptotiques de Lifshitz internes
    • Klopp, F.: Une remarque á propos des asymptotiques de Lifshitz internes, C.R. Acad. Sci. Paris Ser. I 335 (2002), 87-92.
    • (2002) C.R. Acad. Sci. Paris Ser. I , vol.335 , pp. 87-92
    • Klopp, F.1
  • 17
    • 0000505933 scopus 로고
    • Absence of absolutely continuous spectrum for some one-dimensional random but deterministic Schrödinger operators
    • Kirsch, W., Kotani, S. and Simon, B.: Absence of absolutely continuous spectrum for some one-dimensional random but deterministic Schrödinger operators, Ann. Inst. H. Poincare Phys. Théor. 42 (1985), 383-406.
    • (1985) Ann. Inst. H. Poincare Phys. Théor. , vol.42 , pp. 383-406
    • Kirsch, W.1    Kotani, S.2    Simon, B.3
  • 18
    • 0000112074 scopus 로고
    • On the ergodic properties of the spectrum of general random operators
    • Kirsch, W. and Martinelli, F.: On the ergodic properties of the spectrum of general random operators, J. Reine Angew. Math. 334 (1982), 141-156.
    • (1982) J. Reine Angew. Math. , vol.334 , pp. 141-156
    • Kirsch, W.1    Martinelli, F.2
  • 19
    • 0002359044 scopus 로고
    • Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians
    • Kirsch, W. and Martinelli, F.: Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians, Comm. Math. Phys. 89 (1983), 27-40.
    • (1983) Comm. Math. Phys. , vol.89 , pp. 27-40
    • Kirsch, W.1    Martinelli, F.2
  • 20
    • 0010964692 scopus 로고
    • On the essential self adjointness of stochastic Schrödinger operators
    • Kirsch, W. and Martinelli, F.: On the essential self adjointness of stochastic Schrödinger operators, Duke Math. J. 50 (1983), 1255-1260.
    • (1983) Duke Math. J. , vol.50 , pp. 1255-1260
    • Kirsch, W.1    Martinelli, F.2
  • 21
    • 0002351434 scopus 로고
    • Lifshits tails for periodic plus random potentials
    • Kirsch, W. and Simon, B.: Lifshits tails for periodic plus random potentials, J. Statist. Phys. 42 (1986), 799-808.
    • (1986) J. Statist. Phys. , vol.42 , pp. 799-808
    • Kirsch, W.1    Simon, B.2
  • 22
    • 0001130640 scopus 로고
    • Comparison theorems for the gap of Schrödinger operators
    • Kirsch, W. and Simon, B.: Comparison theorems for the gap of Schrödinger operators, J. Funct. Anal. 75 (1987), 396-410.
    • (1987) J. Funct. Anal. , vol.75 , pp. 396-410
    • Kirsch, W.1    Simon, B.2
  • 23
    • 0036942041 scopus 로고    scopus 로고
    • Lifshitz tails for 2-dimensional random Schrödinger operators
    • Klopp, R and Wolff, T.: Lifshitz tails for 2-dimensional random Schrödinger operators, J. Anal. Math. 88 (2002), 63-147.
    • (2002) J. Anal. Math. , vol.88 , pp. 63-147
    • Klopp, R.1    Wolff, T.2
  • 25
    • 17144383025 scopus 로고    scopus 로고
    • A survey of rigorous results on random Schrödinger operators for amorphous solids
    • Leschke, H., Müller, P. and Warzel, S.: A survey of rigorous results on random Schrödinger operators for amorphous solids, Markov Process. Related Fields 9 (2003), 729-760.
    • (2003) Markov Process. Related Fields , vol.9 , pp. 729-760
    • Leschke, H.1    Müller, P.2    Warzel, S.3
  • 26
    • 1842505118 scopus 로고    scopus 로고
    • Quantum-classical transitions in Lifshits tails with magnetic fields
    • Leschke, H. and Warzel, S.: Quantum-classical transitions in Lifshits tails with magnetic fields, Phys. Rev. Lett. 92 (2004), 086402 (1-4).
    • (2004) Phys. Rev. Lett. , vol.92 , Issue.1-4 , pp. 086402
    • Leschke, H.1    Warzel, S.2
  • 27
    • 0000318248 scopus 로고
    • Structure of the energy spectrum of the impurity bands in disordered solid solutions
    • Russian original
    • Lifshitz, I. M.: Structure of the energy spectrum of the impurity bands in disordered solid solutions, Soviet Phys. JETP 17 (1963), 1159-1170. Russian original:
    • (1963) Soviet Phys. JETP , vol.17 , pp. 1159-1170
    • Lifshitz, I.M.1
  • 29
    • 26644439227 scopus 로고
    • Internal Lifshitz singularities for disordered finite-difference operators
    • Mezincescu, G. A.: Internal Lifshitz singularities for disordered finite-difference operators, Comm. Math. Phys. 103 (1986), 167-176.
    • (1986) Comm. Math. Phys. , vol.103 , pp. 167-176
    • Mezincescu, G.A.1
  • 30
    • 26644462567 scopus 로고
    • Lifschitz singularities for periodic operators plus random potential
    • Mezincescu, G. A.: Lifschitz singularities for periodic operators plus random potential, J. Statist. Phys. 49 (1987), 1181-1190.
    • (1987) J. Statist. Phys. , vol.49 , pp. 1181-1190
    • Mezincescu, G.A.1
  • 31
    • 21344498311 scopus 로고
    • Internal Lifshitz singularities for one-dimensional Schrödinger operators
    • Mezincescu, G. A.: Internal Lifshitz singularities for one-dimensional Schrödinger operators, Comm. Math. Phys. 158 (1993), 315-325.
    • (1993) Comm. Math. Phys. , vol.158 , pp. 315-325
    • Mezincescu, G.A.1
  • 32
    • 0036696248 scopus 로고    scopus 로고
    • The uniqueness of the integrated density of states for the Schrödinger operators for the Robin boundary conditions
    • Mine, T.: The uniqueness of the integrated density of states for the Schrödinger operators for the Robin boundary conditions, Publ. Res. Inst. Math. Sci., Kyoto Univ. 38 (2002), 355-385.
    • (2002) Publ. Res. Inst. Math. Sci., Kyoto Univ. , vol.38 , pp. 355-385
    • Mine, T.1
  • 33
    • 0000188166 scopus 로고
    • On the spectral distribution of the Schrödinger operator with random potential
    • Nakao, S.: On the spectral distribution of the Schrödinger operator with random potential, Japan. J. Math. 3 (1977), 111-139.
    • (1977) Japan. J. Math. , vol.3 , pp. 111-139
    • Nakao, S.1
  • 34
    • 1642270952 scopus 로고
    • Behavior of some Wiener integrals as t → ∞ and the density of states of Schrödinger equations with random potential
    • Russian original
    • Pastur, L. A.: Behavior of some Wiener integrals as t → ∞ and the density of states of Schrödinger equations with random potential, Theoret. Math. Phys. 32 (1977), 615-620. Russian original:
    • (1977) Theoret. Math. Phys. , vol.32 , pp. 615-620
    • Pastur, L.A.1
  • 35
    • 26644464777 scopus 로고
    • Teoret. Mat. Fiz, 6 (1977), 88-95.
    • (1977) Teoret. Mat. Fiz , vol.6 , pp. 88-95
  • 38
    • 85016600983 scopus 로고
    • Schrödinger semigroups
    • Erratum: Bull. Amer. Math. Soc. (N.S.) 7 (1982), 447-526
    • Simon, B.: Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 447-526. Erratum: Bull. Amer. Math. Soc. (N.S.) 7 (1982), 447-526.
    • (1982) Bull. Amer. Math. Soc. (N.S.) , vol.7 , pp. 447-526
    • Simon, B.1
  • 39
    • 0002961358 scopus 로고
    • Lifshitz tails for the Anderson model
    • Simon, B.: Lifshitz tails for the Anderson model, J. Statist. Phys. 38 (1985), 65-76.
    • (1985) J. Statist. Phys. , vol.38 , pp. 65-76
    • Simon, B.1
  • 40
    • 0009283963 scopus 로고
    • Internal Lifshitz tails
    • Simon, B.: Internal Lifshitz tails, J. Statist. Phys. 46 (1987), 911-918.
    • (1987) J. Statist. Phys. , vol.46 , pp. 911-918
    • Simon, B.1
  • 42
    • 0012377510 scopus 로고    scopus 로고
    • Lifshitz asymptotics via linear coupling of disorder
    • Stollmann, P.: Lifshitz asymptotics via linear coupling of disorder, Math. Phys. Anal. Geom. 2 (1999), 2679-2689.
    • (1999) Math. Phys. Anal. Geom. , vol.2 , pp. 2679-2689
    • Stollmann, P.1
  • 44
    • 26644460378 scopus 로고    scopus 로고
    • Integrated density of states and Wegner estimates for random Schrödinger operators
    • Veselic, I.: Integrated density of states and Wegner estimates for random Schrödinger operators, Contemp. Math. 340 (2004), 97-183.
    • (2004) Contemp. Math. , vol.340 , pp. 97-183
    • Veselic, I.1
  • 45
    • 0040341936 scopus 로고    scopus 로고
    • Logos, Berlin, 2001. PhD thesis, University Erlangen-Ntirnberg
    • Warzel, S.: On Lifshits Tails in Magnetic Fields, Logos, Berlin, 2001. PhD thesis, University Erlangen-Ntirnberg (2001).
    • (2001) On Lifshits Tails in Magnetic Fields
    • Warzel, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.