메뉴 건너뛰기




Volumn 22, Issue 12, 2009, Pages 2861-2887

Perturbation theory for the nonlinear Schrödinger equation with a random potential

Author keywords

[No Author keywords available]

Indexed keywords


EID: 70450285548     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/12/004     Document Type: Article
Times cited : (46)

References (63)
  • 2
    • 0009289430 scopus 로고
    • Relation between density of states and range of localization for one dimensional random systems
    • Thouless D J 1972 Relation between density of states and range of localization for one dimensional random systems J. Phys. C: Solid State Phys. 5 77
    • (1972) J. Phys. C: Solid State Phys. , vol.5 , Issue.1 , pp. 77
    • Thouless, D.J.1
  • 6
    • 0035535327 scopus 로고    scopus 로고
    • Bose-Einstein condensation in the alkali gases: Some fundamental concepts
    • Leggett A J 2001 Bose-Einstein condensation in the alkali gases: some fundamental concepts Rev. Mod. Phys. 73 307-56
    • (2001) Rev. Mod. Phys. , vol.73 , Issue.2 , pp. 307-356
    • Leggett, A.J.1
  • 8
    • 51249193203 scopus 로고
    • Structure of a quantized vortex in boson systems
    • Gross E P 1961 Structure of a quantized vortex in boson systems Nuovo Cimento 20 454-77
    • (1961) Nuovo Cimento , vol.20 , Issue.3 , pp. 454-477
    • Gross, E.P.1
  • 10
    • 33846513884 scopus 로고    scopus 로고
    • Rigorous derivation of the Gross-Pitaevskii equation
    • Erdös L, Schlein B and Yau H T 2007 Rigorous derivation of the Gross-Pitaevskii equation Phys. Rev. Lett. 98 040404
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.4 , pp. 040404
    • Erdös, L.1    Schlein, B.2    Yau, H.T.3
  • 11
    • 0037193018 scopus 로고    scopus 로고
    • Proof of Bose-Einstein condensation for dilute trapped gases
    • Lieb E H and Seiringer R 2002 Proof of Bose-Einstein condensation for dilute trapped gases Phys. Rev. Lett. 88 170409
    • (2002) Phys. Rev. Lett. , vol.88 , Issue.17 , pp. 170409
    • Lieb, E.H.1    Seiringer, R.2
  • 12
    • 0344444337 scopus 로고    scopus 로고
    • Best mean-field for condensates
    • Cederbaum L S and Streltsov A I 2003 Best mean-field for condensates Phys. Lett. A 318 564-9
    • (2003) Phys. Lett. , vol.318 , Issue.6 , pp. 564-569
    • Cederbaum, L.S.1    Streltsov, A.I.2
  • 13
    • 28844462850 scopus 로고    scopus 로고
    • Pathway from condensation via fragmentation to fermionization of cold bosonic systems
    • Alon O E and Cederbaum L S 2005 Pathway from condensation via fragmentation to fermionization of cold bosonic systems Phys. Rev. Lett. 95 140402
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.14 , pp. 140402
    • Alon, O.E.1    Cederbaum, L.S.2
  • 14
    • 24244444170 scopus 로고
    • Absence of diffusion in certain random lattices
    • Anderson P W 1958 Absence of diffusion in certain random lattices Phys. Rev. 109 1492
    • (1958) Phys. Rev. , vol.109 , Issue.5 , pp. 1492
    • Anderson, P.W.1
  • 15
    • 0002835770 scopus 로고
    • Localization of eigenstates and transport phenomena in one-dimensional disordered system
    • Ishii K 1973 Localization of eigenstates and transport phenomena in one-dimensional disordered system Suppl. Prog, Theor. Phys. 53 77-138
    • (1973) Suppl. Prog, Theor. Phys. , vol.53 , pp. 77-138
    • Ishii, K.1
  • 16
    • 0040793613 scopus 로고
    • Disordered electronic systems
    • Lee P A and Ramakrishnan T V 1985 Disordered electronic systems Rev. Mod. Phys. 57 287-337
    • (1985) Rev. Mod. Phys. , vol.57 , Issue.2 , pp. 287-337
    • Lee, P.A.1    Ramakrishnan, T.V.2
  • 19
    • 33847421519 scopus 로고    scopus 로고
    • Transport and Anderson localization in disordered two-dimensional photonic lattices
    • Schwartz T, Bartal G, Fishman S and Segev M 2007 Transport and Anderson localization in disordered two-dimensional photonic lattices Nature 446 52-5
    • (2007) Nature , vol.446 , Issue.7131 , pp. 52-55
    • Schwartz, T.1    Bartal, G.2    Fishman, S.3    Segev, M.4
  • 20
    • 28844460530 scopus 로고    scopus 로고
    • Ultracold atoms in optical lattices with random on-site interactions
    • Gimperlein H, Wessel S, Schmiedmayer J and Santos L 2005 Ultracold atoms in optical lattices with random on-site interactions Phys. Rev. Lett. 95 170401
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.17 , pp. 170401
    • Gimperlein, H.1    Wessel, S.2    Schmiedmayer, J.3    Santos, L.4
  • 23
    • 33748650326 scopus 로고    scopus 로고
    • Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
    • Clement D, Varon A F, Retter J A, Sanchez-Palencia L, Aspect A and Bouyer P 2006 Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle New J. Phys. 8 165
    • (2006) New J. Phys. , vol.8 , Issue.8 , pp. 165
    • Clement, D.1    Varon, A.F.2    Retter, J.A.3    Sanchez-Palencia, L.4    Aspect, A.5    Bouyer, P.6
  • 26
    • 28844447953 scopus 로고    scopus 로고
    • Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide
    • Fort C, Fallani L, Guarrera V, Lye J E, Modugno M, Wiersma D S and Inguscio M 2005 Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide Phys. Rev. Lett. 95 170410
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.17 , pp. 170410
    • Fort, C.1    Fallani, L.2    Guarrera, V.3    Lye, J.E.4    Modugno, M.5    Wiersma, D.S.6    Inguscio, M.7
  • 27
    • 42549146096 scopus 로고    scopus 로고
    • Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential
    • Akkermans E, Ghosh S and Musslimani Z H 2008 Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential J. Phys. B 41 045302
    • (2008) J. Phys. B , vol.41 , Issue.4 , pp. 045302
    • Akkermans, E.1    Ghosh, S.2    Musslimani, Z.H.3
  • 28
    • 34547245584 scopus 로고    scopus 로고
    • Superfluidity versus Anderson localization in a dilute Bose gas
    • Paul T, Schlagheck P, Leboeuf P and Pavloff N 2007 Superfluidity versus Anderson localization in a dilute Bose gas Phys. Rev. Lett. 98 210602
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.21 , pp. 210602
    • Paul, T.1    Schlagheck, P.2    Leboeuf, P.3    Pavloff, N.4
  • 31
    • 0348047651 scopus 로고    scopus 로고
    • Intraband discrete breathers in disordered nonlinear systems: I. Delocalization
    • Kopidakis G and Aubry S 1999 Intraband discrete breathers in disordered nonlinear systems: I. Delocalization Physica D 130 155-86
    • (1999) Physica , vol.130 , Issue.3-4 , pp. 155-186
    • Kopidakis, G.1    Aubry, S.2
  • 32
    • 0000198338 scopus 로고    scopus 로고
    • Discrete breathers and delocalization in nonlinear disordered systems
    • Kopidakis G and Aubry S 2000 Discrete breathers and delocalization in nonlinear disordered systems Phys. Rev. Lett. 84 3236-9
    • (2000) Phys. Rev. Lett. , vol.84 , Issue.15 , pp. 3236-3239
    • Kopidakis, G.1    Aubry, S.2
  • 33
    • 4243738139 scopus 로고
    • Delocalization of quantum chaos by weak nonlinearity
    • Shepelyansky D L 1993 Delocalization of quantum chaos by weak nonlinearity Phys. Rev. Lett. 70 1787-90
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.12 , pp. 1787-1790
    • Shepelyansky, D.L.1
  • 34
    • 40849094531 scopus 로고    scopus 로고
    • Destruction of Anderson localization by a weak nonlinearity
    • Pikovsky A S and Shepelyansky D L 2008 Destruction of Anderson localization by a weak nonlinearity Phys. Rev. Lett. 100 094101
    • (2008) Phys. Rev. Lett. , vol.100 , Issue.9 , pp. 094101
    • Pikovsky, A.S.1    Shepelyansky, D.L.2
  • 35
    • 70450229842 scopus 로고    scopus 로고
    • Mulansky M 2009 Localization properties of nonlinear disordered lattices. Universität Potsdam Diploma Thesis http://nbn-resolving.de/urn:nbn:de: kobv:517-opus-31469
    • (2009) Diploma Thesis
    • Mulansky, M.1
  • 36
    • 70349501448 scopus 로고    scopus 로고
    • Spreading for the generalized nonlinear Schrödinger equation with disorder
    • Veksler H, Krivolapov Y and Fishman S 2009 Spreading for the generalized nonlinear Schrödinger equation with disorder Phys. Rev. E 80 037201
    • (2009) Phys. Rev. , vol.80 , Issue.3 , pp. 037201
    • Veksler, H.1    Krivolapov, Y.2    Fishman, S.3
  • 37
    • 40849112002 scopus 로고    scopus 로고
    • Absence of wave packet diffusion in disordered nonlinear systems
    • Kopidakis G, Komineas S, Flach S and Aubry S 2008 Absence of wave packet diffusion in disordered nonlinear systems Phys. Rev. Lett. 100 084103
    • (2008) Phys. Rev. Lett. , vol.100 , Issue.8 , pp. 084103
    • Kopidakis, G.1    Komineas, S.2    Flach, S.3    Aubry, S.4
  • 38
    • 0000122681 scopus 로고    scopus 로고
    • Transport of localized and extended excitations in a nonlinear Anderson model
    • Molina M I 1998 Transport of localized and extended excitations in a nonlinear Anderson model Phys. Rev. B 58 12547-50
    • (1998) Phys. Rev. , vol.58 , Issue.19 , pp. 12547-12550
    • Molina, M.I.1
  • 39
    • 59149094074 scopus 로고    scopus 로고
    • Universal spreading of wavepackets in disordered nonlinear systems
    • Flach S, Krimer D and Skokos Ch 2009 Universal spreading of wavepackets in disordered nonlinear systems Phys. Rev. Lett. 102 024101
    • (2009) Phys. Rev. Lett. , vol.102 , Issue.2 , pp. 024101
    • Flach, S.1    Krimer, D.2    Ch, S.3
  • 40
    • 66749175818 scopus 로고    scopus 로고
    • Delocalization of wave packets in disordered nonlinear chains
    • Skokos C, Krimer D O, Komineas and Flach S S 2009 Delocalization of wave packets in disordered nonlinear chains Phys. Rev. E 79 056211
    • (2009) Phys. Rev. , vol.79 , Issue.5 , pp. 056211
    • Skokos, C.1    Krimer, D.O.2    Komineas3    Flach, S.S.4
  • 41
    • 0001026869 scopus 로고
    • Localization for some continuous, random Hamiltonians in d-dimensions
    • Combes J M and Hislop P D 1994 Localization for some continuous, random Hamiltonians in d-dimensions J. Funct. Anal. 124 149-80
    • (1994) J. Funct. Anal. , vol.124 , Issue.1 , pp. 149-180
    • Combes, J.M.1    Hislop, P.D.2
  • 42
    • 0040163789 scopus 로고    scopus 로고
    • Dynamical localization for discrete and continuous random Schrödinger operators
    • Germinet F and De Bièvre S 1998 Dynamical localization for discrete and continuous random Schrödinger operators Commun. Math. Phys. 194 323-41 (Pubitemid 128359969)
    • (1998) Communications in Mathematical Physics , vol.194 , Issue.2 , pp. 323-341
    • Germinet, F.1    De Bievre, S.2
  • 43
    • 21844521255 scopus 로고
    • Localization for some continuous random Schrödinger-operators
    • Klopp F 1995 Localization for some continuous random Schrödinger- operators Commun. Math. Phys. 167 553-69
    • (1995) Commun. Math. Phys. , vol.167 , Issue.3 , pp. 553-569
    • Klopp, F.1
  • 44
    • 0038134845 scopus 로고    scopus 로고
    • Anderson localization for time periodic random Schrödinger operators
    • Soffer A and Wang W-M 2003 Anderson localization for time periodic random Schrödinger operators Commun. Partial Diff. Eqns. 28 333-47
    • (2003) Commun. Partial Diff. Eqns. , vol.28 , Issue.1 , pp. 333-347
    • Soffer, A.1    Wang, W.-M.2
  • 45
    • 3543001642 scopus 로고    scopus 로고
    • Anderson localization for time quasi-periodic random Schrödinger and wave equations
    • Bourgain J and Wang W M 2004 Anderson localization for time quasi-periodic random Schrödinger and wave equations Commun. Math. Phys. 248 429-66
    • (2004) Commun. Math. Phys. , vol.248 , Issue.3 , pp. 429-466
    • Bourgain, J.1    Wang, W.M.2
  • 46
    • 57249090382 scopus 로고    scopus 로고
    • Logarithmic bounds on Sobolev norms for time dependent linear Schrödinger equations
    • Wang W-M 2008 Logarithmic bounds on Sobolev norms for time dependent linear Schrödinger equations Commun. Partial Diff. Eqns. 33 2164-79
    • (2008) Commun. Partial Diff. Eqns. , vol.33 , Issue.12 , pp. 2164-2179
    • Wang, W.-M.1
  • 47
    • 70349678394 scopus 로고    scopus 로고
    • Growth of Sobolev norms and controllability of Schrödinger equation
    • Nersesyan V 2009 Growth of Sobolev norms and controllability of Schrödinger equation Commun. Math. Phys. 290 371-87
    • (2009) Commun. Math. Phys. , vol.290 , Issue.1 , pp. 371-387
    • Nersesyan, V.1
  • 48
    • 67349143002 scopus 로고    scopus 로고
    • Long time Anderson localization for nonlinear random Schrödinger equation
    • Wang W-M and Zhang Z 2009 Long time Anderson localization for nonlinear random Schrödinger equation J. Stat. Phys. 134 953
    • (2009) J. Stat. Phys. , vol.134 , Issue.5-6 , pp. 953
    • Wang, W.-M.1    Zhang, Z.2
  • 49
    • 0010092601 scopus 로고
    • Periodic-solutions of some infinite-dimensional Hamiltonian-systems associated with non-linear partial difference-equations. i
    • Albanese C and Fröhlich J 1988 Periodic-solutions of some infinite-dimensional Hamiltonian-systems associated with non-linear partial difference-equations. I Commun. Math. Phys. 116 475-502
    • (1988) Commun. Math. Phys. , vol.116 , Issue.3 , pp. 475-502
    • Albanese, C.1    Fröhlich, J.2
  • 50
    • 0000109730 scopus 로고
    • Periodic-solutions of some infinite-dimensional Hamiltonian-systems associated with non-linear partial difference-equations. II
    • Albanese C, Fröhlich J and Spencer T 1988 Periodic-solutions of some infinite-dimensional Hamiltonian-systems associated with non-linear partial difference-equations. II Commun. Math. Phys. 119 677-99
    • (1988) Commun. Math. Phys. , vol.119 , Issue.4 , pp. 677-699
    • Albanese, C.1    Fröhlich, J.2    Spencer, T.3
  • 51
    • 0010150837 scopus 로고
    • Perturbation-theory for periodic-orbits in a class of infinite dimensional Hamiltonian-systems
    • Albanese C and Fröhlich J 1991 Perturbation-theory for periodic-orbits in a class of infinite dimensional Hamiltonian-systems Commun. Math. Phys. 138 193-205
    • (1991) Commun. Math. Phys. , vol.138 , Issue.1 , pp. 193-205
    • Albanese, C.1    Fröhlich, J.2
  • 52
    • 36749086903 scopus 로고    scopus 로고
    • Localization length of stationary states in the nonlinear Schrödinger equation
    • Iomin A and Fishman S 2007 Localization length of stationary states in the nonlinear Schrödinger equation Phys. Rev. E 76 056607
    • (2007) Phys. Rev. , vol.76 , Issue.5 , pp. 056607
    • Iomin, A.1    Fishman, S.2
  • 53
    • 58149271157 scopus 로고    scopus 로고
    • Asymptotic localization of stationary states in the nonlinear Schrödinger equation
    • Fishman S, Iomin A and Mallick K 2008 Asymptotic localization of stationary states in the nonlinear Schrödinger equation Phys. Rev. E 78 066605
    • (2008) Phys. Rev. , vol.78 , Issue.6 , pp. 066605
    • Fishman, S.1    Iomin, A.2    Mallick, K.3
  • 54
    • 43049168798 scopus 로고    scopus 로고
    • On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential
    • Fishman S, Krivolapov Y and Soffer A 2008 On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential J. Stat. Phys. 131 843-65
    • (2008) J. Stat. Phys. , vol.131 , Issue.5 , pp. 843-865
    • Fishman, S.1    Krivolapov, Y.2    Soffer, A.3
  • 55
    • 0003175350 scopus 로고
    • A Nekhoroshev-type theorem for Hamiltonian-systems with infinitely many degrees of freedom
    • Benettin G, Fröhlich J and Giorgilli A 1988 A Nekhoroshev-type theorem for Hamiltonian-systems with infinitely many degrees of freedom Commun. Math. Phys. 119 95-108
    • (1988) Commun. Math. Phys. , vol.119 , Issue.1 , pp. 95-108
    • Benettin, G.1    Fröhlich, J.2    Giorgilli, A.3
  • 56
    • 21344491724 scopus 로고
    • Localization at large disorder and at extreme energies-anelementary derivation
    • Aizenman M and Molchanov S 1993 Localization at large disorder and at extreme energies-anelementary derivation Commun. Math. Phys. 157 245-78
    • (1993) Commun. Math. Phys. , vol.157 , Issue.2 , pp. 245-278
    • Aizenman, M.1    Molchanov, S.2
  • 58
    • 0000280495 scopus 로고    scopus 로고
    • Operators with singular continuous spectrum: IV. Hausdorff dimensions, rank one perturbations, and localization
    • del Rio R, Jitomirskaya S, Last Y and Simon B 1996 Operators with singular continuous spectrum: IV. Hausdorff dimensions, rank one perturbations, and localization J. Anal. Math. 69 153-200
    • (1996) J. Anal. Math. , vol.69 , Issue.1 , pp. 153-200
    • Del Rio, R.1    Jitomirskaya, S.2    Last, Y.3    Simon, B.4
  • 59
    • 0034339654 scopus 로고    scopus 로고
    • Dynamical localization for the random dimer Schrödinger operator
    • De Bièvre S and Germinet F 2000 Dynamical localization for the random dimer Schrödinger operator J. Stat. Phys. 98 1135-48
    • (2000) J. Stat. Phys. , vol.98 , pp. 1135-1148
    • De Bièvre, S.1    Germinet, F.2
  • 60
    • 33644530394 scopus 로고    scopus 로고
    • New characterizations of the region of complete localization for random Schrödinger operators
    • Germinet F and Klein A 2006 New characterizations of the region of complete localization for random Schrödinger operators J. Stat. Phys. 122 73-94
    • (2006) J. Stat. Phys. , vol.122 , Issue.1 , pp. 73-94
    • Germinet, F.1    Klein, A.2
  • 62
    • 64549112073 scopus 로고    scopus 로고
    • On the joint distribution of energy levels of random Schrödinger operators
    • Aizenman M and Warzel S 2009 On the joint distribution of energy levels of random Schrödinger operators J. Phys. A: Math Gen. 42 045201
    • (2009) J. Phys. A: Math Gen. , vol.42 , Issue.4 , pp. 045201
    • Aizenman, M.1    Warzel, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.