参考文献#
[Ara05] A. Arai. Generalized Weak Weyl Relation and Decay of Quantum Dynamics. Rev. Math. Phys. 17, 1071–1109, 2005.
[BC09] E. Bédos and R. Conti. On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups. J. Fourier Anal. Appl. 15, 336–365, 2009.
[BES94] J. Bellissard, A. van Elst, and H. Schulz-Baldes. The noncommutative geometry of the quantum Hall effect. J. Math. Phys. 35, 5373–5451, 1994.
[BS98] J. Bellissard and H. Schulz-Baldes. A Kinetic Theory for Quantum Transport in Aperiodic Media. J. Stat. Phys. 91, 991–1027, 1998.
[BLM13] F. Belmonte, M. Lein, and M. M˘antoiu. Magnetic twisted actions on general abelian C∗-algebras. Journal of Operator Theory 69, 33–58, 2013.
[BS87] M. S. Birman and M. Z. Solomyak. L -Theory of the Maxwell operator in arbitrary domains. Uspekhi Mat. Nauk 42, 61–76, 1987.
[BBN13] K. Y. Bliokh, A. Y. Bekshaev, and F. Nori. Dual electromagnetism: helicity, spin, momentum and angular momentum. New Journal of Physics 15, 033026, 2013.
[BGK+05] J.-M. Bouclet, F. Germinet, A. Klein, and J. H. Schenker. Linear response theory for magnetic Schrödinger operators in disordered media. J. Func. Anal. 226, 301–372, 2005.
[BR02] O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics 1. C∗- and W ∗-Algebras, Symmetry Groups, Decomposition of States. Theoretical and Mathematical Physics. Springer-Verlag, 2002.
[BR03] O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics 2. Equilibrium States. Models in Quantum Statistical Mechanics. Theoretical and Mathematical Physics. Springer-Verlag, 2003.
[Bre11] H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer-Verlag, 2011.
[CGH10] J.-M. Combes, F. Germinet, and P. D. Hislop. Conductivity and the current–current correlation measure. J. Phys. A 43, 474010, 2010.
[Con94] A. Connes. Noncommutative Geometry. Academic Press, 1994.
[Dav95] E. B. Davies. The Functional Calculus. J. London Math. Soc. 52, 166–176, 1995.
[de 93] T. de La Rue. Espaces de Lebesgue. Séminaire de Probabilités de Strasbourg 27, 15–21, 1993.
[DL14a] G. De Nittis and M. Lein. Effective Light Dynamics in Perturbed Photonic Crystals. Commun. Math. Phys. 332, 221–260, 2014.
[DL14b] G. De Nittis and M. Lein. On the Role of Symmetries in Photonic Crystals. Annals of Physics 350, 568–587, 2014.
[DL14c] G. De Nittis and M. Lein. The Perturbed Maxwell Operator as Pseudodifferential Operator. Documenta Mathematica 19, 63–101, 2014.
[DL16] G. De Nittis and M. Lein. Derivation of Ray Optics Equations in Photonic Crystals Via a Semiclassical Limit. to appear in Annales Henri Poincaré, 2016.
[DL17] G. De Nittis and M. Lein. Linear Response Theory for Periodic and Random Light Conductors. in preparation, 2017.
[de 07] B. de Pagter. Positivity. In: Trends in Mathematics. Birkhäuser-Verlag, 2007. Chap. Non-commutative Banach function spaces, 197–227.
[dS07] B. de Pagter and F. Sukochev. Commutator Estimates and R-Flows in Non-Commutative Operator Spaces. Proc. Edinburgh Math. Soc. 50, 293– 324, 2007.
[Dix77] J. Dixmier. C∗-algebras. North-Holland, Amsterdam, 1977.
[Dix81] J. Dixmier. Von Neumann Algebras. North-Holland Publishing Co., 1981.
[DDd89] P. G. Dodds, T. K.-Y. Dodds, and B. de Pagter. Non-commutative Banach function spaces. Math. Z. 201, 583–597, 1989.
[DDd93] P. G. Dodds, T. K.-Y. Dodds, and B. de Pagter. Noncommutative Köthe duality. Trans. Amer. Math. Soc. 339, 717–750, 1993.
[DG08] N. Dombrowski and F. Germinet. Linear Response Theory for Random Schrödinger Operators and Noncommutative Integration. Markov Process. Related Fields 14, 403–426, 2008.
[EL69] C. M. Edwards and J. T. Lewis. Twisted group algebras. I. Comm. Math. Phys. 13, 119–130, 1969.
[ES04] A. Elgart and B. Schlein. Adiabatic charge transport and the Kubo formula for Landau-type Hamiltonians. Commun. Pure Appl. Math. 57, 590–615, 2004.
[EN00] K.-J. Engel and R. Nagel. One-Parameter Semigroups for Linear Evolution Equations. Springer-Verlag, 2000.
[FK86] T. Fack and H. Kosaki. Generalized s-numbers of τ-measurable operators. Pacific J. Math. 123, 269–300, 1986.
[FK96] A. Figotin and A. Klein. Localization of Classical Waves I: Acoustic Waves. Commun. Math. Phys. 180, 439–482, 1996.
[FK97] A. Figotin and A. Klein. Localization of Classical Waves II: Electromagnetic Waves. Commun. Math. Phys. 184, 411–441, 1997.
[Fol99] G. B. Folland. Real Analysis: Modern Techniques and Their Applications. John Wiley & Sons Inc., 1999.
[GY83] S. Graffi and K. Yajima. Exterior Complex Scaling and the AC-Stark Effect in a Coulomb Field. Commun. Math. Phys. 89, 277–301, 1983.
[Gre69] F. P. Greenleaf. Invariant means on topological groups and their applications. Van Nostrand Reinhold Co., 1969.
[Gre73] F. P. Greenleaf. Ergodic Theorems and the Construction of Summing Sequences in Amenable Locally Compact Groups. Comm. Pure Appl. Math. 26, 29–46, 1973.
[Gre54] M. S. Green. Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids. J. Chem. Phys. 22, 398–413, 1954.
[Grü73] H. R. Grümm. Two theorems about C . Rep. Math. Phys. 4, 211–215, 1973.
[Hal74] P. R. Halmos. Measure Theory. Springer-Verlag, 1974.
[Hat93] Y. Hatsugai. Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71, 3697–3700, 1993.
[HV86] R. Hempel and J. Voigt. The Spectrum of a Schrödinger Operator in Lp is p-independent. Commun. Math. Phys. 104, 243–250, 1986.
[JOP06] V. Jakši´c, Y. Ogata, and C.-A. Pillet. The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics. Commun. Math. Phys. 265, 721–738, 2006.
[JP02] V. Jakši´c and C.-A. Pillet. Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics. J. Stat. Phys. 108, 787–829, 2002.
[JLW+16] D. Jin, L. Lu, Z. Wang, C. Fang, J. D. Joannopoulos, M. Soljaˇci´c, L. Fu, and N. X. Fang. Topological magnetoplasmon. arXiv 1602.00553, 2016.
[KR97a] R. V. Kadison and J. R. Ringrose. Fundamentals of the Theory of Operator Algebras I. Elementary Theory. Vol. 15. Graduate Studies in Mathematics. Academic Press, Inc., 1997.
[KR97b] R. V. Kadison and J. R. Ringrose. Fundamentals of the Theory of Operator Algebras II. Advanced Theory. Vol. 16. Graduate Studies in Mathematics. Academic Press, Inc., 1997.
[KS04] J. Kellendonk and H. Schulz-Baldes. Quantization of edge currents for continuous magnetic operators. J. Func. Anal. 209, 388–413, 2004.
[KLM07] A. Klein, O. Lenoble, and P. Müller. On Mott's formula for the ac-conductivity in the Anderson model. Ann. of Math. 166, 549–577, 2007.
[KJE82] S. Krein, P. J., and S. E. Interpolation of Linear Operators. Vol. 54. Translations of Mathematical Monographs. AMS, 1982.
[Kub57] R. Kubo. Statistical-Mechanical Theory of Irreversible Processes I. General Theory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jap. 12, 570–586, 1957.
[LS81] H. Leinfelder and C. G. Simader. Schrödingers Operators with Singular Magnetic Vector Potentials. Math. Z. 176, 1–19, 1981.
[LMR10] M. Lein, M. M˘antoiu, and S. Richard. Magnetic pseudodifferential operators with coefficients in C∗-algebras. Publ. RIMS Kyoto Univ. 46, 755– 788, 2010.
[Len99] D. H. Lenz. Random Operators and Crossed Products. Mathematical Physics, Analysis and Geometry 2, 197–220, 1999.
[LPV07] D. Lenz, N. Peyerimhoff, and I. Veseli´c. Groupoids, von Neumann Algebras and the Integrated Density of States. Mathematical Physics, Analysis and Geometry 10, 1–41, 2007.
[LS03] D. Lenz and P. Stollmann. Algebras of Random Operators Associated to Delone Dynamical Systems. Mathematical Physics, Analysis and Geometry 6, 269–290, 2003.
[MP04] M. M˘antoiu and R. Purice. The Magnetic Weyl Calculus. J. Math. Phys. 45, 1394–1417, 2004.
[MPR05] M. M˘antoiu, R. Purice, and S. Richard. Twisted Crossed Products and Magnetic Pseudodifferential Operators. In: Operator Algebras and Mathematical Physics. Theta, 2005, 137–172.
[Nel74] E. Nelson. Notes on Non-Commutative Integration. J. Func. Anal. 15, 103–116, 1974.
[NN81] A. Nenciu and G. Nenciu. Dynamics in Bloch electrons in external electric fields. I. Bounds for interband transitions and effective Wannier Hamiltonians. J. Phys. A 14, 2817–2827, 1981.
[NN82] A. Nenciu and G. Nenciu. Dynamics of Bloch electrons in external electric fields. II. The existence of Stark-Wannier ladder resonances. J. Phys. A 15, 3313–3328, 1982.
[Ohm10] G. S. Ohm. Die galvanische Kette: mathematisch bearbeitet. Kessinger Publishing, LLC, 2010.
[OMN06] M. Onoda, S. Murakami, and N. Nagaosa. Geometrical asepcts in optical wave-packet dynamics. Phys. Rev. E 74, 066610, 2006.
[Pac89] J. A. Packer. Twisted Group C∗-Algebras Corresponding to Nilpotent Discrete Groups. Mathematica Scandinavica 64, 109–122, 1989.
[PST03a] G. Panati, H. Spohn, and S. Teufel. Effective dynamics for Bloch electrons: Peierls substitution. Commun. Math. Phys. 242, 547–578, 2003.
[PST03b] G. Panati, H. Spohn, and S. Teufel. Space-Adiabatic Perturbation Theory. Adv. Theor. Math. Phys. 7, 145–204, 2003.
[Ped79] G. K. Pedersen. C∗-algebras and their automorphism groups. Academic Press, Inc., 1979.
[PB16] E. Prodan and J. Bellissard. Mapping the current–current correlation function near a quantum critical point. Annals of Physics 368, 1–15, 2016.
[PS16] E. Prodan and H. Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators: From K -Theory to Physics. Mathematical Physics Studies. Springer-Verlag, 2016.
[RH08] S. Raghu and F. D. M. Haldane. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834, 2008.
[RZP+13] M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit. Photonic Floquet topological insulators. Nature 496, 196–200, 2013.
[RS72] M. Reed and B. Simon. Methods of Mathematical Physics I: Functional Analysis. Academic Press, 1972.
[RS75] M. Reed and B. Simon. Methods of Mathematical Physics II: Fourier Anal ysis, Self-adjointness. Academic Press, 1975.
[Sak91] S. Sakai. Operator Algebras in Dynamical Systems. Vol. 41. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1991.
[Sch12] K. Schmüdgen. Unbounded Self-adjoint Operators on Hilbert Space. Vol. 265. Graduate Texts in Mathematics. Springer-Verlag, 2012.
[Sch96] F. E. Schroeck Jr. Quantum Mechanics on Phase Space. Vol. 74. Fundamental Theories of Physics. Springer, 1996.
[SB98] H. Schulz-Baldes and J. Bellissard. A kinetic theory for quantum transport in aperiodic media. J. Stat. Phys. 91, 991–1026, 1998.
[Seg53] I. E. Segal. A non-commutative extension of abstract integration. Ann. of Math. 57, 401–457, 1953.
[Str82] P. Strˇeda. Theory of quantised Hall conductivity in two dimensions. J. Phys. C. 15, L717–L721, 1982.
[SH15] R. Süsstrunk and S. D. Huber. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50, 2015.
[SH16] R. Süsstrunk and S. D. Huber. Classification of topological phonons in linear mechanical metamaterials. arXiv 1604.01033, 2016.
[Tak02] M. Takesaki. Theory of Operator Algebras I. Springer-Verlag, 2002.
[Tak03] M. Takesaki. Theory of Operator Algebras II. Springer-Verlag, 2003.
[Ter81] M. Terp. Lp-Spaces Associated with von Neumann Algebras. Copenhagen University, 1981.
[TKN+82] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Den Nijs. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408, 1982.
[Tre67] F. Treves. Topological vector spaces, distributions and kernels. Academic Press, 1967.
[WCJ+09] Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljaˇci´c. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775, 2009.
[Wid71] D. V. Widder. An Introduction to Transform Theory. Academic Press, Inc., 1971.
[Wig39] E. P. Wigner. On Unitary Representations of the Inhomogeneous Lorentz Group. Annals of Mathematics 40, 149–204, 1939.
[Wil07] D. P. Williams. Crossed Products of C∗-Algebras. Vol. 134. Mathematical Surveys and Monographs. AMS, 2007.
[XMY+15] M. Xiao, G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan. Geometric phase and band inversion in periodic acoustic systems. Nature Physics 11, 240–244, 2015.
[Yea73] F. J. Yeadon. Convergence of measurable operators. Proc. Camb. Phil. Soc. 74, 257–268, 1973.
[Yos95] K. Yosida. Functional Analysis. Springer-Verlag, 1995.
[Zhe11] L. Zhe. On some mathematical aspects of the Heisenberg relation. Sci. China Math. 54, 2427–2452, 2011.