B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000).

[CrossRef]

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998);H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998).

[CrossRef]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves, and localization,” Eur. J. Phys. 18, 222–228 (1997).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

I. Dana, E. Eisenberg, and N. Shnerb, “Dynamical localization near quantum antiresonance: exact results and a solvable case,” Phys. Rev. Lett. 74, 686–689 (1995);“Antiresonance and localization in quantum dynamics,” Phys. Rev. E 54, 5948–5963 (1996);E. Eisenberg and I. Dana, “Limited sensitivity to analyticity: a manifestation of quantum chaos,” Found. Phys. 27, 153–170 (1997).

[CrossRef]
[PubMed]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

[CrossRef]
[PubMed]

R. Graham, M. Schlautmann, and P. Zoller, “Dynamical localization of atomic-beam deflection by a modulated standing light wave,” Phys. Rev. A 45, R19–R22 (1992); see also R. Graham, M. Schlautmann, and D. L. Shepelyansky, “Dynamical localization in Josephson junctions,” Phys. Rev. Lett. 67, 255–258 (1991), and references therein.

[CrossRef]
[PubMed]

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

[CrossRef]
[PubMed]

R. E. Prange and S. Fishman, “Experimental realizations of kicked quantum chaotic systems,” Phys. Rev. Lett. 63, 704–707 (1989);O. Agam, S. Fishman, and R. E. Prange, “Experimental realizations of quantum chaos in dielectric waveguides,” Phys. Rev. A 45, 6773–6802 (1992).

[CrossRef]
[PubMed]

L. Liu, “Talbot and Lau effects on incident beams of arbitrary wavefront, and their use,” Appl. Opt. 28, 4668–4678 (1989).

[CrossRef]
[PubMed]

G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein;R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein;E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. 61, 2011–2014 (1988);J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. 63, 364–367 (1989), and references therein;R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. 62, 341–344 (1989);R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A 44, 4521–4540 (1991), and references therein.

[CrossRef]
[PubMed]

J. Krug, “Optical analog of a kicked quantum oscillator,” Phys. Rev. Lett. 59, 2133–2136 (1987).

[CrossRef]
[PubMed]

D. L. Shepelyansky, “Localization of quasienergy eigenfunctions in action space,” Phys. Rev. Lett. 56, 677–680 (1986);“Localization of diffusive excitation in multi-level systems,” Physica D 28, 103–114 (1987).

[CrossRef]
[PubMed]

R. Blumel, S. Fishman, and U. Smilansky, “Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization,” J. Chem. Phys. 84, 2604–2614 (1986).

[CrossRef]

M. Wilkinson, “Critical properties of electron eigenstates in incommensurate systems,” Proc. R. Soc. London, Ser. A 391, 305–350 (1984).

[CrossRef]

D. J. Thouless and Q. Niu, “Wavefunction scaling in a quasi-periodic potential,” J. Phys. A 16, 1911–1919 (1983).

[CrossRef]

R. E. Prange, D. R. Grempel, and S. Fishman, “Wave functions at a mobility edge: an example of a singular continuous spectrum,” Phys. Rev. B 28, 7370–7372 (1983);R. E. Prange, D. R. Grempel, and S. Fishman, “Solvable model of quantum motion in an incommensurate potential,” Phys. Rev. B 29, 6500–6512 (1984);R. E. Prange, D. R. Grempel, and S. Fishman, “Long-range resonance in Anderson insulators: finite-frequency conductivity of random and incommensurate systems,” Phys. Rev. Lett. 53, 1582–1585 (1984).

[CrossRef]

L. A. Pastur and A. L. Figotin, “Localization in an incommensurate potential: exactly solvable multidimensional model,” JETP Lett. 37, 686–688 (1983).

D. R. Grempel, S. Fishman, and R. E. Prange, “Localization in an incommensurate potential: an exactly solvable model,” Phys. Rev. Lett. 49, 833–836 (1982).

[CrossRef]

B. Simon, “Almost periodic Schrödinger operators: a review,” Adv. Appl. Math. 3, 463–490 (1982).

[CrossRef]

P. Sarnak, “Spectral behavior of quasi periodic potentials,” Commun. Math. Phys. 84, 377–401 (1982).

[CrossRef]

J. Avron and B. Simon, “Singular continuous spectrum for a class of almost periodic Jacobi matrices,” Bull. Am. Math. Soc. 6, 81–85 (1982);“Almost periodic Schrödinger operators. II. The integrated density of states,” Duke Math. J. 50, 369–391 (1983).

[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982);D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984).

[CrossRef]

B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, “Dynamical stochasticity in classical and quantum mechanics,” Sov. Sci. Rev. Sect. C 2, 209–267 (1981).

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1979).

M. Ya. Azbel, “Energy spectrum of a conduction electron in a magnetic field,” Sov. Phys. JETP 19, 634–645 (1964).

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).

[CrossRef]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).

[CrossRef]

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1979).

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1979).

J. Avron and B. Simon, “Singular continuous spectrum for a class of almost periodic Jacobi matrices,” Bull. Am. Math. Soc. 6, 81–85 (1982);“Almost periodic Schrödinger operators. II. The integrated density of states,” Duke Math. J. 50, 369–391 (1983).

[CrossRef]

M. Ya. Azbel, “Energy spectrum of a conduction electron in a magnetic field,” Sov. Phys. JETP 19, 634–645 (1964).

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

[CrossRef]
[PubMed]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000).

[CrossRef]

P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos (Hermann, Paris, 1984).

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves, and localization,” Eur. J. Phys. 18, 222–228 (1997).

[CrossRef]

R. Blumel, S. Fishman, and U. Smilansky, “Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization,” J. Chem. Phys. 84, 2604–2614 (1986).

[CrossRef]

G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein;R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein;E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. 61, 2011–2014 (1988);J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. 63, 364–367 (1989), and references therein;R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. 62, 341–344 (1989);R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A 44, 4521–4540 (1991), and references therein.

[CrossRef]
[PubMed]

G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.

B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, “Dynamical stochasticity in classical and quantum mechanics,” Sov. Sci. Rev. Sect. C 2, 209–267 (1981).

G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

[CrossRef]
[PubMed]

I. Dana, E. Eisenberg, and N. Shnerb, “Dynamical localization near quantum antiresonance: exact results and a solvable case,” Phys. Rev. Lett. 74, 686–689 (1995);“Antiresonance and localization in quantum dynamics,” Phys. Rev. E 54, 5948–5963 (1996);E. Eisenberg and I. Dana, “Limited sensitivity to analyticity: a manifestation of quantum chaos,” Found. Phys. 27, 153–170 (1997).

[CrossRef]
[PubMed]

I. Dana, E. Eisenberg, and N. Shnerb, “Dynamical localization near quantum antiresonance: exact results and a solvable case,” Phys. Rev. Lett. 74, 686–689 (1995);“Antiresonance and localization in quantum dynamics,” Phys. Rev. E 54, 5948–5963 (1996);E. Eisenberg and I. Dana, “Limited sensitivity to analyticity: a manifestation of quantum chaos,” Found. Phys. 27, 153–170 (1997).

[CrossRef]
[PubMed]

L. A. Pastur and A. L. Figotin, “Localization in an incommensurate potential: exactly solvable multidimensional model,” JETP Lett. 37, 686–688 (1983).

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000).

[CrossRef]

B. Fischer, A. Rosen, and S. Fishman, “Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber,” Opt. Lett. 24, 1463–1465 (1999).

[CrossRef]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000).

[CrossRef]

B. Fischer, A. Rosen, and S. Fishman, “Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber,” Opt. Lett. 24, 1463–1465 (1999).

[CrossRef]

R. E. Prange and S. Fishman, “Experimental realizations of kicked quantum chaotic systems,” Phys. Rev. Lett. 63, 704–707 (1989);O. Agam, S. Fishman, and R. E. Prange, “Experimental realizations of quantum chaos in dielectric waveguides,” Phys. Rev. A 45, 6773–6802 (1992).

[CrossRef]
[PubMed]

R. Blumel, S. Fishman, and U. Smilansky, “Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization,” J. Chem. Phys. 84, 2604–2614 (1986).

[CrossRef]

R. E. Prange, D. R. Grempel, and S. Fishman, “Wave functions at a mobility edge: an example of a singular continuous spectrum,” Phys. Rev. B 28, 7370–7372 (1983);R. E. Prange, D. R. Grempel, and S. Fishman, “Solvable model of quantum motion in an incommensurate potential,” Phys. Rev. B 29, 6500–6512 (1984);R. E. Prange, D. R. Grempel, and S. Fishman, “Long-range resonance in Anderson insulators: finite-frequency conductivity of random and incommensurate systems,” Phys. Rev. Lett. 53, 1582–1585 (1984).

[CrossRef]

D. R. Grempel, S. Fishman, and R. E. Prange, “Localization in an incommensurate potential: an exactly solvable model,” Phys. Rev. Lett. 49, 833–836 (1982).

[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982);D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984).

[CrossRef]

G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.

R. Graham, M. Schlautmann, and P. Zoller, “Dynamical localization of atomic-beam deflection by a modulated standing light wave,” Phys. Rev. A 45, R19–R22 (1992); see also R. Graham, M. Schlautmann, and D. L. Shepelyansky, “Dynamical localization in Josephson junctions,” Phys. Rev. Lett. 67, 255–258 (1991), and references therein.

[CrossRef]
[PubMed]

R. E. Prange, D. R. Grempel, and S. Fishman, “Wave functions at a mobility edge: an example of a singular continuous spectrum,” Phys. Rev. B 28, 7370–7372 (1983);R. E. Prange, D. R. Grempel, and S. Fishman, “Solvable model of quantum motion in an incommensurate potential,” Phys. Rev. B 29, 6500–6512 (1984);R. E. Prange, D. R. Grempel, and S. Fishman, “Long-range resonance in Anderson insulators: finite-frequency conductivity of random and incommensurate systems,” Phys. Rev. Lett. 53, 1582–1585 (1984).

[CrossRef]

D. R. Grempel, S. Fishman, and R. E. Prange, “Localization in an incommensurate potential: an exactly solvable model,” Phys. Rev. Lett. 49, 833–836 (1982).

[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982);D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984).

[CrossRef]

G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein;R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein;E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. 61, 2011–2014 (1988);J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. 63, 364–367 (1989), and references therein;R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. 62, 341–344 (1989);R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A 44, 4521–4540 (1991), and references therein.

[CrossRef]
[PubMed]

J. Guckenheimer and P. Holmes, Nonlinear Oscillations,Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).

F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

J. Guckenheimer and P. Holmes, Nonlinear Oscillations,Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, “Dynamical stochasticity in classical and quantum mechanics,” Sov. Sci. Rev. Sect. C 2, 209–267 (1981).

G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998);H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998).

[CrossRef]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves, and localization,” Eur. J. Phys. 18, 222–228 (1997).

[CrossRef]

J. Krug, “Optical analog of a kicked quantum oscillator,” Phys. Rev. Lett. 59, 2133–2136 (1987).

[CrossRef]
[PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).

A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).

A. W. Snyder and S. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

[CrossRef]
[PubMed]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

[CrossRef]
[PubMed]

D. J. Thouless and Q. Niu, “Wavefunction scaling in a quasi-periodic potential,” J. Phys. A 16, 1911–1919 (1983).

[CrossRef]

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998);H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998).

[CrossRef]

E. Ott, Chaos in Dynamical Systems (Cambridge U.Cambridge, UK, 1993).

L. A. Pastur and A. L. Figotin, “Localization in an incommensurate potential: exactly solvable multidimensional model,” JETP Lett. 37, 686–688 (1983).

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

[CrossRef]
[PubMed]

P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos (Hermann, Paris, 1984).

R. E. Prange and S. Fishman, “Experimental realizations of kicked quantum chaotic systems,” Phys. Rev. Lett. 63, 704–707 (1989);O. Agam, S. Fishman, and R. E. Prange, “Experimental realizations of quantum chaos in dielectric waveguides,” Phys. Rev. A 45, 6773–6802 (1992).

[CrossRef]
[PubMed]

R. E. Prange, D. R. Grempel, and S. Fishman, “Wave functions at a mobility edge: an example of a singular continuous spectrum,” Phys. Rev. B 28, 7370–7372 (1983);R. E. Prange, D. R. Grempel, and S. Fishman, “Solvable model of quantum motion in an incommensurate potential,” Phys. Rev. B 29, 6500–6512 (1984);R. E. Prange, D. R. Grempel, and S. Fishman, “Long-range resonance in Anderson insulators: finite-frequency conductivity of random and incommensurate systems,” Phys. Rev. Lett. 53, 1582–1585 (1984).

[CrossRef]

D. R. Grempel, S. Fishman, and R. E. Prange, “Localization in an incommensurate potential: an exactly solvable model,” Phys. Rev. Lett. 49, 833–836 (1982).

[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982);D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984).

[CrossRef]

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998);H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998).

[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

[CrossRef]
[PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

[CrossRef]
[PubMed]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000).

[CrossRef]

B. Fischer, A. Rosen, and S. Fishman, “Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber,” Opt. Lett. 24, 1463–1465 (1999).

[CrossRef]

P. Sarnak, “Spectral behavior of quasi periodic potentials,” Commun. Math. Phys. 84, 377–401 (1982).

[CrossRef]

R. Graham, M. Schlautmann, and P. Zoller, “Dynamical localization of atomic-beam deflection by a modulated standing light wave,” Phys. Rev. A 45, R19–R22 (1992); see also R. Graham, M. Schlautmann, and D. L. Shepelyansky, “Dynamical localization in Josephson junctions,” Phys. Rev. Lett. 67, 255–258 (1991), and references therein.

[CrossRef]
[PubMed]

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

[CrossRef]
[PubMed]

G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein;R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein;E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. 61, 2011–2014 (1988);J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. 63, 364–367 (1989), and references therein;R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. 62, 341–344 (1989);R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A 44, 4521–4540 (1991), and references therein.

[CrossRef]
[PubMed]

D. L. Shepelyansky, “Localization of quasienergy eigenfunctions in action space,” Phys. Rev. Lett. 56, 677–680 (1986);“Localization of diffusive excitation in multi-level systems,” Physica D 28, 103–114 (1987).

[CrossRef]
[PubMed]

B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, “Dynamical stochasticity in classical and quantum mechanics,” Sov. Sci. Rev. Sect. C 2, 209–267 (1981).

I. Dana, E. Eisenberg, and N. Shnerb, “Dynamical localization near quantum antiresonance: exact results and a solvable case,” Phys. Rev. Lett. 74, 686–689 (1995);“Antiresonance and localization in quantum dynamics,” Phys. Rev. E 54, 5948–5963 (1996);E. Eisenberg and I. Dana, “Limited sensitivity to analyticity: a manifestation of quantum chaos,” Found. Phys. 27, 153–170 (1997).

[CrossRef]
[PubMed]

See, for example, A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 7.

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B. Simon, “Almost periodic Schrödinger operators: a review,” Adv. Appl. Math. 3, 463–490 (1982).

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R. Blumel, S. Fishman, and U. Smilansky, “Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization,” J. Chem. Phys. 84, 2604–2614 (1986).

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S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).

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B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998);H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998).

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F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995).

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P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos (Hermann, Paris, 1984).

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

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J. Avron and B. Simon, “Singular continuous spectrum for a class of almost periodic Jacobi matrices,” Bull. Am. Math. Soc. 6, 81–85 (1982);“Almost periodic Schrödinger operators. II. The integrated density of states,” Duke Math. J. 50, 369–391 (1983).

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P. Sarnak, “Spectral behavior of quasi periodic potentials,” Commun. Math. Phys. 84, 377–401 (1982).

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G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein;R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein;E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. 61, 2011–2014 (1988);J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. 63, 364–367 (1989), and references therein;R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. 62, 341–344 (1989);R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A 44, 4521–4540 (1991), and references therein.

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L. A. Pastur and A. L. Figotin, “Localization in an incommensurate potential: exactly solvable multidimensional model,” JETP Lett. 37, 686–688 (1983).

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P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).

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S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982);D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984).

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M. Wilkinson, “Critical properties of electron eigenstates in incommensurate systems,” Proc. R. Soc. London, Ser. A 391, 305–350 (1984).

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F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

A. W. Snyder and S. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

For reviews, see D. J. Thouless, “Critical phenomena, random systems, gauge theories,” in Proceedings of the Les-Houches Summer School, K. Osterwalder and R. Stora, eds. (North-Holland, Amsterdam, 1986), p. 681; I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

E. Ott, Chaos in Dynamical Systems (Cambridge U.Cambridge, UK, 1993).

P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos (Hermann, Paris, 1984).

J. Guckenheimer and P. Holmes, Nonlinear Oscillations,Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).

M. J. Giannoni, A. Voros, and J. Zinn-Justin, eds., “Chaos and quantum physics,” in Proceedings of the Les-Houches Summer School, Session LII, 1989 (North-Holland, Amsterdam, 1991).

G. L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson, eds., “Quantum dynamics of simple systems,” in Proceedings of the 44th Scottish Universities Summer School in Physics (Scottish Universities Summer School in Physics Publications and Institute of Physics, Bristol, UK, 1996).

G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.