Abstract
We now turn to time-dependent multilevel systems, which are similar to the two-band models discussed in Chap. 4. The main difference between them and the time-dependent level–band problem discussed in Chap. 5 is in the topology of the transitions; for two-band models the transition topology is much more involved, and a transition from one level to another does not necessarily imply the immediate inverse transition.
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References
Agarwal, G.S.: Control of decoherence and relaxation by frequency modulation of a heat bath. Phys. Rev. A 61, 013809 (2000)
Akulin, V.M.: Contribution of weak and multiphoton transitions to the excitation of polyatomic molecules in an intense laser field. Sov. Phys. JETP 56, 533–538 (1982)
Akulin, V.M.: Singularities of collisional vibrational relaxation processes in strongly excited spectrally complex polyatomic molecules. Sov. Phys. JETP 57, 774–780 (1983)
Akulin, V.M., Karlov, N.V.: Intense Resonant Interactions in Quantum Electronics. Springer, Berlin (1991)
Allen, L., Eberly, J.H.: Optical Resonance and Two-Level Atoms. Wiley, Chichester (1975)
Altshuler, B.L., Aronov, A.G., Khmelnitsky, D.E.: Effects of electron-electron collisions with small energy transfers on quantum localisation. J. Phys. C Solid State Phys. 15, 7367–7386 (1982)
Amico, L., Osterloh, A., Plastina, F., Fazio, R., Palma, G.M.: Dynamics of entanglement in one-dimensional spin systems. Phys. Rev. A 69, 022304 (2004)
Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1957)
Anderson, P.W., Thouless, D.J., Abrahams, E., Fisher, D.S.: New method for a scaling theory of localization. Phys. Rev. B 22, 3519–3526 (1980)
Arnold, V.I., Weinstein, A., Vogtmann, K.: Mathematical Methods of Classical Mechanics. Springer, New York (1989)
Askaryan, G.A.: Excitation and dissociation of molecules in intense light field. Sov. Phys. JETP 19, 273–274 (1964)
Averbukh, S., Perelman, N.F.: Fractional revivals: universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics. Physics Letters A 139, 449–454 (1989)
Barnum, H., Knill, E., Ortiz, G., Somma, R., Viola, L.: A subsystem-independent generalization of entanglement. Phys. Rev. Lett. 92, 107902 (2004)
Barut, A., Raczka, R.: Theory of Group Representations and Applications. Polish Scientific Publisher, Warszava (1977)
Basko, D.M., Skvortsov, M.A., Kravtsov, V.E.: Dynamic localization in quantum dots: analytical theory. Phys. Rev. Lett. 90, 096801–096804 (2003)
Beenakker, C.W.J.: Random matrix theory of quantum transport. Rev. Mod. Phys. 69, 731–808 (1997)
Bell, J.S.: On the Einstein–Podolsky–Rosen Paradox. Physics 1, 195–200 (1964)
Bengtsson, I., Zyczkowski, K.: Geometry of Quantum States. Cambridge University Press, Cambridge (2006)
Berezinskii, V.L.: Kinetics of a quantum particle in a one-dimensional random potential. Sov. Phys. JETP 38, 620–627 (1974)
Bery, M.V., Tabor, M.: Poissonian statistics and clustering. Proc. R. Soc. Lond. 356, 375–394 (1977)
Bixon, M., Jortner, J.: Intramolecular radiationless transitions. J. Chem. Phys. 48, 715–726 (1968)
Bixon, M., Jortner, J.: Long radiative lifetimes of small molecules. J. Chem. Phys. 50, 3284–3290 (1969)
Blanter, Y.M., Mirlin, A.D., Muzykantskii, B.A.: Quantum billiards with surface scattering: ballistic sigma-model approach. Phys. Rev. Lett. 80, 4161 (1998)
Bloch, F.: Nuclear induction. Phys. Rev. 70, 460 (1946)
Bloch, F.: Generalized theory of relaxation. Phys. Rev. 105, 1206–1222 (1957)
Bloch, F., Rabi, I.I.: Atoms in variable magnetic fields. Rev. Mod. Phys. 17, 237–244 (1945)
Blombergen, N.: Nonlinear Optics. Benjamin, New York (1965)
Bohigas, O., Giannoni, M.J., Schmit, C.: Characterization of chaotic quantum spectra and universality of level fluctuation laws. Phys. Rev. Lett. 52, 1–4 (1984)
Bogomolny, E.B., Gerland, U., Schmit, C.: Models of intermediate spectral statistics. Phys. Rev. E 59, R1315–R1318 (1999)
Bogomolny, E.B., Gerland, U., Schmit, C.: Singular statistics. Phys. Rev. E 63, 036206 (2001)
Bogomolny, E., Giraud, O., Schmit, C.: Random matrix ensembles associated with lax matrices. Phys. Rev. Lett. 103, 054103 (2009)
Borland, R.E.: The nature of the electronic states in disordered one-dimensional systems. Proc. Roy. Soc. Lond. A 274, 529–545 (1963)
Breit, G., Wigner, E.: Capture of slow neutrons. Phys. Rev. 40, 519–531 (1936)
Brezin, E., Hikami, S.: Spectral form factor in a random matrix theory. Phys. Rev. E 55, 4067–4083 (1997)
Brezin, E., Hakami, S.: Extension of level-spacing universality. Phys. Rev. E 56, 264–269 (1997)
Brezin, E., Hikami, S.: Universal singularity at the closure of a gap in a random matrix theory. Phys. Rev. E 57, 4140–4149 (1998)
Brezin, E., Hikami, S.: New correlation functions for random matrices and integrals over supergroups. J. Phys. A 36, 711–751 (2003)
Brezin, E., Hikami, S., Zee, A.: Universal correlations for the deterministic plus random Hamiltonians. Phys. Rev. E 51, 5442–5452 (1995)
Brion, E., Carlier, F., Harel, G., Akulin, V.M.: Non-holonomic quantum control. J. Phys. B At. Mol. Opt. Phys. 44, 154001 (2011)
Brixner, T., Stenger, J., Vaswani, H.M., Cho, M., Blankenship, R.E., Fleming, G.R.: Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434, 625–628 (2005)
Brumer, P.W., Shapiro, M.: Principles of the Quantum Control of Molecular Processes. Wiley, New York (2003)
Bunkin, F.V., Prokhorov, A.M.: The excitation and ionization of atoms in a strong radiation field. Sov. Phys. JETP 19, 739–743 (1964)
Bunkin, F.V., Prokhorov, A.M., Karapetyan, R.V.: Dissociation of molecules in a strong radiation field. Sov. Phys. JETP 20, 145–148 (1965)
Burkey, R.S., Cantrell, C.D.: Multichannel excitation of the quasi-continuum. J. Opt. Soc. Am. B 2, 451–457 (1985)
Butkovskiy, G., Samoilenko, Y.I.: Control of Quantum-Mechanical Processes and Systems. Kluwer Academic, Dordrecht (1990)
Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)
Carmeli, B., Nitzan, A.: Kinetic equation for collisionless multiphoton excitation of large molecules. Chem. Phys. Lett. 62, 457–460 (1978)
Carmeli, B., Nitzan, A.: Random coupling model for intramolecular dynamics. J. Chem. Phys. 72, 2054–2080 (1980)
Caruso, F., Chin, A.W., Datta, A., Huelga, S.F., Plenio, M.B.: Entanglement and entangling power of the dynamics in light-harvesting complexes. Phys. Rev. A 81, 062346 (2010)
Casati, G., Chiricov, B.V., Shepelyansky, D.L.: Quantum limitation for chaotic excitation of the hydrogen atom in a monochromatic field. Phys. Rev. Lett. 53, 2525–2528 (1984)
Casati, G., Chirikov, B.V., Guarneri, I., Shepelyansky, D.L.: Dynamical stability of quantum chaotic motion in a hydrogen atom. Phys. Rev. Lett. 23, 2437–2440 (1986)
Casati, G., Guarneri, I., Izrailev, F., Scharf, R.: Scaling behavior of localization in quantum chaos. Phys. Rev. Lett. 64, 5–8 (1990)
Casati, G., Molinari, L., Izrailev, F.: Scaling properties of band random matrices. Phys. Rev. Lett. 64, 1851–1854 (1990)
Chalker, J.T., Lerner, I.V., Smith, R.A.: Random walks through the ensemble: linking spectral statistics with wave-function correlations in disordered metals. Phys. Rev. Lett. 77, 554–557 (1996)
Chirikov, B.V.: Resonance processes in magnetic traps. J. Nucl. Energy C Plasma Phys. 1, 253–260 (1960)
Chirikov, B.V., Shepelyansky, D.L.: Correlation properties of dynamical chaos in Hamiltonian systems. Physica D 13, 395–400 (1984)
Cirac, J.I., Zoller, P.: Quantum computation with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)
Cohen-Tanoudji, C., Diu, B., Laloe, F.: Quantum Mechanics. Wiley, Paris (1977)
Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Atom-Photon Interactions: Basic Processes and Applications. Wiley-Interscience, New York (1998)
D’Alessandro, D.: Introduction to Quantum Control and Dynamics. Chapman & Hall/CRC Applied Mathematics & Nonlinear Science, London (2008)
Delande, D., Zakrzewski, J.: Spontaneous emission of nondispersive Rydberg wave packets. Phys. Rev. A 58, 446–477 (1998)
Delone, N.B., Fedorov, M.V.: Above-threshold ionization. Progr. Quant. Electron. 13, 267–298 (1989)
Delone, N.B., Fedorov, M.V.: New effects in the multiphoton ionization of atoms. Sov. Phys. Uspekhi 32, 500–520 (1989)
Delone, N.B., Krainov, V.P.: Atoms in Strong Light Fields. Springer, Berlin (1985)
Demikhovskii, V.Y., Izrailev, F.M., Malyshev, A.I.: Manifestation of Arnold diffusion in quantum systems. Phys. Rev. Lett. 88, 154101 (2002)
Demkov, Y.N.: Charge transfer at small resonance defects. JETP 18, 138–142 (1964)
Demkov, Y.N., Osherov, V.I.: Stationary and nonstationary problems in quantum mechanics that can be solved by means of contour integration. Sov. Phys. JETP 26, 916–921 (1968)
Deng, Z., Eberly, J.H.: Multiphoton absorption above ionization threshold by atoms in strong laser field. J. Opt. Soc. Am. B 2, 486–493 (1985)
Deych, L.I., Lisyansky, A.A., Altshuler, B.L.: Single parameter scaling in one-dimensional localization revisited. Phys. Rev. Lett. 84, 2678–2681 (2000)
Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954)
Dodonov, V.V.: Universal integrals of motion and universal invariants of quantum systems. J. Phys. A 33, 7721–7738 (2000)
Dodonov, V.V., Man’ko, V.I.: Phase space eigenfunctions of multidimensional quadratic Hamiltonians. Physica A 137, 306–316 (1986)
Dodonov, V.V., Manko, V.I., Nikonov, D.E.: Exact propagators for time-dependent Coulomb, delta and other potentials. Phys. Lett. A 162, 359–364 (1992)
Doucot, B., Feigel’man, M.V., Ioffe, L.B., Ioselevich, A.S.: Protected qubits and Chern–Simons theories in Josephson junction arrays. Phys. Rev. B 71, 024505 (2005)
Drobny, G., Jex, I., Buzek, V.: Mode entanglement in nondegenerate down-conversion with quantized pump. Phys. Rev. A 48, 569–579 (1993)
Dubrovskii, Y.V., Fedorov, M.V., Ivanov, M.Y.: Rydberg atom ionization by an intense laser pulse with smooth time envelope: a model of two closely spaced levels coupled to continuum. Laser Physics 2, 288–298 (1992)
Dur, W., Vidal, G., Cirac, I.J.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)
Durand, P., Paladrova, I., Cadea, F.X.: Theory of Fano profiles. J. Phys. B 34, 1953–1986 (2001)
Dykhne, M.: Adiabatic perturbation of the discrete spectrum states. Sov. Phys. JETP 14, 941–943 (1962)
Dyson, F.J.: The dynamics of a disordered linear chain. Phys. Rev. 92, 1331–1338 (1953)
Dyson, F.: Statistical theory of the energy levels of complex systems. J. Math. Phys. 3, 140–175 (1962)
Dyson, F.: A class of matrix ensembles. J. Math. Phys. 13, 90–97 (1972)
Eberly, J., Narozhny, N.B., Sanchez-Mondregon, J.J.: Periodic spontaneous collapse and revivals in a simple quantum model. Phys. Rev. Lett. 44, 1323–1325 (1980)
Eckhardt, B.: Quantum mechanics of classically non-integrable systems. Phys. Rep. 163, 205–297 (1988)
Einstein, A.: Zur Quantentheorie der Strahlung. Physikalische Zeitschrift 18, 121–128 (1917). The Collected Papers of Albert Einstein, Volume 6: The Berlin Years: Writings, 1914–1917 (English translation supplement). University Press, Princeton
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Efetov, K.: Supersymmetry in Disorder and Chaos. Cambridge University Press, Cambridge (1997)
Fano, U.: Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco. Nuovo Cimento N. S. 12, 154–161 (1935)
Fano, U.: Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866–1878 (1961)
Fedorov, M.V., Ivanov, M.Y., Movsesian, A.M.: Strong-field photoionization of an initially excited hydrogen atom: formation of Rydberg wavepacket, its structure and trapping of population at Rydberg levels. J. Phys. B 23, 2245S–2257S (1990)
Fedorov, M.V., Movsesian, A.M.: Interference suppression of photoionization of Rydberg atoms in strong electromagnetic field. J. Opt. Soc. Am. B 6, 928–936 (1988)
Fedorov, M.V., Movsesian, A.M.: Field-induced effects of narrowing of photoelectron spectra and stabilization of Rydberg atoms. J. Phys. B 21, L155 (1988)
Fermi, E.: Quantum theory of radiation. Rev. Mod. Phys. 4, 87–133 (1932)
Floquet, G.: Sur leséquations différentialles linéairesà coefficients périodiques. Ann. de l’Ecole Normale 2-e serie 12, 47–88 (1889)
Frydryszak, A.M.: Pure state entanglement in terms of nilpotent variables: eta-toolbox. In: Olkiewicz, R., Cegla, W., Frydryszak, A., Garbaczewski, P., Jakobczyk, L. (eds.) Quantum Dynamics and Information. World Scientific, Singapore (2011)
Fyodorov, Y.V., Mirlin, A.D.: Scaling properties of localization in random band matrices: a sigma-model approach. Phys. Rev. Lett. 67, 2405–2409 (1991)
Fyodorov, Y.V., Mirlin, A.: Statistical properties of random banded matrices with strongly fluctuating diagonal elements. Phys. Rev. B 52, R11580–R11583 (1995)
Fyodorov, Y.V., Chubykalo, O.A., Izrailev, F.M., Casati, G.: Wigner random banded matrices with sparse structure: local spectral density of states. Phys. Rev. Lett. 76, 1603–1606 (1996)
Fyodorov, Y.V., Mirlin, A.D., Sommers, H.-J.: A novel field theoretical approach to the Anderson localization: sparse random hopping model. J. Phys. I France 2, 1571–1605 (1992)
Gallager, R.G.: Information Theory and Reliable Communications. Wiley, New York (1968)
Gallagher, T.F.: Rydberg Atoms. Cambridge University Press, Cambridge (1994)
Garanin, D.A., Schilling, R.: Effect of nonlinear sweep in the Landau-Zener-Stueckelberg effect. Phys. Rev. B 66, 174438 (2002)
Gardiner, W., Zoller, P.: Quantum Noise. Springer, Berlin (2004)
Gavrila, M., Kaminski, J.Z.: Free-free transitions in intense high-frequency laser fields. Phys. Rev. Lett. 52, 613–616 (1984)
Ghosh, P.K.: Ion Traps. Clarendon, Oxford (1995)
Grahm, G., Shepelyansky, D.: A solid-state model for photonic localization in molecular quasi-continua. Europhys. Lett. 14, 211–215 (1991)
Greenberger, D.M., Horn, M.A., Zeilinger, A.: Going beyond Bell’s theorem. In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, pp. 73–76. Kluwer Academic, Dordrecht (1989)
Gruebele, M.: Intramolecular vibrational dephasing obeys a power law at intermediate times. Proc. Natl. Acad. Sci. USA 95, 5965–5970 (1998)
Guérin, S., Jauslin, H.R.: Control of quantum systems by pulses: adiabatic Floquet theory. Adv. Chem. Phys. 125, 1–75 (2003)
Gutzwiller, M.: Chaos in Classical and Quantum Mechanics. Springer, New York (1990)
Haake, F.: Quantum Signatures of Chaos. Springer, Berlin (2001)
Hahn, E.L.: Spin echoes. Phys. Rev. 80, 580–594 (1950)
Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a “bound” entanglement in nature? Phys. Rev. Lett. 80, 5239–5242 (1998)
Hubbard, J.: Electron correlations in narrow energy bands. Proc. R. Soc. Lond. Ser. A 276, 238–257(1963); 277, 237–259 (1964); 281, 401–419 (1964)
Huckestein, B.: Scaling theory of the integer quantum Hall effect. Rev. Mod. Phys. 67, 375–396 (1995)
Husimi, K.: Miscellanea in elementary quantum mechanics. Prog. Theor. Phys. 9, 238–244, 381–402 (1953)
Imry, J.: Introduction to Mesoscopic Physics. Oxford University Press, Oxford (2002)
Iserles, A., Marthinsenet, A., Nörsett, S.P.: On the implementation of the method of Magnus series for linear differential equations. BIT Numer. Math. 39, 281–304 (1999)
Ishii, K.: Localization of eigenstates and transport phenomena in the one-dimensional disordered systems. Supl. Prog. Theor. Phys. 53, 77–138 (1972)
Ivanov, M.Y.: Suppression of resonant multiphoton ionization via Rydberg states. Phys. Rev. A 49, 1165–1170 (1994)
Izrailev, F.M.: Simple models of quantum chaos: spectrum and eigenfunctions. Physics Reports 5–6, 299–392 (1990)
Jaksch, D., Briegel, H., Cirac, J.I., Gardiner, C.W., Zoller, P.: Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999)
Javanainen, J., Kyrölä, E.: Long-time limit of a quasicontinuum model. Opt. Commun. 56, 17–21 (1985)
Joannopoulos, J.D., Meade, R.D., Winn, J.N.: Photonic Crystals. Princeton University Press, Princeton (1995)
J. Phys. A 36(12) (28 March 2003)
Jungen, C.: Molecular Applications of Quantum Defect Theory. Institute of Physics Publisher, Philadelphia (1996)
Jurdevic, V., Sussmann, H.J.: Control systems on Lie groups. J. Differ. Eq. 12, 313–329 (1972)
Karczmarek, J., Scott, M., Ivanov, M.: Two-color control of localization: from lattices to spin systems. Phys. Rev. A 60, R4225–R4228 (1999)
Karplus, R., Schwinger, J.: A note on saturation in microwave spectroscopy. Phys. Rev. 73, 1020–1026 (1948)
Kitaev, Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003)
Knight, P.L., Lauder, M.A., Dalton, B.J.: Laser-induced continuum structure. Phys. Rep. 190, 1–61 (1990)
Khodjasteh, K., Viola, L.: Dynamically error-corrected gates for universal quantum computation. Phys. Rev. Lett. 102, 080501 (2009)
Kofman, G.: Theory of single-photon bound-free transitions: extension of the pole approximation. J. Phys. B 30, 5141–5156 (1997)
Kofman, G.: Relaxation of a two-level system strongly coupled to a reservoir: anomalously slow decoherence. Phys. Rev. A 64, 033809 (2001)
Kofman, G., Kurizki, G.: Universal dynamical control of quantum mechanical decay: modulation of the coupling to the continuum. Phys. Rev. Lett. 87, 270405 (2001)
Kostelecky, V.A., Manko, V.I., Nieto, M.M., Traux, D.R.: Supersymmetry and time-dependent Landau system. Phys. Rev. A 48, 951–963 (1993)
Kravtsov, V.E.: Time reversal symmetry breaking by ac field: effect of commensurability in frequency domain. Pramana J. Phys. 58, 183–193 (2002)
Kravtsov, V.E., Lerner, I.V., Altshuler, B.L., Aronov, A.G.: Universal spectral correlations at the mobility edge. Phys. Rev. Lett. 72, 888–891 (1994)
Kubo, R.: A general expression for the conductivity tensor. Can. J. Phys. 34, 1274–1277 (1956)
Kurizki, G., Kofman, A.G., Yudson, V.: Resonant photon exchange by atom pairs in high-Q cavities. Phys. Rev. A 53, R35–R38 (1996)
Kuznetsov, D., Bulgak, A., Dang, G.D.: Quantum Lévy process and fractional kinetics. Phys. Rev. Lett. 82, 1136–1139 (1999)
Kyrölä, E., Eberly, J.: Quasicontinuum effects in molecular excitation. J. Chem. Phys. 82, 1841–1853 (1985)
Kyrölä, E., Lindberg, M.: Serial and parallel multilevel systems. Phys. Rev. A 35, 4207–4225 (1987)
Laflamme, R., Miquel, C., Paz, J.P., Zurek, W.H.: Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198–201 (1996)
Landau, L.D.: Das Dämpfungsproblem in der Wellenmechanik. Zeitschrift Phys. Bd XLV, 430–441 (1927)
Landau, L.D., Lifshits, E.M.: Quantum mechanics. Butterworth-Heinemann, Oxford (1975–1999)
Lechtle, C., Averbukh, I.S., Schleich, W.P.: Generic structure of multilevel quantum beats. Phys. Rev. Lett. 77, 3999–4002 (1996)
Levine, R.D.: Representation of one-dimensional motion in a Morse potential by a quadratic Hamiltonian. Chem. Phys. Lett. 95, 87–90 (1983)
Levitov, L.S., Tsvelik, A.M.: Narrow-gap Luttinger liquid in carbon nanotubes. Phys. Rev. Lett. 90, 016401 (2003)
Lichtenberg, A.J., Liberman, M.A.: Regular and Stochastic Motion. Springer, Berlin (1982)
Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998)
Lifshits, I.M., Gredeskul, S.A., Pastur, L.A.: Introduction to the Theory of Disordered Systems. Wiley, New York (1988)
Lindberg, M., Kyrölä, E.: Infinite multilevel system coupled to a quantum-field mode. J. Opt. Soc. Am. B 9, 595–604 (1992)
Linden, N., Popescu, S.: On multi-particle entanglement. Fortschr. Phys. 4–5, 567–578 (1998)
Lloyd, P.: Exactly solvable model of electronic states in a three-dimensional disordered Hamiltonian: non-existence of localized states. J. Phys. C Solid State Phys. 2, 1717–1725 (1969)
Makarov, A.: Coherent excitation of equidistant multilevel systems in a resonant monochromatic field. Sov. Phys. JETP 45, 918–924 (1977)
Mandilara, A., Akulin, V.M., Smilga, A., Viola, L.: Description of quantum entanglement with nilpotent polynomials. Phys. Rev. A 74, 022331 (2006)
Mandilara, A., Akulin, V.M., Kolar, M., Kurizki, G.: Control of multiatom entanglement in a cavity. Phys. Rev. A 75, 022327 (2007)
Massey, H.S.W., Mott, N.F.: The Theory of Atomic Collisions. Clarendon, Oxford (1997)
Mathews, J., Walker, R.L.: Mathematical Methods of Physics. Addison-Wesley, New York (1971)
McCall, S.L., Hahn, E.L.: Self-induced transparency. Phys. Rev. 183, 457–485 (1969)
Mehring, M., Muller, K., Averbukh, I.Sh., Merkel, W., Schleich, W.P.: NMR experiment factors numbers with gauss sums. Phys. Rev. Lett. 98, 120502 (2007)
Metha, M.L.: Random Matrices and Statistical Theory of Energy Levels. Academic, New York (1967)
Meystre, P.: Atom Optics. Springer, New York (2001)
Mezard, M., Parisi, G., Zee, A.: Spectra of Euclidean random matrices. Nucl. Phys. B 59, 689–701 (1999)
Mirlin, D., Fyodorov, Y.V., Dittes, F.-M., Quezada, J., Seligman, T.H.: Transition from localized to extended eigenstates in the ensembles of power-law random banded matrices. Phys. Rev. E 54, 3221–3230 (1996)
Mott, N.F., Twose, W.D.: The theory of impurity conduction. Adv. Phys. 10, 107–163 (1961)
Mourachko, I., Comparat, D., de Tomasi, F., Fioretti, A., Nosbaum, P., Akulin, V.M., Pillet, P.: Many-body effects in a frozen Rydberg gas. Phys. Rev. Lett. 80, 253–256 (1998)
Mower, L.: Decay theory of closely coupled unstable states. Phys. Rev. 142, 799–816 (1966)
Mudry, P.W., Brouwer, B.I., Halperin, V., Gurarie, A.Z.: Density of states in the non-Hermitian Lloyd model. Phys. Rev. B 58, 13539 (1998)
Mukamel, S., Jortner, J.: A model for isotope separation via molecular multiphoton dissociation. Chem. Phys. Lett. 40, 150–156 (1976)
Narevich, R., Prange, R.E., Zaitsev, O.: Square billiard with an Aharonov-Bohm flux line. Physica E 9, 578–582 (2001)
Nikitin, E.E.: Theory Elementary Atomic and Molecular Processes. Oxford University Press, Oxford (1985)
Nikitin, E.E., Umanskii, S.Y.: Theory of Slow Atomic Collisions. Springer, New York (1984)
Offer, C.R., Simons, B.D.: Field theory of Euclidean random matrix ensembles. J. Phys. A Math. Gen. 33, 7567 (2000)
Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)
Parisi, G.: Euclidean random matrices: solved and open problems. In: Brezin, E., Kazakov, V., Serban, D., Wiegmann, P. (Eds.), Application of Random Matrices in Physics. NATO Science Series 206, vol. 21, pp. 219–260. Springer, Berlin (2006)
Pastur, L.A.: On the spectrum of random matrices. Theor. Math. Phys. (USSR) 10, 67–74 (1972)
Pechukas, P.: Quantum chaos in the irregular spectrum. Chem. Phys. Lett. 86, 553–557 (1982)
Pechukas, P.: Distribution of energy eigenvalues in the irregular spectrum. Phys. Rev. Lett. 51, 943–946 (1983)
Perelomov, M.: Integrable Systems of Classical Mechanics and Lie Algebras. Springer, Berlin (1990); Generalized Coherent States and Their Applications, Springer, Berlin (1986)
Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1418 (1996)
Porter, E.: Statistical Theories of Spectra: Fluctuations. Academic, New York (1965)
Porter, C.E., Thomas, R.G.: Fluctuation of nuclear reaction width. Phys. Rev. 104, 483–491 (1956)
Quack, M.: Theory of unimolecular reactions induced by monochromatic infrared radiation. J. Chem. Phys. 69, 1282–1307 (1978)
Rabi, I.I., Ramsey, N.F., Schwinger, J.: Use of rotating coordinates in magnetic resonance problem. Rev. Mod. Phys. 26, 167–171 (1954)
Reichl, L.E.: The Transition to Chaos. Springer, New York (1992)
Rhodes, K., Szöke, A., Javan, A.: The influence of level degeneracy on the self-induced transparency effect. Phys. Rev. Lett. 21, 1151–1155 (1968)
Ritus, V.I.: Shift and splitting of atomic energy levels by the field of an electromagnetic wave. Sov. Phys. JETP 24, 1041–1044 (1967)
Sargent, M., Lamb, W.E., Scully, M.O.: Laser Physics. Addison-Wesley, Reading (1987)
Schafer, K.J., Kulander, K.C.: Phase dependent effects in multiphoton ionization induced by a laser field and its second harmonic. Phys. Rev. A 45, 8026–8033 (1992)
Schlag, W.: ZEKE Spectroscopy. Cambridge University Press, Cambridge (1998)
Schleich, W.: Quantum Optics in Phase Space. Wiley, Weinheim (2001)
Schofield, S.A., Wolynes, P.G.: A scaling perspective of quantum energy flow in molecules. J. Chem. Phys. 98, 1123–1131 (1992)
Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935). English translation: Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philosoph. Soc. 31, 555–563 (1935)
Seba, P.: Wave chaos in singular quantum billiard. Phys. Rev. Lett. 64, 1855–1858 (1990)
Shepelyansky, L.: Localization of diffusive excitation in multi-level systems. Phys. D Nonlinear Phenom. 28, 103–114 (1987)
Shepelyansky, L.: Coherent propagation of two interacting particles in a random potential. Phys. Rev. Lett. 73, 2607–2610 (1994)
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)
Shore, W., Eberly, J.H.: Analytic approximations in multi-level excitation theory. Opt. Comm. 24, 83–88 (1978)
Sinai, Y.G.: On the concept of entropy for a dynamic system. Sov. Phys. Doklady 124, 768–771 (1959)
Sinai, Y.G.: Introduction to Ergodic Theory. Princeton University Press, Princeton (1976)
Sinai, Y.G.: Anderson localization for one-dimensional difference Schrödinger operator with quasi-periodic potential. J. Stat. Phys. 46, 861–909 (1987)
Sinai, Y.G.: Topics in Ergodic Theory. Princeton University Press, Princeton (1994)
Sinai, Y.G., Soshnikov, A.B.: A refinement of Wigner’s semicircle in a neighbourhood of the spectrum edge for random symmetric matrices. Funct. Anal. Appl. 32, 114–131 (1998)
Skvortsov, M.A., Basko, D.M., Kravtsov, V.E.: Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization. JETP Lett. 80, 60–66 (2004)
Sobelman, I.I., Vainshtain, L.A., Yukov, E.A.: Excitation of Atoms and Broadening of Spectral Lines. Springer, New York (1981)
Stelmachovi, P., Buzek, V.: Quantum-information approach to Ising model: entanglement in chains of qubits. Phys. Rev. A 70, 032313 (2004)
Stenholm, S.: Quantum theory of electromagnetic fields interacting with atoms and molecules. Physics Reports 6, 1–122 (1973)
Thouless, J.: Maximum metallic resistance in thin wires. Phys. Rev. Lett. 39, 1167–1169 (1977)
Vedral, V., Plenio, M.P., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275–2279 (1997)
Verstraete, F., Dehaene, J., De Moor, B., Verschelde, H.: Four qubits can be entangled in nine different ways. Phys. Rev. A 65, 052112 (2002)
Vogel, K., Akulin, V.M., Schleich, W.P.: Quantum state engineering of the radiation field. Phys. Rev. Lett. 71, 1816–1819 (1993)
Weisskopf, V., Wigner, E.: Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie. Z. Phys. 63, 54–73 (1930)
Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)
Wigner, E.: On a class of analytic functions from the quantum theory of collisions. Ann. Math. 53(36) (1951)
Wigner, E.: On the distribution of the roots of certain symmetric matrices. Ann. Math 65, 203–207 (1957)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)
Yurovsky, V.A., Ben-Reuven, A.: Saturated transition in exactly soluble models of two-state curve crossing with time-dependent potentials. Phys. Rev. A 60, 4561–4566 (1999)
Yurovsky, V.A., Ben-Reuven, A., Julienne, P.S., Brand, Y.B.: Counterintuitive transitions in multistate curve crossing involving linear potentials. J. Phys. B 32, 1845–1857 (1999)
Zaslavski, M., Sagdeev, R.Z., Usikov, D.A., Chernikov, A.A.: Weak Chaos and Quasi-Regular Patterns. Cambridge University Press, Cambridge (1991)
Zeldovich, Y.B.: The quasienergy of a quantum mechanical system subjected to a periodic action. Sov. Phys. JETP 24, 1006–1008 (1967)
Zeldovich, Y.B.: Scattering and emission of a quantum system in a strong electromagnetic wave. Sov. Phys. Uspekhi 16, 427–433 (1973)
Zirnbauer, M.: Anderson localization and non linear sigma-model with graded symmetry. Nucl. Phys. B 265, 375–408 (1986)
Zwanzig, R.: Memory effects in irreversible thermodynamics. Phys. Rev. 124, 983–992 (1961). See also the book by Zwanzig, R. (Ed.), Nonequilibrium Statistical Mechanics. Oxford University Press, Oxford (2001)
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Akulin, V.M. (2014). Time-Dependent Complex Systems. In: Dynamics of Complex Quantum Systems. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7205-2_6
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