Figotin's Research

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Alex Figotin’s Research Group

Department of Mathematics
University of California at Irvine
Irvine, CA 92697-3875

Publications

1

Exactly Solvable Model in Spin Glass, Sov.J. of Low Temp. Phys., 6, pp. 378-383, (1977), (with L. Pastur)

2

Exactly Solvable Model in Spin Glass, JETP Let., 2, pp. 323-326, (1977), (with L. Pastur)

3

Ergodic Properties of the Distribution of the Eigenvalues of Certain Classes of Random Self-Adjoint Operators, Dif. Ur. Funk. Anal., pp. 117-133, (1978) ; transl. Sel. Math. Sov., 3, pp. 69-86, (1983/1984), (with L. Pastur)

4

On the Theory of Disordered Spin System, Theor. Math. Phys ., 35, pp. 403-414, (1978), (with L. Pastur)

5

The Criterion of the Essential Self-Adjointness of Generalized Jacobi Matrices with Random Elements, (in Sb. Tr. Tashkent St. U.), 570, (1979), pp. 97-100.

6

Asymptotic behaviour of Some Wiener Integrals for large time, Dokl. Ak. Nauk Uzb. SSR, 10, pp. 10-12, (1979).

7

Asymptotic behaviour of Some Wiener Integrals for large time, Teor. Funk. Funk. l. 32, (1979), pp. 88-91; 33, pp. 132-135, (1980).

8

On the Exponential Growth of Solutions of the Finite Difference Second-Order Equations with Random Coefficients, Dokl. Ak. Nauk Uzb. SSR, 2, (1980), pp. 9-10.

9

The Distribution of Eigenvalues of the Schrödinger Equation with Random Potential and Asymptotic Behaviour of Certain Wiener Integral for Large Time, Dokl. Ak. Nauk Ukr. SSR, 6, pp. 27-29, (1981).

10

Infinite Range Limit for a Class of Disordered Spin Systems , Theor. Math. Phys., 51, pp. 564-569, (1982), (with L. Pastur)

11

On the Absence of the Absolutely Continuous Components of Random Jacobi Matrices Spectra , Funk. Anal. Pr. Mat., pp. 192-208, (1983).

12

Essential Self-Adjointness and Ergodic Properties of the Schrödinger Operator with Random Potential, Dokl. Ak. Nauk Ukr. SSR, 8, (1983), pp. 18-20.

13

Localization in an Incommensurate Potential: An Exactly Soluble Multidimensional Model, JETP Let., 37, pp. 686-688, (1983), (with L. Pastur)

14

The Positivity of the Lyapunov Exponent and the Absence of the Absolutely Continuous Spectrum for Almost-Mathieu Equation, J. Math. Phys., 25, pp. 774-777, (1984), (with L. Pastur)

15

An Exactly Soluble Model of Multidimensional Incommensurate Structure , Comm. Math. Phys., 95, 401-425, (1984), (with L. Pastur)

16

Ergodic Properties and Essential Self-Adjointness of Random matrix Operators , Oper. Funk. Pr. , pp. 13-27, (1987).

17

An Example of an Almost-Periodic Operator with Intersecting Point and Continuous Spectra, Oper. Funk. Pr., pp. 94-101, (1988), (with L. Pastur)

18

The Schrödinger Operator with a Nonlocal Quasiperiodic Potential whose Absolutely Continuous and Point Spectra Coexist , Comm. Math. Phys., 130, pp. 357-380, (1990)(with L. Pastur)

19

The Localization Properties of a Random Steady Flow on a Lattice Journal of Statistical Physics, 66, pp. 1599-1612, (1992).

20

One Model of a Nonhomogeneous Medium Conducting Light, Journal of Statistical Physics, 69, pp. 969-993, (1992).

21

Existence of Gaps in the Spectrum of Periodic Structures on a Lattice, Journal of Statistical Physics, 73, pp. 571-585, (1993).

22

Band-Gap Structure of the Spectrum of Periodic Maxwell Operator, Journal of Statistical Physics, 74, pp. 447-455, (1994), (with P. Kuchment)

23

Photonic Pseudogaps for Periodic Dielectric Structures, Journal of Statistical Physics, 74, pp. 433-446, (1994).

24

Localization Phenomenon in Gaps of the Spectrum of Random Lattice Operators, Journal of Statistical Physics, 75, pp. 997-1021, (1994), (with A. Klein)

25

Localization of Electromagnetic and Acoustic Waves in Random Media. Lattice Model, Journal of Statistical Physics, 76, pp. 985-1003, (1994), (with A. Klein)

26

Band-Gap Structure of the Spectrum of Periodic Dielectric and Acoustic Media. I. Scalar model, SIAM Journal on Applied Mathematics, 56, No. 1, pp. 68-88, (1996), (with P. Kuchment)

27

Band-Gap Structure of the Spectrum of Periodic Dielectric and Acoustic Media. II. 2D Photonic Crystals, SIAM Journal on Applied Mathematics, 56, No. 6, pp. 1561-1620, (1996), (with P. Kuchment)

28

2D Photonic Crystals with Cubic Structure: Asymptotic Analysis, in ``Wave Propagation in Complex Media'', IMA Proceedings 96, G. Papanicolaou, ed., Springer-Verlag, pp. 23-30, (1997), (with P. Kuchment).

29

Localization of Classical Waves I. Acoustic Waves, Communications in Mathematical Physics, 180, pp. 439-482, (1996), (with A. Klein).

30

Localized Classical Waves Created by Defects, Journal of Statistical Physics, 86, pp. 165-177, (1997), (with A. Klein).

31

Localization of Classical Waves II. Electromagnetic Waves , Communications in Mathematical Physics, 184, pp. 411-441, (1997), (with A. Klein).

32

The computation of spectra of some 2D photonic crystals, Journal of Computational Physics, 136, pp. 585-598, (1997), (with Yu. Godin).

33

Bound states of a one-band model for 3D periodic medium, Journal of Computational Physics, 138, pp. 153-170, (1997), (with I. Khalfin).

34

Midgap Defect Modes in Dielectric and Acoustic Media, SIAM Journal on Applied Mathematics, 58, 6, pp. 1748-1773, (1998), (with A. Klein).

35

Tunable Photonic Crystals, Phys. Rev. B 57, 5, pp. 2841-2848, (1998), (with Yu. Godin and I. Vitebsky).

36

Localization of Light in Lossless Inhomogeneous Dielectrics, Journal of the Optical Society of America A 15 , No. 5, pp. 1423-1435, (1998) (Feature Issue on Mathematics and Modeling in Modern Optics), (with A. Klein).

37

Spectral properties of classical waves in high contrast periodic media, SIAM J. Appl. Math., 58, No. 2, pp. 683-702, (1998)(with P. Kuchment).

38

Localized Electromagnetic Waves in a Periodic-Layered Dielctric Medium with a Defect, Phys. Rev. B 58, 1, pp. 180-189, (1998), (with V. Gorentsveig).

39

High-contrast Photonic Crystals, in ''Diffusive Waves in Complex Media''. Ed. J. P. Fouque, Kluwer, 1999, pp. 109-136.

40

41

Nonlinear Photonic Crystals. I. Quadratic Nonlinearity, Waves in Random Media, 11, pp. R31-R102 (2001). (with A. Babin).

42

Spectra of Periodic Nonreciprocal Electric Circuits, SIAM J. Appl. Math., 61, No. 6, pp. 1959-1979 (2001). (with I. Vitebsky)

43

Spectral Properties of Thin-film Photonic Crystals, SIAM J. Appl. Math., 61, No. 6, pp. 2008-2035 (2001) (with Yu. Godin).

44

Nonreciproal Magnetic Photonic Crystals, Phys. Rev. E, 63, 066609, pp. 1-17, (2001), (with I. Vitebsky).

45

Resolvent Method for Computation of Localized Defect Modes of H-polarization in 2D Photonic crystals, Phys. Rev., E, 64 , 056623, pp. 1-16, (2001), (with V. Gorentsveig).

46

Generalized Quantum Statistics and Testing of Randomizers with and without Asymptotic Assumptions, Monter Carlo Methods and Appl., 7, No. 1-2, pp. 167-175 (2001) (with A. Gordon, S. Molchanov, J. Quinn and N. Stavrakas).

47

Occupancy Numbers in Testing of Random Number Generator, SIAM J. Appl. Math, 62, No. 6, pp. 1980-2011 (2002) (with A. Gordon, S. Molchanov, J. Quinn and N. Stavrakas).

48

Nonlinear Photonic Crystals: II. Interaction Classification for Quadratic Nonlinearities, Waves in Random Media, 12, pp. R25-R52 (2002). (with A. Babin).

49

Effect of the inversion symmetry of dispersion relations on four-wave interactions in photonic crystals, Ultra-Wideband, Short Pulse Electromagnetics 6, to appear (with A. Babin).

50

Multilinear Spectral Decomposition for Nonlinear Maxwell Equations, Amer. Math. Soc. Transl., (2), Vol. 206, pp. 1-28, (2002) (with A. Babin).

51

Electromagnetic Unidirectionality in Magnetic Photonic Crystal, Phys. Rev., B, 67, 165210, pp. 1-20, (2003), (with I. Vitebskiy).

52

Nonlinear Maxwell Equations in Inhomogeneous Media, Comm. Math. Phys., appeared online September 2003, (with A. Babin).

53

Nonlinear Photonic Crystals: III. Cubic Nonlinearity, Waves in Random Media, 13, pp. R41-R69 (2003). (with A. Babin).

54

Oblique Frozen Modes in Periodic Layered Media, Phys. Rev., E, 68, 036609, pp. 1-16, (2003), (with I. Vitebskiy).