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444
Critical Energies in Random Palindrome Models
 J. Math. Phys
, 2002
"... We investigate the occurrence of critical energies { where the Lyapunov exponent vanishes { in random Schrodinger operators when the potential have some local order, which we call random palindrome models. ..."
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Cited by 1 (1 self)
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We investigate the occurrence of critical energies { where the Lyapunov exponent vanishes { in random Schrodinger operators when the potential have some local order, which we call random palindrome models.
NorthHolland Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr6dinger equation*
, 1991
"... The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension an ..."
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The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension
A THEOREM ON "LOCALIZED" SELFADJOINTNESS OF $CHRDINGER OPERATORS WITH L [ocPOTENTIALS
, 1982
"... ABSTRACT. We prove a result which concludes the selfadjointness of a Schr6"dinger operator from the selfadjointness of the associated "localized" Schr6"dinger oper ..."
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ABSTRACT. We prove a result which concludes the selfadjointness of a Schr6"dinger operator from the selfadjointness of the associated "localized" Schr6"dinger oper
ArnouxRauzy Subshifts: Linear Recurrence, Powers, And Palindromes
, 2002
"... We consider ArnouxRauzy subshifts X and study various combinatorial questions: When is X linearly recurrent? What is the maximal power occurring in X? What is the number of palindromes of a given length occurring in X? We present applications of our combinatorial results to the spectral theory of d ..."
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We consider ArnouxRauzy subshifts X and study various combinatorial questions: When is X linearly recurrent? What is the maximal power occurring in X? What is the number of palindromes of a given length occurring in X? We present applications of our combinatorial results to the spectral theory
(c) 1989 Birkh~user Verlag, Basel On the Almost Unper turbed SchrSdlnger pair of Operators
"... The pair of unbounded selfadjoint operators {U, V} satisfying the condition that i[V, V] c Z + D, where D is in the trace class, is investigated. Some theorems on symbols, the integrodifferential model, the principal distribution and the determining function of this {U, V} are established. 1. Int ..."
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roduct ion. The basic operators in the quantum mechanics i the SchrSdinger pair of operators q,p on L2([R) defined by (qf)(x) = xf(x) for f E P(q) = ( f E L2([R) : ()f() E L2(~)} and (pf)(x) = id f (x) for f E P(p) = { f E Lz(IR) : f is absolutely continuous on IR and ft E L2(IR)}. This Schr
NONLINEAR $\mathrm{S}\mathrm{C}\mathrm{H}\mathrm{R}\tilde{\mathrm{O}}$DINGER EQUATIONS IN FRACTIONAL ORDER SOBOLEV SPACES
"... In this note I describe some recent work on nonlinear $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{r}\tilde{\mathrm{o}}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r} $ equations, done jointly with M. Nakamura $[27, 28] $. We consider the nonlinear Schr\"odinger equations of the form $i\ ..."
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In this note I describe some recent work on nonlinear $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{r}\tilde{\mathrm{o}}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r} $ equations, done jointly with M. Nakamura $[27, 28] $. We consider the nonlinear Schr\"odinger equations of the form $i
A General Formula for RayleighSchrWnger Perturbation Energy Utilizing a Power Series Expansion of the Quantum Mechanical Hamiltonian
, 1997
"... under the provisions of a contract with the Department of Energy. I DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express o ..."
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under the provisions of a contract with the Department of Energy. I DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infXnge privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Reproduced from the best available copy.
I Integral Equations and Operator Theory SUBORDINATE SOLUTIONS AND SPECTRAL MEASURES OF CANONICAL SYSTEMS
"... The theory of 2 x 2 tracenormed canonical systems of differential equations on II { + can be put in the framework of abstract extension theory, cf. [9]. This includes the theory of strings as developed by I.S. Kac and M.G. Kre~n. In the present paper the spectral properties of such canonical system ..."
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systems are characterized by means of subordinate solutions. The theory of subordinacy for Schr6dinger operators on the halfline R +, was originally developed D.J. Gilbert and D.B. Pearson. Its extension to the framework of canonical systems makes it possible to describe the spectral measure of any
Results 1  10
of
444