Exact solutions for the cubic-quintic nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Zhu Jiamin; Ma Zhengyi
2007-01-01
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions
Study of nonlinear waves described by the cubic Schroedinger equation
International Nuclear Information System (INIS)
Walstead, A.E.
1980-01-01
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables
Study of nonlinear waves described by the cubic Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Walstead, A.E.
1980-03-12
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.
International Nuclear Information System (INIS)
Wu Hongyu; Fei Jinxi; Zheng Chunlong
2010-01-01
An improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schroedinger equation. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and the external potential. Some simple self-similar waves are presented. (general)
A reliable treatment for nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.
2007-01-01
Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
The phase space of the focused cubic Schroedinger equation: A numerical study
Energy Technology Data Exchange (ETDEWEB)
Burlakov, Yuri O. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
1998-05-01
In a paper of 1988 [41] on statistical mechanics of the nonlinear Schroedinger equation, it was observed that a Gibbs canonical ensemble associated with the nonlinear Schroedinger equation exhibits behavior reminiscent of a phase transition in classical statistical mechanics. The existence of a phase transition in the canonical ensemble of the nonlinear Schroedinger equation would be very interesting and would have important implications for the role of this equation in modeling physical phenomena; it would also have an important bearing on the theory of weak solutions of nonlinear wave equations. The cubic Schroedinger equation, as will be shown later, is equivalent to the self-induction approximation for vortices, which is a widely used equation of motion for a thin vortex filament in classical and superfluid mechanics. The existence of a phase transition in such a system would be very interesting and actually very surprising for the following reasons: in classical fluid mechanics it is believed that the turbulent regime is dominated by strong vortex stretching, while the vortex system described by the cubic Schroedinger equation does not allow for stretching. In superfluid mechanics the self-induction approximation and its modifications have been used to describe the motion of thin superfluid vortices, which exhibit a phase transition; however, more recently some authors concluded that these equations do not adequately describe superfluid turbulence, and the absence of a phase transition in the cubic Schroedinger equation would strengthen their argument. The self-induction approximation for vortices takes into account only very localized interactions, and the existence of a phase transition in such a simplified system would be very unexpected. In this thesis the authors present a numerical study of the phase transition type phenomena observed in [41]; in particular, they find that these phenomena are strongly related to the splitting of the phase space into
Stochastic effects on the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Flessas, G P; Leach, P G L; Yannacopoulos, A N
2004-01-01
The aim of this article is to provide a brief review of recent advances in the field of stochastic effects on the nonlinear Schroedinger equation. The article reviews rigorous and perturbative results. (review article)
Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation
International Nuclear Information System (INIS)
Ren Ji; Ruan Hangyu
2008-01-01
We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained
International Nuclear Information System (INIS)
Palacios, Sergio L.
2004-01-01
We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media
Mobile localization in nonlinear Schroedinger lattices
International Nuclear Information System (INIS)
Gomez-Gardenes, J.; Falo, F.; Floria, L.M.
2004-01-01
Using continuation methods from the integrable Ablowitz-Ladik lattice, we have studied the structure of numerically exact mobile discrete breathers in the standard discrete nonlinear Schroedinger equation. We show that, away from that integrable limit, the mobile pulse is dressed by a background of resonant plane waves with wavevectors given by a certain selection rule. This background is seen to be essential for supporting mobile localization in the absence of integrability. We show how the variations of the localized pulse energy during its motion are balanced by the interaction with this background, allowing the localization mobility along the lattice
Generalized non-linear Schroedinger hierarchy
International Nuclear Information System (INIS)
Aratyn, H.; Gomes, J.F.; Zimerman, A.H.
1994-01-01
The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy
International Nuclear Information System (INIS)
Senthilvelan, M; Torrisi, M; Valenti, A
2006-01-01
By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation
Cubication of conservative nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, Augusto; Alvarez, Mariela L; Fernandez, Elena; Pascual, Inmaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
On the invariant measure for the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Zhidkov, P.R.
1991-01-01
The invariant measure for the nonlinear Schroedinger equation is constructed. In fact, it is assumed that the nonlinearity in the equation is semilinear. The main aim of the paper is the explanation of the Fermi - Past - Ulam phenomenon. Poincare theorem gives the answer to this question. 17 refs
Exact solutions to two higher order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Xu Liping; Zhang Jinliang
2007-01-01
Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)
Energy Technology Data Exchange (ETDEWEB)
Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)
2009-09-21
The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schroedinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves in discrete systems is a signature of the modulation instability is used. With the help of this notion we conjecture that instability effects on moving solitons can be qualitative estimated from the analytical solutions. Results from numerical simulations are presented to support this conjecture.
Quantum osp-invariant non-linear Schroedinger equation
International Nuclear Information System (INIS)
Kulish, P.P.
1985-04-01
The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.; Baer, M.
2000-01-01
We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast
Integrability of a system of two nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhukhunashvili, V.Z.
1989-01-01
In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants
Integrable discretization s of derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tsuchida, Takayuki
2002-01-01
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)
Strong phase correlations of solitons of nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.
1994-06-01
We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs
The quantum nonlinear Schroedinger model with point-like defect
International Nuclear Information System (INIS)
Caudrelier, V; Mintchev, M; Ragoucy, E
2004-01-01
We establish a family of point-like impurities which preserve the quantum integrability of the nonlinear Schroedinger model in 1+1 spacetime dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the spacetime symmetry of the bulk scattering matrix, are also discussed. (letter to the editor)
Inhomogeneous critical nonlinear Schroedinger equations with a harmonic potential
International Nuclear Information System (INIS)
Cao Daomin; Han Pigong
2010-01-01
In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i∂ t u=-div(f(x)∇u)+|x| 2 u-k(x)|u| 4/N u, x is an element of R N , N≥1, which models the remarkable Bose-Einstein condensation. We discuss the existence and nonexistence results and investigate the limiting profile of blow-up solutions with critical mass.
Iteration of some discretizations of the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Ross, K.A.; Thompson, C.J.
1986-01-01
We consider several discretizations of the nonlinear Schroedinger equation which lead naturally to the study of some symmetric difference equations of the form PHIsub(n+1) + PHIsub(n-1) = f(PHIsub(n)). We find a variety of interesting and exotic behaviour from simple closed orbits to intricate patterns of orbits and loops in the (PHIsub(n+1),PHIsub(n)) phase-plane. Some analytical results for a special case are also presented. (orig.)
Derivation of an applied nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-01-01
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
Properties of some nonlinear Schroedinger equations motivated through information theory
International Nuclear Information System (INIS)
Yuan, Liew Ding; Parwani, Rajesh R
2009-01-01
We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Calvo, Gabriel F.
2009-01-01
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions
Travelling solitons in the damped driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.
2003-01-01
The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable
International Nuclear Information System (INIS)
Theodorakis, Stavros
2003-01-01
We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions
Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua
2009-01-01
The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.
Analytical exact solution of the non-linear Schroedinger equation
International Nuclear Information System (INIS)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da
2011-01-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Center manifold for nonintegrable nonlinear Schroedinger equations on the line
International Nuclear Information System (INIS)
Weder, R.
2000-01-01
In this paper we study the following nonlinear Schroedinger equation on the line, where f is real-valued, and it satisfies suitable conditions on regularity, on growth as a function of u and on decay as x → ± ∞. The generic potential, V, is real-valued and it is chosen so that the spectrum of H:= -d 2 /dx 2 +V consists of one simple negative eigenvalue and absolutely-continuous spectrum filling (0,∞). The solutions to this equation have, in general, a localized and a dispersive component. The nonlinear bound states, that bifurcate from the zero solution at the energy of the eigenvalue of H, define an invariant center manifold that consists of the orbits of time-periodic localized solutions. We prove that all small solutions approach a particular periodic orbit in the center manifold as t→ ± ∞. In general, the periodic orbits are different for t→ ± ∞. Our result implies also that the nonlinear bound states are asymptotically stable, in the sense that each solution with initial data near a nonlinear bound state is asymptotic as t→ ± ∞ to the periodic orbits of nearby nonlinear bound states that are, in general, different for t→ ± ∞. (orig.)
Nonlinear Schroedinger equation with U(p,q) isotopical group
International Nuclear Information System (INIS)
Makhankov, V.G.; Pashaev, O.K.
1981-01-01
The properties of the nonlinear Schroedinger equation (NLS) with U(1,1) isogroup are considered in detail. This example illustrates the essential difference between the system and the well-known ''vector'' NLS, i.e. the large set of allowed boundary conditions on the fields that leads to a rich set of solutions of the system. Four types of boundary conditions and related soliton solutions are considered. The Bohr-Sommerfeld quantization allows to interpret them in terms of ''drops'' and ''bubbles'' as bound states of a large number of constituent bosons subject to the thermodynamical relations for gas mixtures. The U(1,1) system under the vanishing boundary conditions may be considered as continuous analog of the Hubbard model and therefore the paper is concluded by studying the inverse scattering equations for this case [ru
Collective states of externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Spinning solitons in cubic-quintic nonlinear media ... features of families of bright vortex solitons (doughnuts, or 'spinning' solitons) in both conservative and dissipative cubic-quintic nonlinear media. ... Pramana – Journal of Physics | News.
International Nuclear Information System (INIS)
Steudel, H.
1980-01-01
It is shown that the two-parameter manifold of Baecklund transformations known for the nonlinear Schroedinger equation can be generated from one Baecklund transformation with specified parameters by use of scale transformation and Galilean transformation. (orig.)
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients
International Nuclear Information System (INIS)
Zhang Jiefang; Tian Qing; Wang Yueyue; Dai Chaoqing; Wu Lei
2010-01-01
We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.
Integrable peakon equations with cubic nonlinearity
International Nuclear Information System (INIS)
Hone, Andrew N W; Wang, J P
2008-01-01
We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation
International Nuclear Information System (INIS)
Yang Qin; Dai Chaoqing; Zhang Jiefang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.
Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent
2018-02-01
We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.
Filamentary structures of the cosmic web and the nonlinear Schroedinger type equation
International Nuclear Information System (INIS)
Tigrak, E; Weygaert, R van de; Jones, B J T
2011-01-01
We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schroedinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.
International Nuclear Information System (INIS)
Yang Xiao; Du Dianlou
2010-01-01
The Poisson structure on C N xR N is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schroedinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.
Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Sun Chengfeng; Gao Hongjun
2009-01-01
The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.
Non self-similar collapses described by the non-linear Schroedinger equation
International Nuclear Information System (INIS)
Berge, L.; Pesme, D.
1992-01-01
We develop a rapid method in order to find the contraction rates of the radially symmetric collapsing solutions of the nonlinear Schroedinger equation defined for space dimensions exceeding a threshold value. We explicitly determine the asymptotic behaviour of these latter solutions by solving the non stationary linear problem relative to the nonlinear Schroedinger equation. We show that the self-similar states associated with the collapsing solutions are characterized by a spatial extent which is bounded from the top by a cut-off radius
Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations
International Nuclear Information System (INIS)
Tang Chen; Zhang Fang; Yan Haiqing; Luo Tao; Chen Zhanqing
2005-01-01
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three-step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
International Nuclear Information System (INIS)
Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong
2011-01-01
In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.
Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions
International Nuclear Information System (INIS)
Geng Xianguo; Su Ting
2007-01-01
A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived
International Nuclear Information System (INIS)
Sen, S.; Roy Chowdhury, A.
1989-06-01
The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs
On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations
International Nuclear Information System (INIS)
Dietrich, K.; Vautherin, D.
1985-01-01
We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr
Interrelation of alternative sets of Lax-pairs for a generalized nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Iino, Kazuhiro; Ichikawa, Yoshihiko; Wadati, Miki.
1982-05-01
Examination of the inverse scattering transformation schemes for a generalized nonlinear Schroedinger equation reveals the fact that the algorithm of Chen-Lee-Liu gives rise to the Lax-pairs for the squared eigenfunctions of the Wadati-Konno-Ichikawa scheme, which has been formulated as superposition of the Ablowitz-Kaup-Newell-Segur scheme and the Kaup-Newell scheme. (author)
International Nuclear Information System (INIS)
Khrennikov, A.Yu.
2005-01-01
One derived the general evolutionary differential equation within the Hilbert space describing dynamics of the wave function. The derived contextual model is more comprehensive in contrast to a quantum one. The contextual equation may be a nonlinear one. Paper presents the conditions ensuring linearity of the evolution and derivation of the Schroedinger equation [ru
International Nuclear Information System (INIS)
Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.
1977-12-01
The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)
Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation
International Nuclear Information System (INIS)
Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.
2009-01-01
Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.
Chirped self-similar solutions of a generalized nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics
2011-01-15
An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)
Global Well-Posedness for Cubic NLS with Nonlinear Damping
Antonelli, Paolo
2010-11-04
We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.
International Nuclear Information System (INIS)
Li Biao; Chen Yong
2007-01-01
In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction
Quantum Gelfand-Levitan equations for nonlinear Schroedinger model of spin-1/2 particles
International Nuclear Information System (INIS)
Pu, F.; Zhao, B.
1984-01-01
The quantum Gelfand-Levitan equations for the nonlinear Schroedinger model of spin-(1/2) particles are obtained. Two Izergin-Korepin relations are used in the derivation. A new type commutation relation of L operators is introduced to get the commutation relations which are needed for the study of S matrices and Green's functions. As examples, the four-point Green's functions and the two-body S matrices are given
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Slavov, S.I.
1989-01-01
Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs
On exact solitary wave solutions of the nonlinear Schroedinger equation with a source
International Nuclear Information System (INIS)
Raju, T Solomon; Kumar, C Nagaraja; Panigrahi, Prasanta K
2005-01-01
We use a fractional transformation to connect the travelling wave solutions of the nonlinear Schroedinger equation (NLSE), phase locked with a source, to the elliptic equations satisfying, f-Prime ± af ± λf 3 = 0. The solutions are necessarily of rational form, containing both trigonometric and hyperbolic types as special cases. Bright and dark solitons, as well as singular solitons, are obtained in a suitable range of parameter values. (letter to the editor)
International Nuclear Information System (INIS)
Ravi Kanth, A.S.V.; Aruna, K.
2009-01-01
In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential
International Nuclear Information System (INIS)
Sacchetti, Andrea
2009-01-01
Here we consider stationary states for nonlinear Schroedinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.
Embedded solitons in the third-order nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Pal, Debabrata; Ali, Sk Golam; Talukdar, B
2008-01-01
We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion
Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation
Barashenkov, I V
2003-01-01
The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.
International Nuclear Information System (INIS)
Yan, Z.; Zhang, H.
2001-01-01
In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed
Blow-up in nonlinear Schroedinger equations. II. Similarity structure of the blow-up singularity
DEFF Research Database (Denmark)
Rypdal, K.; Juul Rasmussen, Jens
1986-01-01
invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity....
KAM for the non-linear Schroedinger equation
Eliasson, L H
2006-01-01
We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep|u|^2u;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it If $|\\ep|$ is sufficiently small, then there is a large subset $U'$ of $U$ such that for all $...
Genus two finite gap solutions to the vector nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Woodcock, Thomas; Warren, Oliver H; Elgin, John N
2007-01-01
A recently published article presents a technique used to derive explicit formulae for odd genus solutions to the vector nonlinear Schroedinger equation. In another article solutions of genus two are derived using a different approach which assumes a separable ansatz. In this communication, the extension of the first technique to the even genus case is discussed, and this extension is carried out explicitly for genus two. Furthermore, a birational mapping is found between the spectral curves that arise in the two approaches. (fast track communication)
International Nuclear Information System (INIS)
Ding Qing
2007-01-01
We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model
On form factors of the conjugated field in the non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2011-05-15
Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
International Nuclear Information System (INIS)
Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang
2011-01-01
By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.
International Nuclear Information System (INIS)
Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss
International Nuclear Information System (INIS)
Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin
2010-01-01
We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.
Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Martin, D.U.; Yuen, H.C.; Saffman, P.G.
1980-01-01
The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)
Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schroedinger model
International Nuclear Information System (INIS)
Basu-Mallick, B.; Bhattacharyya, Tanaya
2002-01-01
We find that the quantum monodromy matrix associated with a derivative nonlinear Schroedinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse scattering method which is directly applicable to field theoretical models, we derive all possible commutation relations among the operator valued elements of such monodromy matrix. Thus, we obtain the commutation relation between creation and annihilation operators of quasi-particles associated with DNLS model and find out the S-matrix for two-body scattering. We also observe that, for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles which can form a soliton state for the quantum DNLS model
Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Shin, H J
2004-01-01
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave
Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity
International Nuclear Information System (INIS)
Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru
2003-01-01
We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity
Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru
2003-03-01
We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.
Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation
International Nuclear Information System (INIS)
Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)
1982-01-01
The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru
Energy Technology Data Exchange (ETDEWEB)
Helal, M A [Mathematics Department, Faculty of Science, Cairo University (Egypt); Seadawy, A R [Mathematics Department, Faculty of Science, Beni-Suef University (Egypt)], E-mail: mahelal@yahoo.com, E-mail: aly742001@yahoo.com
2009-09-15
The derivative nonlinear Schroedinger equation (DNLSE) arises as a physical model for ultra-short pulse propagation. In this paper, the existence of a Lagrangian and the invariant variational principle (i.e. in the sense of the inverse problem of calculus of variations through deriving the functional integral corresponding to a given coupled nonlinear partial differential equations) for two-coupled equations describing the nonlinear evolution of the Alfven wave with magnetosonic waves at a much larger scale are given and the functional integral corresponding to those equations is derived. We found the solutions of DNLSE by choice of a trial function in a region of a rectangular box in two cases, and using this trial function, we find the functional integral and the Lagrangian of the system without loss. Solution of the general case for the two-box potential can be obtained on the basis of a different ansatz where we approximate the Jost function using polynomials of order n instead of the piecewise linear function. An example for the third order is given for illustrating the general case.
International Nuclear Information System (INIS)
Al Khawaja, U.
2010-01-01
We derive the integrability conditions of nonautonomous nonlinear Schroedinger equations using the Lax pair and similarity transformation methods. We present a comparative analysis of these integrability conditions with those of the Painleve method. We show that while the Painleve integrability conditions restrict the dispersion, nonlinearity, and dissipation/gain coefficients to be space independent and the external potential to be only a quadratic function of position, the Lax Pair and the similarity transformation methods allow for space-dependent coefficients and an external potential that is not restricted to the quadratic form. The integrability conditions of the Painleve method are retrieved as a special case of our general integrability conditions. We also derive the integrability conditions of nonautonomous nonlinear Schroedinger equations for two- and three-spacial dimensions.
Excitation of multiphase waves of the nonlinear Schroedinger equation by capture into resonances
International Nuclear Information System (INIS)
Friedland, L.; Shagalov, A.G.
2005-01-01
A method for adiabatic excitation and control of multiphase (N-band) waves of the periodic nonlinear Schroedinger (NLS) equation is developed. The approach is based on capturing the system into successive resonances with external, small amplitude plane waves having slowly varying frequencies. The excitation proceeds from zero and develops in stages, as an (N+1)-band (N=0,1,2,...), growing amplitude wave is formed in the (N+1)th stage from an N-band solution excited in the preceding stage. The method is illustrated in simulations, where the excited multiphase waves are analyzed via the spectral approach of the inverse scattering transform method. The theory of excitation of 0- and 1-band NLS solutions by capture into resonances is developed on the basis of a weakly nonlinear version of Whitham's averaged variational principle. The phenomenon of thresholds on the driving amplitudes for capture into successive resonances and the stability of driven, phase-locked solutions in these cases are discussed
Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential
International Nuclear Information System (INIS)
Alfimov, G. L.; Konotop, V. V.; Pacciani, P.
2007-01-01
We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed
Electron–soliton dynamics in chains with cubic nonlinearity
International Nuclear Information System (INIS)
Sales, M O; Moura, F A B F de
2014-01-01
In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron–soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling. (paper)
International Nuclear Information System (INIS)
Xu Guiqiong; Li Zhibin
2005-01-01
It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests
International Nuclear Information System (INIS)
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino
2006-01-01
The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel
2016-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...
On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations
International Nuclear Information System (INIS)
Barannik, A.F.; Marchenko, V.A.; Fushchich, V.I.
1991-01-01
With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered
Directory of Open Access Journals (Sweden)
S.H. Chen
1996-01-01
Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.
Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
Directory of Open Access Journals (Sweden)
Henri Schurz
2010-09-01
Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
Nonlinear modulation of ion acoustic waves in a magnetized plasma
International Nuclear Information System (INIS)
Bharuthram, R.; Shukla, P.K.
1987-01-01
The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations
International Nuclear Information System (INIS)
Xiao Yafeng; Xue Haili; Zhang Hongqing
2011-01-01
Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)
Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity
Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza
2018-02-01
The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.
International Nuclear Information System (INIS)
Hoffmann, D.
1984-01-01
Erwin Schroedinger (1887-1961) belongs without doubt to the most outstanding physicists of our century. His name is inseparably connected with the development of quantum theory with the formulation of his famous wave equation being his greatest achievement. This relation became generally known as the Schroedinger equation and its understanding was fundamental to the progress of modern quantum theory. In 1933 Schroedinger's work was honoured by the award of the Nobel Prize in physics. In the booklet Schroedinger's life, work and philosophical views are outlined against the social and physico-historical background of his time
A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Nash, Patrick L.
2008-01-01
Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros; Mitsotakis, Dimitrios
2016-01-01
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank
Nonlinear bias compensation of ZiYuan-3 satellite imagery with cubic splines
Cao, Jinshan; Fu, Jianhong; Yuan, Xiuxiao; Gong, Jianya
2017-11-01
Like many high-resolution satellites such as the ALOS, MOMS-2P, QuickBird, and ZiYuan1-02C satellites, the ZiYuan-3 satellite suffers from different levels of attitude oscillations. As a result of such oscillations, the rational polynomial coefficients (RPCs) obtained using a terrain-independent scenario often have nonlinear biases. In the sensor orientation of ZiYuan-3 imagery based on a rational function model (RFM), these nonlinear biases cannot be effectively compensated by an affine transformation. The sensor orientation accuracy is thereby worse than expected. In order to eliminate the influence of attitude oscillations on the RFM-based sensor orientation, a feasible nonlinear bias compensation approach for ZiYuan-3 imagery with cubic splines is proposed. In this approach, no actual ground control points (GCPs) are required to determine the cubic splines. First, the RPCs are calculated using a three-dimensional virtual control grid generated based on a physical sensor model. Second, one cubic spline is used to model the residual errors of the virtual control points in the row direction and another cubic spline is used to model the residual errors in the column direction. Then, the estimated cubic splines are used to compensate the nonlinear biases in the RPCs. Finally, the affine transformation parameters are used to compensate the residual biases in the RPCs. Three ZiYuan-3 images were tested. The experimental results showed that before the nonlinear bias compensation, the residual errors of the independent check points were nonlinearly biased. Even if the number of GCPs used to determine the affine transformation parameters was increased from 4 to 16, these nonlinear biases could not be effectively compensated. After the nonlinear bias compensation with the estimated cubic splines, the influence of the attitude oscillations could be eliminated. The RFM-based sensor orientation accuracies of the three ZiYuan-3 images reached 0.981 pixels, 0.890 pixels, and 1
International Nuclear Information System (INIS)
Lue Xing; Zhu Hongwu; Yao Zhenzhi; Meng Xianghua; Zhang Cheng; Zhang Chunyi; Tian Bo
2008-01-01
In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schroedinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Baecklund transformation transforms between (N - 1)- and N-soliton solutions
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
International Nuclear Information System (INIS)
Dubrovsky, V.G.; Formusatik, I.B.
2003-01-01
The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular
Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Pando L, C.L.
2003-08-01
We have studied the discrete nonlinear Schrodinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators are destroyed. However, we show that synchronization of symbolic information of suitable amplitude signals is possible in this hamiltonian system. (author)
Directory of Open Access Journals (Sweden)
Akira Abe
2010-01-01
and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.
Nonlinear effects on mode-converted lower-hybrid waves
International Nuclear Information System (INIS)
Kuehl, H.H.
1976-01-01
Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived
Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Jingdong Wei
2015-06-01
Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.
Solutions to the equations describing materials with competing quadratic and cubic nonlinearities
International Nuclear Information System (INIS)
Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong
2009-01-01
The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros
2016-07-05
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Cummings, Patrick
We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.
International Nuclear Information System (INIS)
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity
International Nuclear Information System (INIS)
Dasanayaka, Sahan; Atai, Javid
2010-01-01
We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.
International Nuclear Information System (INIS)
Basko, D.M.
2011-01-01
Research highlights: → In a one-dimensional disordered chain of oscillators all normal modes are localized. → Nonlinearity leads to chaotic dynamics. → Chaos is concentrated on rare chaotic spots. → Chaotic spots drive energy exchange between oscillators. → Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.
KAM for the non-linear Schroedinger equation a short presentation
Eliasson, H L
2006-01-01
We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep \\frac{\\p F}{\\p \\bar u}(x,u,\\bar u) ;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real and $F$ is a real analytic function in $\\Re u$, $\\Im u$ and $x$. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it ...
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Crosta, M.; Fratalocchi, Andrea; Trillo, S.
2011-01-01
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Tran Hy, J
1998-01-01
This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...
International Nuclear Information System (INIS)
Gao Yitian; Tian Bo
2003-01-01
A variable-coefficient unstable nonlinear Schroedinger model is hereby investigated, which arises in such applications as the electron-beam plasma waves and Rayleigh-Taylor instability in nonuniform plasmas. With computerized symbolic computation, families of exact analytic dark- and bright-soliton-like solutions are found, of which some previously published solutions turn out to be the special cases. Similarity solutions also come out, which are expressible in terms of the elliptic functions and the second Painleve transcendent. Some observable effects caused by the variable coefficient are predicted, which may be detected in the future with the relevant space or laboratory plasma experiments with nonuniform background existing
International Nuclear Information System (INIS)
Tian Bo; Gao Yitian; Zhu Hongwu
2007-01-01
Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schroedinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Baecklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Baecklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management
Facão, M.; Carvalho, M. I.
2017-10-01
In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.
International Nuclear Information System (INIS)
Kan, K.K.
1983-01-01
The relationship of nuclear internal flow and collective inertia, the difference of this flow from that of a classical fluid, and the approach of this flow to rigid flow in independent-particle model rotation are elucidated by reviewing the theory of Schroedinger fluid and its implications for collective vibration and rotation. (author)
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Alberto Lastra
2018-02-01
Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.
Partial regularity of weak solutions to a PDE system with cubic nonlinearity
Liu, Jian-Guo; Xu, Xiangsheng
2018-04-01
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.
Bifurcation of cubic nonlinear parallel plate-type structure in axial flow
International Nuclear Information System (INIS)
Lu Li; Yang Yiren
2005-01-01
The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)
Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun
2018-01-01
In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.
International Nuclear Information System (INIS)
Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C
2006-01-01
With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods
How additive noise generates a phantom attractor in a model with cubic nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina; Ryashko, Lev, E-mail: lev.ryashko@urfu.ru
2016-10-07
Two-dimensional nonlinear system forced by the additive noise is studied. We show that an increasing noise shifts random states and localizes them in a zone far from deterministic attractors. This phenomenon of the generation of the new “phantom” attractor is investigated on the base of probability density functions, mean values and variances of random states. We show that increasing noise results in the qualitative changes of the form of pdf, sharp shifts of mean values, and spikes of the variance. To clarify this phenomenon mathematically, we use the fast–slow decomposition and averaging over the fast variable. For the dynamics of the mean value of the slow variable, a deterministic equation is derived. It is shown that equilibria and the saddle-node bifurcation point of this deterministic equation well describe the stochastic phenomenon of “phantom” attractor in the initial two-dimensional stochastic system. - Highlights: • Two-dimensional nonlinear system with cubic nonlinearity is studied. • Additive noise generates a new phantom attractor. • By averaging over the fast variable one-dimensional equation is derived. • Phantom attractor appearance is analyzed by bifurcation analysis of this equation.
Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
Directory of Open Access Journals (Sweden)
Idris Addou
2000-01-01
Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Terras, V. [CNRS, ENS Lyon (France). Lab. de Physique
2010-12-15
We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)
International Nuclear Information System (INIS)
Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo
2007-01-01
For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers
International Nuclear Information System (INIS)
Kozlowski, K.K.; Terras, V.
2010-12-01
We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....
Energy Technology Data Exchange (ETDEWEB)
Lubkin, E [Wisconsin Univ., Madison (USA). Dept. of Physics
1979-08-01
The issue is to seek quantum interference effects in an arbitrary field, in particular in psychology. For this a digest of quantum mechanics over finite-n-dimensional Hilbert space is invented. In order to match crude data not only von Neumann's mixed states are used but also a parallel notion of unsharp tests. The mathematically styled text (and earlier work on multibin tests, designated MB) deals largely with these new tests. Quantum psychology itself is only given a foundation. It readily engenders objections; its plausibility is developed gradually, in interlocking essays. There is also the empirically definite proposal that (state, test, outcome)-indexed counts be gathered to record data, then fed to a matrix format (MF) search for quantum models. A previously proposed experiment in visual perception which has since failed to find significant quantum correlations, is discussed. The suspicion that quantum mechanics is all around goes beyond MF, and Schroedinger's cat symbolizes this broader perspective.
International Nuclear Information System (INIS)
Lubkin, E.
1979-01-01
The issue is to seek quantum interference effects in an arbitrary field, in particular in psychology. For this a digest of quantum mechanics over finite-n-dimensional Hilbert space is invented. In order to match crude data not only von Neumann's mixed states are used but also a parallel notion of unsharp tests. The mathematically styled text (and earlier work on multibin tests, designated MB) deals largely with these new tests. Quantum psychology itself is only given a foundation. It readily engenders objections; its plausibility is developed gradually, in interlocking essays. There is also the empirically definite proposal that (state, test, outcome)-indexed counts be gathered to record data, then fed to a 'matrix format' (MF) search for quantum models. A previously proposed experiment in visual perception which has since failed to find significant quantum correlations, is discussed. The suspicion that quantum mechanics is all around goes beyond MF, and 'Schroedinger's cat' symbolizes this broader perspective. (author)
The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions
International Nuclear Information System (INIS)
Tang Xiaoyan; Ding Wei
2008-01-01
The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
Creation and annihilation of solitons in the string nonlinear equation
International Nuclear Information System (INIS)
Aguero G, M.A.; Espinosa G, A.A.; Martinez O, J.
1997-01-01
Starting from the cubic-quintic Schroedinger equation it is obtained the nonlinear string equation. This system supports regular and singular solitons. It is shown that two singular solitons could be generated after the interaction of two regular solitons and viceversa. (Author)
Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.
2001-01-01
The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...
International Nuclear Information System (INIS)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin; Xue, Long; Aviation Univ. of Air Force, Liaoning
2015-01-01
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin
2014-09-01
We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Directory of Open Access Journals (Sweden)
Magdy A. El-Tawil
2009-01-01
Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
Explicit solutions of the cubic matrix nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Demontis, Francesco; Mee, Cornelis van der
2008-01-01
In this paper, we derive a class of explicit solutions, global in (x, t) is an element of R 2 , of the focusing matrix nonlinear Schrödinger equation using straightforward linear algebra. We obtain both the usual and multiple pole multisoliton solutions as well as a new class of solutions exponentially decaying as x → ±∞
Vaibhav, V.
2011-04-01
The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.
An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation
Directory of Open Access Journals (Sweden)
S. Sampath
2014-11-01
Full Text Available This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB, depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304. Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the feasibility of the theoretical model.
Durand, S.; Tellier, C. R.
1996-02-01
This paper constitutes the first part of a work devoted to applications of piezoresistance effects in germanium and silicon semiconductors. In this part, emphasis is placed on a formal explanation of non-linear effects. We propose a brief phenomenological description based on the multi-valleys model of semiconductors before to adopt a macroscopic tensorial model from which general analytical expressions for primed non-linear piezoresistance coefficients are derived. Graphical representations of linear and non-linear piezoresistance coefficients allows us to characterize the influence of the two angles of cut and of directions of alignment. The second part will primarily deal with specific applications for piezoresistive sensors. Cette publication constitue la première partie d'un travail consacré aux applications des effets piézorésistifs dans les semiconducteurs germanium et silicium. Cette partie traite essentiellement de la modélisation des effets non-linéaires. Après une description phénoménologique à partir du modèle de bande des semiconducteurs nous développons un modèle tensoriel macroscopique et nous proposons des équations générales analytiques exprimant les coefficients piézorésistifs non-linéaires dans des repères tournés. Des représentations graphiques des variations des coefficients piézorésistifs linéaires et non-linéaires permettent une pré-caractérisation de l'influence des angles de coupes et des directions d'alignement avant l'étude d'applications spécifiques qui feront l'objet de la deuxième partie.
DEFF Research Database (Denmark)
Bang, Ole; Corney, Joel Frederick
2001-01-01
In continuous-wave operation asymmetric induced nonlinearities induce an intensity-dependent phase mismatch that implies a nonzero so-called separatrix intensity, the crossing of which changes the one-period phase shift of the fundamental by Pi , with obvious use in switching applications.......We derived a formula for this QPM-induced separatrix intensity that corrects earlier estimates by a factor of 5.3, and we found the optimum crystal lengths for a flat phase-versus-intensity response on each side of the separatrix...
Blow-up criteria for the 3D cubic nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Holmer, Justin; Platte, Rodrigo; Roudenko, Svetlana
2010-01-01
We consider solutions u to the 3D nonlinear Schrödinger equation i∂ t u + Δu + |u| 2 u = 0. In particular, we are interested in finding criteria on the initial data u 0 that predict the asymptotic behaviour of u(t), e.g., whether u(t) blows up in finite time, exists globally in time but behaves like a linear solution for large times (scatters), or exists globally in time but does not scatter. This question has been resolved (at least for H 1 data) (Duyckaerts–Holmer–Roudenko) if M[u]E[u] ≤ M[Q]E[Q], where M[u] and E[u] denote the mass and energy of u and Q denotes the ground state solution to −Q + ΔQ + |Q| 2 Q = 0. Here we consider the complementary case M[u]E[u] > M[Q]E[Q]. In the first (analytical) part of the paper, we present a result due to Lushnikov, based on the virial identity and the generalized uncertainty principle, giving a sufficient condition for blow-up. By replacing the uncertainty principle in his argument with an interpolation-type inequality, we obtain a new blow-up condition that in some cases improves upon Lushnikov's condition. Our approach also allows for an adaptation to radial infinite-variance initial data that has a conceptual interpretation: for real-valued initial data, if a certain fraction of the mass is contained within the ball of radius M[u], then blow up occurs. We also show analytically (if one takes the numerically computed value of ||Q|| .H 1/2 ) that there exist Gaussian initial data u 0 with negative quadratic phase such that ||u 0 || .H 1/2 .H 1/2 but the solution u(t) blows up. In the second (numerical) part of the paper, we examine several different classes of initial data—Gaussian, super Gaussian, off-centred Gaussian, and oscillatory Gaussian—and for each class give the theoretical predictions for scattering or blow-up provided by the above theorems as well as the results of numerical simulation. We find that depending upon the form of the initial conditions, any of the three analytical criteria for blow
The paradox of Schroedinger's waves
International Nuclear Information System (INIS)
Gribben, John.
1987-01-01
The paper examines the contribution of the work of Erwin Schroedinger in quantum physics. The Schroedinger equation was developed to explain the behavior of electrons within an atom in terms of waves, and it has proved one of the most useful tools in quantum physics. The Schroedinger 'Cat' experiment is also described and discussed. Finally Schroedinger's ideas on chromosomes in molecular biology are briefly outlined. (U.K.)
Crystallized Schroedinger cat states
International Nuclear Information System (INIS)
Castanos, O.; Lopez-Pena, R.; Man'ko, V.I.
1995-01-01
Crystallized Schroedinger cat states (male and female) are introduced on the base of extension of group construction for the even and odd coherent states of the electromagnetic field oscillator. The Wigner and Q functions are calculated and some are plotted for C 2 , C 3 , C 4 , C 5 , C 3v Schroedinger cat states. Quadrature means and dispersions for these states are calculated and squeezing and correlation phenomena are studied. Photon distribution functions for these states are given explicitly and are plotted for several examples. A strong oscillatory behavior of the photon distribution function for some field amplitudes is found in the new type of states
Almost periodic Schroedinger operators
International Nuclear Information System (INIS)
Bellissard, J.; Lima, R.
1984-01-01
These lectures are devoted to recent developments in the theory of almost-periodic Schroedinger Operators. We specially describe the algebraic point of view, with applications to gap-labelling theorems. Particular models are also presented which exhibit various spectral properties. (orig.)
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
Schroedinger covariance states in anisotropic waveguides
International Nuclear Information System (INIS)
Angelow, A.; Trifonov, D.
1995-03-01
In this paper Squeezed and Covariance States based on Schroedinger inequality and their connection with other nonclassical states are considered for particular case of anisotropic waveguide in LiNiO 3 . Here, the problem of photon creation and generation of squeezed and Schroedinger covariance states in optical waveguides is solved in two steps: 1. Quantization of electromagnetic field is provided in the presence of dielectric waveguide using normal-mode expansion. The photon creation and annihilation operators are introduced, expanding the solution A-vector(r-vector,t) in a series in terms of the Sturm - Liouville mode-functions. 2. In terms of these operators the Hamiltonian of the field in a nonlinear waveguide is derived. For such Hamiltonian we construct the covariance states as stable (with nonzero covariance), which minimize the Schroedinger uncertainty relation. The evolutions of the three second momenta of q-circumflex j and p-circumflex j are calculated. For this Hamiltonian all three momenta are expressed in terms of one real parameters s only. It is found out how covariance, via this parameter s, depends on the waveguide profile n(x,y), on the mode-distributions u-vector j (x,y), and on the waveguide phase mismatching Δβ. (author). 37 refs
Directory of Open Access Journals (Sweden)
R. Talebitooti
Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.
Philosophy of Erwin Schroedinger: a diachronic view of Schroedinger's thoughts
International Nuclear Information System (INIS)
Melgar, M.F.
1988-01-01
There is no agreement within the scientific community about the philosophy of Schroedinger. Some people think that he was a realist, while others defend him as an idealist. In this paper we study a number of Schroedinger's works and we show that the epithets of realist and idealist do not do him justice. Toward the end we conclude that it would be more adequate to place him in the trend known as the philosophy of immanence
International Nuclear Information System (INIS)
Pando L, C.L.; Doedel, E.J.
2006-08-01
We investigate the nonlinear dynamics in a trimer, described by the one-dimensional discrete nonlinear Schrodinger equation (DNLSE), with periodic boundary conditions in the presence of a single on-site defect. We make use of numerical continuation to study different families of stationary and periodic solutions, which allows us to consider suitable perturbations. Taking into account a Poincare section, we are able to study the dynamics in both a thin stochastic layer solution and a global stochasticity solution. We find that the time series of the transit times, the time intervals to traverse some suitable sets in phase space, generate 1/f noise for both stochastic solutions. In the case of the thin stochastic layer solution, we find that transport between two almost invariant sets along with intermittency in small and large time scales are relevant features of the dynamics. These results are reflected in the behaviour of the standard map with suitable parameters. In both chaotic solutions, the distribution of transit times has a maximum and a tail with exponential decay in spite of the presence of long-range correlations in the time series. We motivate our study by considering a ring of weakly-coupled Bose-Einstein condensates (BEC) with attractive interactions, where inversion of populations between two spatially symmetric sites and phase locking take place in both chaotic solutions. (author)
Properties of squeezed Schroedinger cats
International Nuclear Information System (INIS)
Obada, A.S.F.; Omar, Z.M.
1995-09-01
In this article we investigate some statistical properties of the even and odd squeezed (squeezed Schroedinger cat) states. The quasi-probability distribution functions especially W(α) and Q(α) are calculated and discussed for these states. The phase distribution function is discussed. A generation scheme is proposed for either the squeezed generalized Schroedinger cat, or the squeezed number state. (author). 35 refs, 5 figs
Directory of Open Access Journals (Sweden)
Idris Addou
2000-07-01
Full Text Available We study boundary-value problems of the type $$displaylines{ -(varphi_{p}( u' ' =lambda f( u ,hbox{ in }(0,1 cr u( 0 =u( 1 =0, }$$ where $p>1$, $varphi_{p}( x =left| x ight| ^{p-2}x$, and $lambda >0$. We provide multiplicity results when $f$ behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter $q>1$. We shall show how changes in the position of $q$ with respect to $p$ lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that $f$ is {it half-odd}; a condition generalizing the usual oddness. We use a quadrature method.
Directory of Open Access Journals (Sweden)
M.G. Hafez
2016-06-01
Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.
International Nuclear Information System (INIS)
Da Costa, N.C.A.; Krause, D.; French, S.
1992-01-01
Schroedinger introduced discussions about the inconsistency between the classical conception of particles as individual entities and the way in which modern physics treats such particles. In particular, it is noted that quantal particles apparently appear to lack individuality, and that certain suppositions of quantum theory imply that permutations of 'identical' particles are not regarded as observable, hence implying that they must be taken as 'non-individuals' of some kind. An overview is presented in this paper of some results obtained by the authors in the field of non-reflexive logics, which have some bearings on these problems and which can perhaps provide an adequate mathematical tool for dealing with some of the fundamental features of elementary particles, such as for instance the fact that identity apparently lacks sense with respect to them, that particle permutations are not regarded as observable and that a collection of these entities cannot be considered as a set in the sense of the usual theories of sets. The main objective of the paper is to show that the nature of elementary particles can be described in terms of certain non-classical logics, despite the problems regarding their individuality. (authors). 28 refs
A life of Erwin Schroedinger; Erwin Schroedinger. Eine Biographie
Energy Technology Data Exchange (ETDEWEB)
Moore, Walter J.
2012-07-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientists of the 20th century at all and - a charming Austrian. He was a man with a passionate interest in people and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he got the Nobel prize for physics and naturally by the famous thought experiment ''Schroedinger's cat''. Walter Moore's biography is very close to the person of Schroedinger and presents his scientific work in the context of his private friendships, his interest in mysticism, and in front of the moving background of the political events in Germany and Austria.
Schroedinger's variational method of quantization revisited
International Nuclear Information System (INIS)
Yasue, K.
1980-01-01
Schroedinger's original quantization procedure is revisited in the light of Nelson's stochastic framework of quantum mechanics. It is clarified why Schroedinger's proposal of a variational problem led us to a true description of quantum mechanics. (orig.)
Scale calculus and the Schroedinger equation
International Nuclear Information System (INIS)
Cresson, Jacky
2003-01-01
This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions
International Nuclear Information System (INIS)
Luzyanin, I.D.; Khavronin, V.P.
1984-01-01
Results are presented of an experimental investigation of the behaviour of the nonlinear dynamic susceptibility in the phase transition region the cubic, weakly anisotropic ferromagnetics CdCr 2 S 4 and CdCr 2 Se 4 . It is shown that above the Curie point Tsub(C) two temperature regions, a scaling and anomalous, can be distinguished which involve critical phenomena of different nature. In the scaling region which corresponds to 4πchisub(0)) < or approximately 25, the behaviour found for the linear and nonlinear susceptibilities are in satisfactory agreement with the theoretical predictions based on similarity considerations. The anomalous region is directly adjacent to Tsub(C). In this region phenomena are observed which are not consistent with current concepts regarding the nature of second order phase transitions e.g. hysteresis with respect to magnetic field, a ''residual'' second order signal which persists a long time after switching off of the external stationary field and an anomalous behavioUr of the susceptibility at low frequencies. The resemblence of the phenomena observed in the anomalous region with those occurring in spin glasses is noted
International Nuclear Information System (INIS)
Moore, Walter J.
2012-01-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientists of the 20th century at all and - a charming Austrian. He was a man with a passionate interest in people and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he got the Nobel prize for physics and naturally by the famous thought experiment ''Schroedinger's cat''. Walter Moore's biography is very close to the person of Schroedinger and presents his scientific work in the context of his private friendships, his interest in mysticism, and in front of the moving background of the political events in Germany and Austria.
Schroedinger and the wave mechanics
International Nuclear Information System (INIS)
Bassalo, J.M.F.
1987-01-01
In commemoration of the centennial of Schroedinger's birth, in 1987, we show in this paper some aspects of his academic life, and his philosophical and scientific work. Among Schroedinger's innumerable contributions to almost all areas of philosophy and science, we choose here the creation of quantum mechanics (1926), considered one of the pillars of Modern quantum theory, and the importance of his philosophical essay What is life (1944). This publication was responsible for a great in the studies of biology, culminating in the discovery of the DNA molecular structure, in 1953, by Crick and Watson, thanks to the X-rays diffraction technique of the DNA developed by Wilkens. (author) [pt
Dynamics of electron wave packet in a disordered chain with delayed nonlinear response
International Nuclear Information System (INIS)
Zhu Hongjun; Xiong Shijie
2010-01-01
We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
International Nuclear Information System (INIS)
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
Schroedinger operators and evolutionary strategies
International Nuclear Information System (INIS)
Asselmeyer, T.
1997-01-01
First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution
A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Directory of Open Access Journals (Sweden)
L. S. Konev
2015-09-01
Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.
Correspondence passed between Einstein and Schroedinger
International Nuclear Information System (INIS)
Balibar, F.
1992-01-01
The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories
P-adic Schroedinger type equation
International Nuclear Information System (INIS)
Vladimirov, V.S.; Volovich, I.V.
1988-12-01
In p-adic quantum mechanics a Schroedinger type equation is considered. We discuss the appropriate notion of differential operators. A solution of the Schroedinger type equation is given. A new set of vacuum states for the p-adic quantum harmonic oscillator is presented. The correspondence principle with the standard quantum mechanics is discussed. (orig.)
In search of Schroedinger's cat
International Nuclear Information System (INIS)
Gribbin, John.
1984-01-01
The book explains how the paradox of Schroedinger's cat led to an understanding of reality in quantum physics. The contents of the book is divided into three parts. Part one concerns light, atoms and Bohr's atom. Quantum mechanics is discussed in Part Two, including photons and electrons, matrices and waves, and applications of quanta. The last part deals with chance and uncertainty, paradoxes and possibilities, the experimental proof of the paradoxical reality of the quantum world, and the many-worlds interpretation of quantum mechanics. (U.K.)
Introduction to Schroedinger inverse scattering
International Nuclear Information System (INIS)
Roberts, T.M.
1991-01-01
Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)
Weakly nonlinear electromagnetic waves in an electron-ion positron plasma
International Nuclear Information System (INIS)
Rizzato, F.B.; Schneider, R.S.; Dillenburg, D.
1987-01-01
The modulation of a high-frequency electromagnetic wave which is circulary polarized and propagates in a plasma made up of electrons, ions and positrons is investigated. The coefficient of the cubic nonlinear term in the Schroedinger equation may change sign as the relative particle concentrations vary, and consequently a marginal state of modulation instability may exist. To described the system in the neighbourhood of this state an appropriate equation is derived. Particular stationary solutions of this equation are envelope solitary waves, envelope Kinks and envelope hole solitary waves. The dependence of the amplitude of the solutions on the propagation velocity and the particle concentrations is discussed. (author) [pt
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
On quantization, the generalised Schroedinger equation and classical mechanics
International Nuclear Information System (INIS)
Jones, K.R.W.
1991-01-01
A ψ-dependent linear functional operator, was defined, which solves the problem of quantization in non-relativistic quantum mechanics. Weyl ordering is implemented automatically and permits derivation of many of the quantum to classical correspondences. The parameter λ presents a natural C ∞ deformation of the dynamical structure of quantum mechanics via a non-linear integro-differential 'Generalised Schroedinger Equation', admitting an infinite family of soliton solutions. All these solutions are presented and it is shown that this equation gives an exact dynamic and energetic reproduction of classical mechanics with the correct measurement theoretic limit. 23 refs
Some threshold spectral problems of Schroedinger operators
International Nuclear Information System (INIS)
Jia, X.
2009-01-01
This Ph.D. thesis deals with some spectral problems of the Schroedinger operators. We first consider the semi-classical limit of the number of bound states of unique two-cluster N-body Schroedinger operator. Then we use Dirichlet-Neumann bracket to get semi-classical limit of Riesz means of the discrete eigenvalues of N-body Schroedinger operator. The effective potential of N-body Schroedinger operator with Coulomb potential is also considered and we find that the effective potential has critical decay at infinity. Thus, the Schroedinger operator with critical potential is studied in this thesis. We study the coupling constant threshold of Schroedinger operator with critical potential and the asymptotic expansion of resolvent of Schroedinger operator with critical potential. We use that expansion to study low-energy asymptotics of derivative of spectral shift function for perturbation with critical decay. After that, we use this result and the known result for high-energy asymptotic expansion of spectral shift function to obtain the Levinson theorem. (author)
The Schroedinger operator as a generalized Laplacian
International Nuclear Information System (INIS)
Grabowska, Katarzyna; Urbanski, Pawel; Grabowski, Janusz
2008-01-01
The Schroedinger operators on the Newtonian spacetime are defined in a way which make them independent of the class of inertial observers. In this picture the Schroedinger operators act not on functions on the spacetime but on sections of a certain one-dimensional complex vector bundle-the Schroedinger line bundle. This line bundle has trivializations indexed by inertial observers and is associated with an U(1)-principal bundle with an analogous list of trivializations-the Schroedinger principal bundle. If an inertial frame is fixed, the Schroedinger bundle can be identified with the trivial bundle over spacetime, but as there is no canonical trivialization (inertial frame), these sections interpreted as 'wavefunctions' cannot be viewed as actual functions on the spacetime. In this approach, the change of an observer results not only in the change of actual coordinates in the spacetime but also in a change of the phase of wavefunctions. For the Schroedinger principal bundle, a natural differential calculus for 'wave forms' is developed that leads to a natural generalization of the concept of the Laplace-Beltrami operator associated with a pseudo-Riemannian metric. The free Schroedinger operator turns out to be the Laplace-Beltrami operator associated with a naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger principal bundle. The presented framework does not involve any ad hoc or axiomatically introduced geometrical structures. It is based on the traditional understanding of the Schroedinger operator in a given reference frame-which is supported by producing right physics predictions-and it is proven to be strictly related to the frame-independent formulation of analytical Newtonian mechanics and Hamilton-Jacobi equations that makes a bridge between the classical and quantum theory
Schroedinger representation in quantum field theory
International Nuclear Information System (INIS)
Luescher, M.
1985-01-01
Until recently, the Schroedinger representation in quantum field theory had not received much attention, even more so because there were reasons to believe that in the presence of interactions it did not exist in a mathematically well-defined sense. When Symanzik set out to solve this problem, he was motivated by a special 2-dimensional case, the relativistic string model, in which the Schroedinger wave functionals are the primary objects of physical interest. Also, he knew that if it were possible to demonstrate the existence of the Schroedinger representation, the (then unproven) ultraviolet finiteness of the Casimir force in renormalizable quantum field theories would probably follow. (orig./HSI)
Erwin Schroedinger, Francis Crick and epigenetic stability
Directory of Open Access Journals (Sweden)
Ogryzko Vasily V
2008-04-01
Full Text Available Abstract Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.
Erwin Schroedinger, Francis Crick and epigenetic stability.
Ogryzko, Vasily V
2008-04-17
Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.
Reparametrization invariance and the Schroedinger equation
International Nuclear Information System (INIS)
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
1999-01-01
A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation
Spectral Target Detection using Schroedinger Eigenmaps
Dorado-Munoz, Leidy P.
Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and
Simulation of the Schroedinger equation on SHAC
International Nuclear Information System (INIS)
Stewart, A.
1976-01-01
A simulation of the Schroedinger wave equation for the hydrogen atom, on SHAC, a simple homogeneous analogue computer primarily intended for use in schools, is described. Due to the incorporation of FET switches very high speed switching from initial conditions to compute modes is possible. The techniques employed in the multiplier and divider are discussed and the flow diagram for the Schroedinger program shown. Results and photographs are discussed. (U.K.)
Nonlinear von Neumann equations for quantum dissipative systems
International Nuclear Information System (INIS)
Messer, J.; Baumgartner, B.
1978-01-01
For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)
Nonlinear von Neumann equations for quantum dissipative systems
International Nuclear Information System (INIS)
Messer, J.; Baumgartner, B.
For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)
Nonlinearity management in higher dimensions
International Nuclear Information System (INIS)
Kevrekidis, P G; Pelinovsky, D E; Stefanov, A
2006-01-01
In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management
Energy Technology Data Exchange (ETDEWEB)
Balibar, F. [Paris-7 Univ., 75 (France)
1992-12-31
The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories.
International Nuclear Information System (INIS)
Pelinovsky, D. E.; Stefanov, A.
2008-01-01
Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0
Some studies of Schroedinger operators
International Nuclear Information System (INIS)
Liu Yang.
1993-09-01
This thesis consists of three papers. Paper 1 deals with the semiclassical approximation for a Schroedinger operator in one dimension with an arbitrary continuous potential. The basic result is that function in the range of a spectral projection associated with an interval are exponentially small (with respect to Plancks parameter h) in places where the potential exceeds the interval. As an application of this result, it is shown that the eigenvalues of the operator localized to the wells appear as resonances of the global operator. This is true also when the potential is not bounded from below. Such results were proved before for analytic potentials by analytic dilatation. In Paper 2, the potential is assumed to have the form of χ + V(χ) (the Stark Hamiltonian) with a well-behaved V(χ), an explicit spectral and scattering theory for such an operator was presented using the time-independent approach. In particular, we derive an eigenfunction expansion theorem which, combined with a construction of an intertwining operator, gives a solution of the inverse scattering problem according to L. Daddeev and A. Melin. The direct part of the second paper has a generalization to higher dimensions, and this was done in the third paper. Also in that paper, the condition on the potentials for doing the inverse scattering theory was relaxed, and an explicit formula for the potentials involving the first approximation of the scattering data was given
On the connection between Schroedinger- and Dirichlet forms
International Nuclear Information System (INIS)
Albeverio, S.; Bochum Univ.; Gesztesy, F.; Karwowski, W.; Streit, L.; Bielefeld Univ.
Relations between Schroedinger forms associated with Schroedinger operators in L 2 (Ω;dsup(n)x), Ω is contained in Rsup(n) open, n >= 1 and the corresponding Dirichlet forms are investigated. Various concrete examples are presented. (orig.)
Nonrelativistic Schroedinger equation in quasi-classical theory
International Nuclear Information System (INIS)
Wignall, J.W.G.
1987-01-01
The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field chi(x,t), interacting with each other via nonlinearity in the equation of motion for chi. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from chi a configuration-space wave function Psi(x 1 , X 2 , t), and that the theory requires that Psi satisfy the two-particle Schroedinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schroedinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials
Unifying quanta and relativity. Schroedinger`s attitude to relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Kragh, H. [Roskilde Universitetscenter (Denmark)
1992-12-31
A considerable part of Schroedinger`s scientific work focused on the relationship between quantum theory and the theory of relativity. This paper provides a historical analysis of his occupation on this subject in the period 1925-1934. The first section surveys the role played by relativity in Schroedinger`s formation of wave mechanics in 1925-1926; the second section analyzes his attempt to make sense of Dirac`s theory of the electron by proposing a relativistic wave equation with positive energies only. In this work, which took place in 1930-1931, Schroedinger discovered the Zitterbewegung that Dirac electrons will exhibit even in a field-free case. Schroedinger`s failed attempt to introduce an alternative to the Dirac theory was part of his general dissatisfaction with the current state of quantum mechanics. It is argued that, to a large extent, his work on the Dirac theory was philosophically motivated and that it contributed to his alienation from mainstream quantum physics in the 1930s. (author). 54 refs.
Single-particle Schroedinger fluid. I. Formulation
International Nuclear Information System (INIS)
Kan, K.K.; Griffin, J.J.
1976-01-01
The problem of a single quantal particle moving in a time-dependent external potential well is formulated specifically to emphasize and develop the fluid dynamical aspects of the matter flow. This idealized problem, the single-particle Schroedinger fluid, is shown to exhibit already a remarkably rich variety of fluid dynamical features, including compressible flow and line vortices. It provides also a sufficient framework to encompass simultaneously various simplified fluidic models for nuclei which have earlier been postulated on an ad hoc basis, and to illuminate their underlying restrictions. Explicit solutions of the single-particle Schroedinger fluid problem are studied in the adiabatic limit for their mathematical and physical implications (especially regarding the collective kinetic energy). The basic generalizations for extension of the treatment to the many-body Schroedinger fluid are set forth
A life of Erwin Schroedinger. 2. ed.
International Nuclear Information System (INIS)
Moore, Walter J.
2015-01-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.
Some physical applications of fractional Schroedinger equation
International Nuclear Information System (INIS)
Guo Xiaoyi; Xu Mingyu
2006-01-01
The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given
Quantum derivatives and the Schroedinger equation
International Nuclear Information System (INIS)
Ben Adda, Faycal; Cresson, Jacky
2004-01-01
We define a scale derivative for non-differentiable functions. It is constructed via quantum derivatives which take into account non-differentiability and the existence of a minimal resolution for mean representation. This justify heuristic computations made by Nottale in scale-relativity. In particular, the Schroedinger equation is derived via the scale-relativity principle and Newton's fundamental equation of dynamics
The Universe according to Schroedinger and Milo
Wolff, Milo
2009-10-01
The puzzling electron is due to the belief that it is a discrete particle. Schroedinger, (1937) eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). Thus he rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff using a Scalar Wave Equation in 3D quantum space to find wave solutions. The resulting Wave Structure of Matter (WSM) contains all the electron's properties including the Schroedinger Equation. Further, Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. These the origin of all the Natural Laws. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips and to correct errors of Maxwell's Equations. Applications of the WSM describe matter at molecular dimensions: Industrial alloys, catalysts, biology and medicine, molecular computers and memories. See book ``Schroedinger's Universe'' - at Amazon.com. Pioneers of the WSM are growing rapidly. Some are: SpaceAndMotion.com, QuantumMatter.com, treeincarnation.com/audio/milowolff.htm, daugerresearch.com/orbitals/index.shtml, glafreniere.com/matter.html =A new Universe.
Schroedinger's Wave Structure of Matter (WSM)
Wolff, Milo; Haselhurst, Geoff
2009-10-01
The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com
Some spectral equivalences between Schroedinger operators
International Nuclear Information System (INIS)
Dunning, C; Hibberd, K E; Links, J
2008-01-01
Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schroedinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators
Abelian Higgs mechanism in the Schroedinger picture
International Nuclear Information System (INIS)
Kim, S.K.; Namgung, W.; Soh, K.S.; Yee, J.H.
1990-01-01
We have studied symmetry-breaking phenomena in scalar electrodynamics by evaluating the effective potential at one-loop order in the Schroedinger picture. Contributions to the effective potential by the Higgs particle and the transverse and longitudinal components of a photon are compared with other previous works, and they are found to be consistent
Spectral problem for the radial Schroedinger equation
International Nuclear Information System (INIS)
Vshivtsev, A.S.; Tatarintsev, A.V.; Prokopov, A.V.; Sorokin, V. N.
1998-01-01
For the first time, a procedure for determining spectra on the basis of generalized integral transformations is implemented for a wide class of radial Schroedinger equations. It is shown that this procedure works well for known types of potentials. Concurrently, this method makes it possible to obtain new analytic results for the Cornell potential. This may prove important for hadron physics
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Averaging of nonlinearity-managed pulses
International Nuclear Information System (INIS)
Zharnitsky, Vadim; Pelinovsky, Dmitry
2005-01-01
We consider the nonlinear Schroedinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons
Considerations on Bohr's, Heisenberg's and Schroedinger's philosophy
International Nuclear Information System (INIS)
Shimony, A.
1981-01-01
In denying that the words 'physical reality' are meaningful without reference to an experimental arrangement, Bohr renounces any knowledge of the 'thing-in-itself'. However, the relation of his epistemology to both idealism and positivism remains obscure. Heisenberg departs from Bohr in enunciating a metaphysical implication of quantum mechanics. Heisenberg asserts that there is an intermediate modality -potentiality- between logical possibility and existence. His attempts to explain the transition from potentiality to existence are not convincing. Schroedinger rejects Bohr's interpretation of quantum mechanics as a positivist exercise and seeks instead a realist interpretation. Nevertheless, the metaphysics of Schroedinger is fundamentally idealistic, maintaining that the material aspect of the world is composed of the same elements as mind, but in a different order [fr
Schroedinger and the interpretation of quantum mechanics
International Nuclear Information System (INIS)
Rohrlich, F.
1987-01-01
On the occasion of the centennial of his birth, Schroedinger's life and views are sketched and his critique of the interpretation of quantum mechanics accepted at his time is examined. His own interpretation, which he had to abandon after a short time, provides a prime example of the way in which the tentative meaning of central theoretical terms in a new and revolutionary theory often fails. Schroedinger's strong philosophical convictions have played a key role in his refusal to break with many of the notions of classical physics. At the same time, they made him into a keen and incisive critic of the Copenhagen interpretation. His criticism is compared with present views on quantum mechanics
Measurement theory and the Schroedinger equation
International Nuclear Information System (INIS)
Schwarz, A.S.; Tyupkin, Yu.S.
1987-01-01
The paper is an analysis of the measuring process in quantum mechanics based on the Schroedinger equation. The arguments employed use an assumption reflecting, to some extent, the statistical properties of the vacuum. A description is given of the cases in which different incoherent superpositions of pure states in quantum mechanics are physically equivalent. The fundamental difference between quantum and classical mechanics as explained by the existence of unobservable variables is discussed. (U.K.)
Exchange effects in Relativistic Schroedinger Theory
International Nuclear Information System (INIS)
Sigg, T.; Sorg, M.
1998-01-01
The Relativistic Schroedinger Theory predicts the occurrence of exchange and overlap effects in many-particle systems. For a 2-particle system, the interaction energy of the two particles consists of two contributions: Coulomb energy and exchange energy, where the first one is revealed to be the same as in standard quantum theory. However the exchange energy is mediated by an exchange potential, contrary to the kinematical origin of the exchange term in the standard theory
The Schroedinger equation and canonical perturbation theory
International Nuclear Information System (INIS)
Graffi, S.; Paul, T.
1987-01-01
Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)
Nonlinear de Broglie waves and the relation between relativistic and nonrelativistic solitons
International Nuclear Information System (INIS)
Barut, A.O.; Baby, B.V.
1988-07-01
It is shown that the well-known envelope soliton and kink solutions of the nonlinear Schroedinger equation are the nonrelativistic limit of the corresponding solutions of the nonlinear Klein-Gordon equation. 34 refs
A life of Erwin Schroedinger. 2. ed.; Erwin Schroedinger. Eine Biographie
Energy Technology Data Exchange (ETDEWEB)
Moore, Walter J.
2015-07-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.
An implicit spectral formula for generalized linear Schroedinger equations
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan
2009-01-01
We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)
Higher-Order Approximation of Cubic-Quintic Duffing Model
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Babazadeh, H.
2011-01-01
We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...
Feynman path integral related to stochastic schroedinger equation
International Nuclear Information System (INIS)
Belavkin, V.P.; Smolyanov, O.G.
1998-01-01
The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru
Solving the Schroedinger equation using Smolyak interpolants
International Nuclear Information System (INIS)
Avila, Gustavo; Carrington, Tucker Jr.
2013-01-01
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased
Dual Schroedinger Equation as Global Optimization Algorithm
International Nuclear Information System (INIS)
Huang Xiaofei; eGain Communications, Mountain View, CA 94043
2011-01-01
The dual Schroedinger equation is defined as replacing the imaginary number i by -1 in the original one. This paper shows that the dual equation shares the same stationary states as the original one. Different from the original one, it explicitly defines a dynamic process for a system to evolve from any state to lower energy states and eventually to the lowest one. Its power as a global optimization algorithm might be used by nature for constructing atoms and molecules. It shall be interesting to verify its existence in nature.
Inversion transformation in the Schroedinger equation
International Nuclear Information System (INIS)
Demkov, Yu.N.; Semenova, N.V.
1984-01-01
Using the inversion with respect to a sphere in the coordinate space, the equivalence between the Schroedinger equations with different potentials is established. It is shown that the zero-energy equation for a spherically symmetric potential is equivalent to the equation with an axially symmetric potential of a special form. The particular exact solutions of the zero-energy problem for the motion of a particle in the field of two Maxwell ''fish-eye'' potentials and potentials with the two Coulomb singularities are found
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Quasi-classical derivation of the Dirac and one-particle Schroedinger equations
International Nuclear Information System (INIS)
Wignall, J.W.G.
1990-08-01
The quasi-classical approach, in which particles are regarded as extended periodic excitations of a classical nonlinear field, is for the first time applied quantitatively in the quantum domain. It is shown that the twofold intrinsic 'spin' degree of freedom possessed by an electron can be interpreted in a purely classical way, and that the Lorentz covariant incorporation of this degree of freedom requires that the spacetime evolution of an electron excitation in a prescribed external field be given by the Dirac equation and hence, in the nonrelativistic limit, by the Pauli or Schroedinger one-particle equations. 17 refs
Energy Technology Data Exchange (ETDEWEB)
Asselmeyer, T.
1997-12-22
First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution.
Nonlinear temporal modulation of pulsar radioemission
International Nuclear Information System (INIS)
Chian, A.C.-L.
1984-01-01
A nonlinear theory is discussed for self-modulation of pulsar radio pulses. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave intensity induced relativistic particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary wave forms may account for the formation of pulsar microstructures. (Author) [pt
On the Schroedinger equation for the minisuperspace models
International Nuclear Information System (INIS)
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
2000-01-01
We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator
Interaction of Schroedinger electrons and photons
International Nuclear Information System (INIS)
Haller, K.; Sohn, R.B.
1979-01-01
The effect of transformations carried out on the Hamiltonian for the Schroedinger electron-photon system is studied. These transformations include gauge transformations and certain similarity and ''hybrid'' transformations. The last named involve unitary transformations of either operators or states, but not both. Unitary and hybrid transformation are discussed, which affect the transverse components of the electromagnetic vector potentials and therefore are distinct from gauge transformations. A hybrid transformation is identified which leads to a form of the Hamiltonian that contains no reference to the transverse vector potential and includes electric and magnetic fields as well as nonlocal interactions of charges and currents. The behavior of the scattering matrix under the influence of these hybrid transformations is discussed. Comments are made on two-photon absorption calculations
Formalism and physical interpretation in Schroedinger
International Nuclear Information System (INIS)
Paty, M.
1992-01-01
The question of the relation between a formalism and its physical interpretation arises not only when theoretical and conceptual systems are reorganized, but in the theoretical elaboration as well. The Schroedinger's work and thought are examined in this paper with this double concern. His work on the mathematical formalism is constantly sustained by a proper physical thought which takes the form of a wave intuition that guarantees him intelligibility. Concerning his interpretation of quantum mechanics, his thought remains characterized, through its evolution, by a w ave image of the world . The way he deals with space-time structure in General Relativity and favours the possibility of a direct interpretation of space-time geometrical quantities, is also studied. (author). 75 refs
Structural invariance of the Schroedinger equation and chronoprojective geometry
International Nuclear Information System (INIS)
Burdet, G.; Perrin, M.
1983-07-01
We describe an extension of the chronoprojective geometry and show how its automorphisms are related to the invariance properties of the Schroedinger equation describing a quantum test particle in any Newton-Cartan structure
Monodromy of the matrix Schroedinger equations and Darboux transformations
Goncharenko, V M
1998-01-01
A Schroedinger operator L=-d sup 2 /dz sup 2 +U(z) with a matrix-valued rational potential U(z) is said to have trivial monodromy if all the solutions of the corresponding Schroedinger equations L psi=lambda psi are single-valued in the complex plane z is an element of C for any lambda. A local criterion of this property in terms of the Laurent coefficients of the potential U near its singularities, which are assumed to be regular, is found. It is proved that any such operator with a potential vanishing at infinity can be obtained by a matrix analogue of the Darboux transformation from the Schroedinger operator L sub o =-d sup 2 /dz sup 2. This generalizes the well known Duistermaat-Gruenbaum result to the matrix case and gives the explicit description of the Schroedinger operators with trivial monodromy in this case. (author)
Schroedinger operators - geometric estimates in terms of the occupation time
International Nuclear Information System (INIS)
Demuth, M.; Kirsch, W.; McGillivray, I.
1995-01-01
The difference of Schroedinger and Dirichlet semigroups is expressed in terms of the Laplace transform of the Brownian motion occupation time. This implies quantitative upper and lower bounds for the operator norms of the corresponding resolvent differences. One spectral theoretical consequence is an estimate for the eigenfunction for a Schroedinger operator in a ball where the potential is given as a cone indicator function. 12 refs
Wigner function and Schroedinger equation in phase-space representation
International Nuclear Information System (INIS)
Chruscinski, Dariusz; Mlodawski, Krzysztof
2005-01-01
We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation
Discrete transparent boundary conditions for Schroedinger-type equations
International Nuclear Information System (INIS)
Schmidt, F.; Yevick, D.
1997-01-01
We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schroedinger-type equations. Our method supplies boundary conditions for the θ-family of implicit one-step discretizations of Schroedinger's equation in time. The use of Mikusinski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. 14 refs., 9 figs
Linearised collective Schroedinger equation for nuclear quadrupole surface vibrations
International Nuclear Information System (INIS)
Greiner, M.; Heumann, D.; Scheid, W.
1990-11-01
The linearisation of the Schroedinger equation for nuclear quadrupole surface vibrations yields a new spin degree of freedom, which is called collective spin and has a value of 3/2. With the introduction of collective spin dependent potentials, this linearised Schroedinger equation is then used for the description of low energy spectra and electromagnetic transition probabilities of some even-odd Xe, Ir and Au nuclei which have a spin 3/2 in their groundstate. (orig.)
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive...
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality...
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Singular continuous spectrum for palindromic Schroedinger operators
International Nuclear Information System (INIS)
Hof, A.; Knill, O.; Simon, B.
1995-01-01
We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)
Spectrum of the ballooning Schroedinger equation
International Nuclear Information System (INIS)
Dewar, R.L.
1997-01-01
The ballooning Schroedinger equation (BSE) is a model equation for investigating global modes that can, when approximated by a Wentzel-Kramers-Brillouin (WKB) ansatz, be described by a ballooning formalism locally to a field line. This second order differential equation with coefficients periodic in the independent variable θ k is assumed to apply even in cases where simple WKB quantization conditions break down, thus providing an alternative to semiclassical quantization. Also, it provides a test bed for developing more advanced WKB methods: e.g. the apparent discontinuity between quantization formulae for open-quotes trappedclose quotes and open-quotes passingclose quotes modes, whose ray paths have different topologies, is removed by extending the WKB method to include the phenomena of tunnelling and reflection. The BSE is applied to instabilities with shear in the real part of the local frequency, so that the dispersion relation is inherently complex. As the frequency shear is increased, it is found that trapped modes go over to passing modes, reducing the maximum growth rate by averaging over θ k
Independent particle Schroedinger Fluid: moments of inertia
International Nuclear Information System (INIS)
Kan, K.K.; Griffin, J.J.
1977-10-01
This philosophy of the Single Particle Schroedinger Fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent Fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment have the rigid value. Counterexamples are utilized to reject some conditions, and the conjecture is argued that Unconstrained Shape Equilibrium might be the necessary and sufficient condition. The spheroidal square well problem is identified as a promising test case
Generalized Born-Infeld actions and projective cubic curves
Energy Technology Data Exchange (ETDEWEB)
Ferrara, S. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati (Italy); Porrati, M. [CCPP, Department of Physics, NYU, 4 Washington Pl., New York, NY, 10003 (United States); Sagnotti, A. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); Stora, R. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); Laboratoire d' Annecy-le-Vieux de Physique Theorique (LAPTH), F-74941, Annecy-le-Vieux, Cedex (France); Yeranyan, A. [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati (Italy); Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89A, 00184, Roma (Italy)
2015-04-01
We investigate U(1){sup n} supersymmetric Born-Infeld Lagrangians with a second non-linearly realized supersymmetry. The resulting non-linear structure is more complex than the square root present in the standard Born-Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
Schroedinger operators with singular perturbation potentials
International Nuclear Information System (INIS)
Harrell, E.M. II.
1976-01-01
This is a perturbative analysis of the eigenvalues and eigenfunctions of Schroedinger operators of the form -Δ + A + lambda V, defined on the Hilbert space L 2 (R/sup n/). A is a potential function (a smooth, real multiplication operator), and V is a ''spikelike'' perturbation, i.e., a perturbative potential function which diverges at some finite point. Lambda is a small real or complex parameter. The emphasis is on one-dimensional problems, and in particular the typical example is the ''spiked harmonic oscillator'' Hamiltonian, -d 2 /dx 2 + x 2 + lambda x/sup -α/, where α is a positive constant. An earlier study by L. Detwiler and J. R. Klauder [Phys. Rev. D 11 (1975) 1436] indicated that the lowest-order corrections to the ground-state eigenvalue of the spiked harmonic oscillator with lambda greater than 0 were proportional to lambda ln lambda when α = 3, and to lambda/sup 1/(α-2) when α is greater than 3. These and analogous results for a large class of operators and arbitrary eigenvalues are proved. Explicit constants in a modified perturbation series with a complicated dependence on lambda are determined and exhibited. Higher-order corrections for real lambda and lowest-order corrections for complex lambda are also discussed. While the substance of the dissertation is mathematical, its main applications are to quantum physics. The immediate cause of interest in such problems was the use of their peculiar convergence properties by J. R. Klauder as models for the behavior of nonrenormalizable quantum field theories. However, the results of this study are likely to be of greater importance in chemical or nuclear physics, as positive spikelike perturbations represent repulsive core interactions for quantum mechanical particles. The modified perturbation series are a new calculation technique for this situation
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
International Nuclear Information System (INIS)
Chierchia, L.
1986-01-01
In the first chapter, the eigenvalue problem for a periodic Schroedinger operator, Lf = (-d 2 /dx 2 + v)f = Ef, is viewed as a two-dimensional Hamiltonian system which is integrable in the sense of Arnold and Liouville. With the aid of the Floquet-BLoch theory, it is shown that such a system is conjugate to two harmonic oscillators with frequencies α and omega, being the rotation number for L and 2π/omega the period of the potential v. This picture is generalized in the second chapter, to quasi periodic Schroedinger operators, L/sub epsilon/, with highly irrational frequencies (omega 1 , ..., omega/sub d/), which are a small perturbation of periodic operators. In the last chapter, the absolutely continuous spectrum σ/sub ac/ of a general quasi-periodic Schroedinger operators is considered. The Radon-Nikodym derivatives (with respect to Lebesgue measure) of the spectral measures are computed in terms of special independent eigensolutions existing for almost ever E in σ/sub ac/. Finally, it is shown that weak Bloch waves always exist for almost ever E in σ/sub ac/ and the question of the existence of genuine Bloch waves is turned into a regularity problem for a certain nonlinear partial differential equation on a d-dimensional torus
Generalized fractional Schroedinger equation with space-time fractional derivatives
International Nuclear Information System (INIS)
Wang Shaowei; Xu Mingyu
2007-01-01
In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum
Dispersive estimates for the Schroedinger and Klein-Gordon equations
Energy Technology Data Exchange (ETDEWEB)
Kopylova, Elena A [Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)
2010-01-01
This is a survey of results on the long-time asymptotic behaviour of solutions of the Schroedinger and Klein-Gordon equations in weighted energy norms. Results obtained from 1975 to 2001 in the spectral scattering theory of Agmon, Jensen-Kato, Jensen-Nenciu, and Murata are described for the Schroedinger equation, along with the author's recent results obtained jointly with A.I. Komech for the Klein-Gordon equation. The methods used develop the spectral approach as applied to relativistic equations. Bibliography: 40 titles.
Nonlinear propagation of the extraordinary mode in a hot magnetoplasma
International Nuclear Information System (INIS)
Khiet, Tu; Furutani, Y.; Ichikawa, Y.H.
1978-07-01
Kinetic theory for a nonlinear propagation of quasi-monochromatic extraordinary waves is presented. It reveals that propagation of an envelope of the extraordinary carriers is described by the nonlinear Schroedinger equation. In a cold plasma limit, a detailed analysis is carried out on a behaviour of the envelope of the upper- and the lower-hybrid waves at respective resonant frequency ranges. (author)
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
International Nuclear Information System (INIS)
Bai Yongqiang; Wu Ke; Zhao Weizhong; Guo Hanying
2007-01-01
Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schroedinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
Nonlinear scalar field equations. Pt. 1
International Nuclear Information System (INIS)
Berestycki, H.; Lions, P.L.
1983-01-01
This paper as well as a subsequent one is concerned with the existence of nontrivial solutions for some semi-linear elliptic equations in Rsup(N). Such problems are motivated in particular by the search for certain kinds of solitary waves (stationary states) in nonlinear equations of the Klein-Gordon or Schroedinger type. (orig./HSI)
Nonlinear modulation of ionization waves
International Nuclear Information System (INIS)
Bekki, Naoaki
1981-01-01
In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
The number of bound states for a discrete Schroedinger operator on ZN, N≥1, lattices
International Nuclear Information System (INIS)
Karachalios, N I
2008-01-01
We consider the discrete Schroedinger operator -Δ d +U in Z N , N≥1 in the case of a potential with negative part in an appropriate l σ -space (decays with an appropriate rate). We present a discrete analog of the method of Li and Yau (1983 Commun. Math. Phys. 88 309-18), proving an explicit upper estimate on the number of bound states N d (0)={j:μ j ≤0}, which is independent of the dimension of the lattice. This is a major difference with the continuous counterpart estimate, which is not valid when N = 1, 2. As a consequence, a dimension-independent smallness criterion for the existence of bound states is derived in contrast to the continuous case as well as to the discrete case of vanishing potential. A short comment is made on possible applications of the results to the study of the dynamics of some particular spatially discrete nonlinear systems
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Numerical Clifford Analysis for the Non-stationary Schroedinger Equation
International Nuclear Information System (INIS)
Faustino, N.; Vieira, N.
2007-01-01
We construct a discrete fundamental solution for the parabolic Dirac operator which factorizes the non-stationary Schroedinger operator. With such fundamental solution we construct a discrete counterpart for the Teodorescu and Cauchy-Bitsadze operators and the Bergman projectors. We finalize this paper with convergence results regarding the operators and a concrete numerical example
Studying the gradient flow coupling in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Fritzsch, P. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-08-15
We discuss the setup and features of a new definition of the running coupling in the Schroedinger functional scheme based on the gradient flow. Its suitability for a precise continuum limit in QCD is demonstrated on a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm.
Chronoprojective invariance of the five-dimensional Schroedinger formalism
International Nuclear Information System (INIS)
Perrin, M.; Burdet, G.; Duval, C.
1984-10-01
Invariance properties of the five-dimensional Schroedinger formalism describing a quantum test particle in the Newton-Cartan theory of gravitation are studied. The geometry which underlies these invariance properties is presented as a reduction of the 0(5,2) conformal geometry various applications are given
New method for solving three-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Melezhik, V.S.
1990-01-01
The method derived recently for solving a multidimensional scattering problem is applied to a three-dimensional Schroedinger equation. As compared with direct three-dimensional calculations of finite elements and finite differences, this approach gives sufficiently accurate upper and lower approximations to the helium-atom binding energy, which demonstrates its efficiency. 15 refs.; 1 fig.; 2 tabs
Consequences of the Schroedinger equation for atomic and molecular physics
International Nuclear Information System (INIS)
Thirring, W.E.
1986-01-01
The non-relativistic Schroedinger equation for a system of nuclei and electrons is considered and general properties of Hamiltonian H are treated and commented: self-adjontness of H, the spectrum of H, the discrete spectrum, the continuous spectrum, the limit of infinite nuclear mass, the limit of infinite nuclear charge. (G.Q.)
Remarks on the Schroedinger operator with singular complex potentials
International Nuclear Information System (INIS)
Brezis, Haim; Kato, Tosio
1979-01-01
To describe this method in a simple case Section 2 begin with real valued potentials. The main results in Section 2 are essentially known. In Section 3 the case of complex potentials is exposed. Schroedinger operators with complex potentials have been studied by Nelson. This results were extended. Here more general singularities are exposed
Asymptotic Value Distribution for Solutions of the Schroedinger Equation
International Nuclear Information System (INIS)
Breimesser, S. V.; Pearson, D. B.
2000-01-01
We consider the Dirichlet Schroedinger operator T=-(d 2 /d x 2 )+V, acting in L 2 (0,∞), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,λ) of the equation Tf(x,λ)=λf(x,λ), for λ in the support of the absolutely continuous part μ a.c. of the spectral measure μ, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,λ)/v(N,λ) approaches the associated value distribution of the Herglotz function m N (z) in the limit N → ∞, where m N (z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d 2 /d x 2 )+Vacting in L 2 (N,∞), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space
Erwin Schroedinger, Philosophy and the birth of quantum mechanics
International Nuclear Information System (INIS)
Bitbol, M.; Darrigol, O.
1992-01-01
The purpose of this collection of articles is to highlight the relation between Schroedinger's less well known research and his thoughts on quantum mechanics: philosophy, statistical mechanics, general relativity, cosmology, unified field theories, etc. Some articles are devoted to contemporary extensions of his work, and in particular on current echoes of his interpretation of quantum mechanics
Interpolation of natural cubic spline
Directory of Open Access Journals (Sweden)
Arun Kumar
1992-01-01
Full Text Available From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.
Erwin Schroedinger: Collected papers V. 1. Contributions to statistical mechanics
International Nuclear Information System (INIS)
Schroedinger, E.
1984-01-01
38 publications reprinted in this volume show that the interest for statistical problems accompanied Schroedinger during his entire scientific career. Already in his second paper he worked on the magnetism of solid states. The classical considerations come close to the heart of diamagnetism and also to the origin of paramagnetism. In classical investigations of the specific heat Schroedinger helped through abstract theory but also by analysing a gigantic amount of experimental material. In 1926 he and F. Kohlrausch actually played the 'Urngame of Ehrenfest' as a model of the H-curve and published the results. Inclination towards experimenting, sequences of measurements and statistical evaluation of experimental data led to papers on the foundation of the theory of probability, where he tries to put the subjective probability concept on into a systematic framework. Two earlier papers on dynamics of the elastic chain remained particularly valuable. By solving the initial value problem with Bessel-functions this many-body-problem is led to an explicit discussion. These studies are likely to be the roots of another keynote in Schroedinger's thinking, namely, the irreversibility. 1945 a statistical theory of chain-reactions was published under the inconspicuous title of 'Probability Problems in Nuclear Chemistry'. In his last work Schroedinger turns off in a wrong direction: it is that energy should only be a statistical concept and should not be conserved in elementary processes, but somehow only in the mean. These short remarks only illuminate the diversity of the material in this volume, but testify Schroedinger's deep understanding in this field. (W.K.)
Averaging for solitons with nonlinearity management
International Nuclear Information System (INIS)
Pelinovsky, D.E.; Kevrekidis, P.G.; Frantzeskakis, D.J.
2003-01-01
We develop an averaging method for solitons of the nonlinear Schroedinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations
Classical Mechanics as Nonlinear Quantum Mechanics
International Nuclear Information System (INIS)
Nikolic, Hrvoje
2007-01-01
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
Solution of the Schroedinger equation by a spectral method
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.
1982-01-01
A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential
New method for solving three-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Melezhik, V.S.
1992-01-01
A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)
Schroedinger operators with point interactions and short range expansions
International Nuclear Information System (INIS)
Albeverio, S.; Hoeegh-Krohn, R.; Oslo Univ.
1984-01-01
We give a survey of recent results concerning Schroedinger operators with point interactions in R 3 . In the case where the point interactions are located at a discrete set of points we discuss results about the resolvent, the spectrum, the resonances and the scattering quantities. We also discuss the approximation of point interactions by short range local potentials (short range or low energy expansions) and the one electron model of a 3-dimensional crystal. Moreover we discuss Schroedinger operators with Coulomb plus point interactions, with applications to the determination of scattering lengths and of level shifts in mesic atoms. Further applications to the multiple well problem, to multiparticle systems, to crystals with random impurities, to polymers and quantum fields are also briefly discussed. (orig.)
The Schroedinger-Newton equation as model of self-gravitating quantum systems
International Nuclear Information System (INIS)
Grossardt, Andre
2013-01-01
The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem
Nonlinear wave beams in a piezo semiconducting layer
International Nuclear Information System (INIS)
Bagdoev, A.G.; Shekoyan, A.V.; Danoyan, Z.N.
1997-01-01
The propagation of quasi-monochromatic nonlinear wave in a piezo semiconducting layer taking into account electron-concentration nonlinearity is considered. For such medium the evolution equations for incoming and reflected waves are derived. Nonlinear Schroedinger equations and solutions for narrow beams are obtained. It is shown that symmetry of incoming and reflected waves does not take place. The focusing of beams is investigated.18 refs
The Schroedinger equation as a singular perturbation problem
International Nuclear Information System (INIS)
Jager, E.M. de; Kuepper, T.
1978-01-01
Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)
Schroedinger propagation of initial discontinuities leads to divergence of moments
International Nuclear Information System (INIS)
Marchewka, A.; Schuss, Z.
2009-01-01
We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.
Schroedinger propagation of initial discontinuities leads to divergence of moments
Energy Technology Data Exchange (ETDEWEB)
Marchewka, A., E-mail: avi.marchewka@gmail.co [Ruppin Academic Center, Emek-Hefer 40250 (Israel); Schuss, Z., E-mail: schuss@post.tau.ac.i [Department of Mathematics, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv (Israel)
2009-09-21
We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.
The Schroedinger's paradox and the tranformation of quantum systems
International Nuclear Information System (INIS)
Bitsakis, E.I.
1980-01-01
The Schroedinger's paradox is analysed, as an illustration of certain weaknesses of the Copenhagen's interpretation of quantum mechanics and of the limits of the quantum-mechanical description of phenomena. A realistic approach of the paradox indicates the necessity of a theory that would permit not only the calculation of probabilities, but also the description of physical processes, as taking place in space and time
Integrability in the theory of Schroedinger operator and harmonic analysis
International Nuclear Information System (INIS)
Chalykh, O.A.; Veselov, A.P.
1993-01-01
The algebraic integrability for the Schroedinger equation in R n and the role of the quantum Calogero-Sutherland problem and root systems in this context are discussed. For the special values of the parameters in the potential the explicit formula for the eigenfunction of the corresponding Sutherland operator is found. As an application the explicit formula for the zonal spherical functions on the symmetric spaces SU 2 * n /Sp n (type A II in Cartan notations) is presented. (orig.)
Improved Rosen's conditions on bound states of Schroedinger operators
International Nuclear Information System (INIS)
Exner, P.
1984-01-01
We derive a necessary condition on a Schroedinger operator H=-Δ+V on Lsup(2)(Rsup(d)), d>=3 to have a bound state below a given energy epsilon, and a lower bound to the ground-state energy of H. These conditions are expressed in terms of the potential V alone, and generalize the recent results of Rosen to the dimensions d>3 and to the potentials that are not necessarily rapidly decreasing. Some examples are given
Quantum field theory in flat Robertson-Walker space-time functional Schroedinger picture
International Nuclear Information System (INIS)
Pi, S.Y.
1989-01-01
Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schroedinger picture provides a useful description. We discuss free and self-interacting bosonic quantum field theories: Schroedinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schroedinger picture. The techniques introduced can be used to study various dynamical questions in early universe processes. (author)
International Nuclear Information System (INIS)
Mehra, J.
1987-01-01
This paper, the first part of a three-part article, gives an account of Erwin Schroedinger's growing up and studies in Vienna, his scientific work--first in Vienna from 1911 to 1920, then in Zurich from 1920 to 1925--on the dielectric properties of matter, atmospheric electricity and radioactivity, general relativity, color theory and physiological optics, and on kinetic theory and statistical mechanics
Exact bright and dark spatial soliton solutions in saturable nonlinear media
International Nuclear Information System (INIS)
Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.
2009-01-01
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
Nonlinear wave mechanics from classical dynamics and scale covariance
International Nuclear Information System (INIS)
Hammad, F.
2007-01-01
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Bistable Helmholtz solitons in cubic-quintic materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-01-01
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations
Modulated Langmuir waves and nonlinear Landau damping
International Nuclear Information System (INIS)
Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.
1975-01-01
The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)
An introduction to the self-adjointness and spectral analysis of Schroedinger operators
International Nuclear Information System (INIS)
Simon, B.
1977-01-01
The author first explains the basic results about self adjointness, from a point of view which emphasizes the connection with solvability of the Schroedinger equation. He then describes four methods that define self ajoint Hamiltonians, for most Schroedinger operators and discusses types of spectra, closing by considering the essential spectrum in the two body case. (P.D.)
The frictional Schroedinger-Newton equation in models of wave function collapse
Energy Technology Data Exchange (ETDEWEB)
Diosi, Lajos [Research Institute for Particle and Nuclear Physics, H-1525 Budapest 114, PO Box 49 (Hungary)
2007-05-15
Replacing the Newtonian coupling G by -iG, the Schroedinger--Newton equation becomes {sup f}rictional{sup .} Instead of the reversible Schroedinger-Newton equation, we advocate its frictional version to generate the set of pointer states for macroscopic quantum bodies.
On the solution of the Schroedinger equation through continued fractions
International Nuclear Information System (INIS)
Mignaco, J.A.
1979-05-01
The domain of interest for the applications of a method to solve the Schroedinger equation through continued fractions is studied. It is argued that the method applies almost equally well to quantum mechanical regimes (lower energy levels, low energy scattering) as well as to semiclassical ones simultaneously; this is illustrated by the example of the central power law potentials r sup(ν)(ν>o). The explanation of this behaviour is given in terms of the mathematical approximations involved and its relationship to physically interesting quantities. (Author) [pt
Schroedinger operators with Rudin-Shapiro potentials are not palindromic
International Nuclear Information System (INIS)
Allouche, J.
1997-01-01
We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. 174, 149 endash 159 (1995)] by showing that the Rudin-Shapiro sequence is not palindromic, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. copyright 1997 American Institute of Physics
Numerical solution of the Schroedinger equation with a polynomial potential
International Nuclear Information System (INIS)
Campoy, G.; Palma, A.
1986-01-01
A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables
Perturbative approach to non-Markovian stochastic Schroedinger equations
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)
The gradient flow coupling in the Schroedinger functional
International Nuclear Information System (INIS)
Fritzsch, Patrick; Ramos, Alberto
2013-01-01
We study the perturbative behavior of the Yang-Mills gradient flow in the Schroedinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N f =2 gauge field ensembles in a physical volume of L∝0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.
A new method for the solution of the Schroedinger equation
International Nuclear Information System (INIS)
Amore, Paolo; Aranda, Alfredo; De Pace, Arturo
2004-01-01
We present a new method for the solution of the Schroedinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings
Localization for random Schroedinger operators with correlated potentials
Energy Technology Data Exchange (ETDEWEB)
Von Dreifus, H [Princeton Univ., NJ (USA). Dept. of Physics; Klein, A [California Univ., Irvine (USA). Dept. of Mathematics
1991-08-01
We prove localization at high disorder or low energy for lattice Schroedinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance function C(x,y) decays as vertical strokex-yvertical stroke{sup -{theta}}, where {theta}>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate. (orig.).
Schroedinger invariant solutions of type IIB with enhanced supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences
2009-07-15
We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schroedinger algebra. The solutions depend on a five-dimensional Sasaki- Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve. (orig.)
Numerical stochastic perturbation theory in the Schroedinger functional
International Nuclear Information System (INIS)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron
2013-11-01
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Philosophical and methodological aspects of the Schroedinger paradox
International Nuclear Information System (INIS)
Juha, L.; Krajca, R.; Smatera, M.
1989-01-01
Methodological aspects of the foundations of quantum theory are dealt with in relation to the quantum description of macroscopic systems, biological in particular. Attention is paid to the philosophical content of the problems of 1) the logical status of the reduction postulate in quantum mechanics, and 2) the paradox of Schroedinger's cat, whose physical solution has not yet been attained. The problem of the quantum description of complex macroscopic systems is also treated, as is Herbert Froehlich's important concept of the excitation of dominant modes in biological systems. (author). 61 refs
Equivalence of two alternative approaches to Schroedinger equations
International Nuclear Information System (INIS)
Goenuel, B; Koeksal, K
2006-01-01
A recently developed simple approach for the exact/approximate solution of Schroedinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one leading to the construction of exactly solvable potentials via the solution of second-order differential equations in terms of known special functions. The formalism in the former solves difficulties encountered in the latter in revealing the corrections explicitly to the unperturbed piece of the solutions whereas the other obviates cumbersome procedures used in the calculations of the former
Numerical stochastic perturbation theory in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-11-15
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Quantum gravitational corrections to the functional Schroedinger equation
International Nuclear Information System (INIS)
Kiefer, C.; Singh, T.P.
1990-10-01
We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs
Energy Technology Data Exchange (ETDEWEB)
Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)
2016-07-01
The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.
2015-05-07
associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving
Chern--Simons theory in the Schroedinger representation
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1989-01-01
We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles---a calculation which is especially simple in the functional Schroedinger representation. copyright 1989 Academic Press, Inc
Inverse Schroedinger equation and the exact wave function
International Nuclear Information System (INIS)
Nakatsuji, Hiroshi
2002-01-01
Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem
On the Schroedinger representation of the Euclidean quantum field theory
International Nuclear Information System (INIS)
Semmler, U.
1987-04-01
The theme of the present thesis is the Schroedinger representation of the Euclidean quantum field theory: We define the time development of the quantum field states as functional integral in a novel, mathematically precise way. In the following we discuss the consequences which result from this approach to the Euclidean quantum field theory. Chapter 1 introduces the theory of abstract Wiener spaces which is here proved as suitable mathematical tool for the treatment of the physical problems. In chapter 2 the diffusion theory is formulated in the framework of abstract Wiener spaces. In chapter 3 we define the field functional ψ 5 u, t 7 as functional integral, determine the functional differential equation which ψ satisfies (Schroedinger equation), and summarize the consequences resulting from this. Chapter 4 is dedicated to the attempt to determine the kernel of the time-development operator, by the knowledge of which the time development of each initial state is fixed. In chapter 5 the consequences of the theory presented in chapter 3 and 4 are discussed by means of simple examples. In chapter 6 the renormalization which results for the φ 4 potential from the definition of the functional integral in chapter 3 is calculated up to the first-order perturbation theory, and it is shown that the problems in the Symanzik renormalization procedure can be removed. (orig./HSI) [de
Directory of Open Access Journals (Sweden)
Gary R. Nicklason
2015-07-01
Full Text Available We consider center conditions for plane polynomial systems of Abel type consisting of a linear center perturbed by the sum of 2 homogeneous polynomials of degrees n and 2n-1 where $n \\ge 2$. Using properties of Abel equations we obtain two general systems valid for arbitrary values on n. For the cubic n=2 systems we find several sets of new center conditions, some of which show that the results in a paper by Hill, Lloyd and Pearson which were conjectured to be complete are in fact not complete. We also present a particular system which appears to be a counterexample to a conjecture by Zoladek et al. regarding rational reversibility in cubic polynomial systems.
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
Randomized Block Cubic Newton Method
Doikov, Nikita; Richtarik, Peter
2018-01-01
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\cal O}(1/\\epsilon)$, ${\\cal O}(1/\\sqrt{\\epsilon})$ and ${\\cal O}(\\log (1/\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
Randomized Block Cubic Newton Method
Doikov, Nikita
2018-02-12
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\\\cal O}(1/\\\\epsilon)$, ${\\\\cal O}(1/\\\\sqrt{\\\\epsilon})$ and ${\\\\cal O}(\\\\log (1/\\\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
Bound State Eigenvalues of the Schroedinger Eq. in two Spatial Variables.
Rawitscher, George H.; Koltracht, Israel
2002-08-01
An efficient spectral integral equation method (SIEM) has recently been developed for obtaining the scattering solution of a one-dimensional Schroedinger equation.(R.A. Gonzales, S.-Y. Kang, I. Koltracht and G. Rawitscher, J. of Comput. Phys. 153, 160 (1999).) The purpose of the present study is to extend this method to the case of bound-states in more than one dimension. Even though other methods have already been developed for this case, such as finite element methods, the application we have in mind is to solve the non-linear Bose-Einstein condensate case in the presence of an optical lattice. In the presence of a trapping potential alone, a B-E condensate solution has been obtained by a new iterative spectral method which solves the differential equation.(Y.-S. Choi, J. Javanainen, I. Koltracht, M. Koš)trun, P.J. McKenna and N. Savytska "A Fast Algorithm for the Solution of the Time-Independent Gross-Pitaevskii Equation," Submitted to Computational Physics. But this method becomes inadequate for the case that several potential barriers are also present. The reason that the SIEM is expected to be better suited is that it distributes the collocation points much more efficiently into partitions of variable size.
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
A global numerical solution of the radial Schroedinger equation by second-order perturbation theory
International Nuclear Information System (INIS)
Adam, G.
1979-01-01
A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)
Cubic metaplectic forms and theta functions
Proskurin, Nikolai
1998-01-01
The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Cathodoluminescence of cubic boron nitride
International Nuclear Information System (INIS)
Tkachev, V.D.; Shipilo, V.B.; Zajtsev, A.M.
1985-01-01
Three optically active defects are detected in mono- and polycrystal cubic boron nitride (β-BN). Analysis of intensity of temperature dependences, halfwidth and energy shift of 1.76 eV narrow phononless line (center GC-1) makes it possible to interprete the observed cathodoluminescence spectra an optical analog of the Moessbaner effect. Comparison of the obtained results with the known data for diamond monocrystals makes it possible to suggest that the detected center GC-1 is a nitrogen vacancy . The conclusion, concerning the Moessbauer optical spectra application, is made to analyze structural perfection of β-BN crystal lattice
Soliton-like solutions to the ordinary Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria
2011-07-01
In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)
Fractional integration, Morrey spaces and a Schroedinger equation
International Nuclear Information System (INIS)
Olsen, P.A.
1995-01-01
Let V : R 3 → R be the potential for the 3-dimensional Schroedinger operator -Δ + V. It was shown by Cwikel, Lieb and Rosenblum, [8], that the number of bound states, N(V), of -Δ + V is bounded by N(V) ≤ C ∫ R3 |V(x)| 3/2 dx. Later Fefferman and phong, [4], improved on this inequality. Make a dyadic decomposition of R 3 into cubes. Define a dyadic cube Q to be minimal with respect to ε > 0 if ∫ q |V(x)| p dx ≥ ε p |Q| 1-2p/3 and ∫ Q ' |V(x)| p dx p |Q'| 1-2p/3 for all dyadic cubes Q' contained-in Q. 10 refs., 4 figs., 1 tab
The Schroedinger and Dirac free particle equations without quantum mechanics
International Nuclear Information System (INIS)
Ord, G.N.
1996-01-01
Einstein close-quote s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schroedinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. copyright 1996 Academic Press, Inc
Lower bounds for solutions of the Schroedinger equation
International Nuclear Information System (INIS)
Froese, R.G.
1983-01-01
For a large class of generalized N-body Hamiltonians H = -Δ + V the large absolute value x behavior of solutions to the Schroedinger equation H psi = H psi is studied. If E lies below the essential spectrum of H, then it is proved that lim R -1 log (absolute value psi/sub R/) = -α 0 R → infinity where absolute value psi/sub R/ 2 is the integral of absolute value psi 2 over a sphere of radius R and α 0 2 + E is a threshold or α 0 0. For E not necessarily below the essential spectrum of H, the same equation holds with absolute value psi/sub R/ 2 replaced by an integral of absolute value psi 2 over a spherical shell
Soliton-like solutions to the ordinary Schroedinger equation
International Nuclear Information System (INIS)
Zamboni-Rached, Michel; Recami, Erasmo
2011-01-01
In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)
Limited-diffraction solutions to Maxwell and Schroedinger equations
International Nuclear Information System (INIS)
Lu, Jian-yu; Greenleaf, J.F.
1996-10-01
The authors have developed a new family of limited diffraction electromagnetic X-shaped waves based on the scalar X-shaped waves discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain their shape as they propagate to an infinite distance. The 'X waves' possess (theoretically) infinitely extended 'arms' and - at least, the ones studied in this paper - have an infinite total energy: therefore, they are not physically realizable. However, they can be truncated in both space and time and 'approximated' by means of a finite aperture radiator so to get a large enough depth of interest (depth of field). In addition to the Maxwell equations, X wave solutions to the free Schroedinger equation are also obtained. Possible applications of these new waves are discussed. Finally, the authors discuss the appearance of the X-shaped solutions from the purely geometric point of view of the special relativity theory
The gradient flow coupling in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, Alberto [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-01-15
We study the perturbative behavior of the Yang-Mills gradient flow in the Schroedinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.
Extensions of the auxiliary field method to solve Schroedinger equations
International Nuclear Information System (INIS)
Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien
2008-01-01
It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed
Extensions of the auxiliary field method to solve Schroedinger equations
Energy Technology Data Exchange (ETDEWEB)
Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be
2008-10-24
It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.
Bound states for non-symmetric evolution Schroedinger potentials
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana-Azcapotalco, Atzcapotzalco, DF (Mexico)). E-mail: ccg@correo.azc.uam.mx
2001-09-14
We consider the spectral problem associated with the evolution Schroedinger equation, (D{sup 2}+ k{sup 2}){phi}=u{phi}, where u is a matrix-square-valued function, with entries in the Schwartz class defined on the real line. The solution {phi}, called the wavefunction, consists of a function of one real variable, matrix-square-valued with entries in the Schwartz class. This problem has been dealt for symmetric potentials u. We found for the present case that the bound states are localized similarly to the scalar and symmetric cases, but by the zeroes of an analytic matrix-valued function. If we add an extra condition to the potential u, we can determine these states by an analytic scalar function. We do this by generalizing the scalar and symmetric cases but without using the fact that the Wronskian of a pair of wavefunction is constant. (author)
Global spacetime symmetries in the functional Schroedinger picture
International Nuclear Information System (INIS)
Halliwell, J.J.
1991-01-01
In the conventional functional Schroedinger quantization of field theory, the background spacetime manifold is foliated into a set of three-surfaces and the quantum state of the field is represented by a wave functional of the field configurations on each three-surface. Although this procedure may be covariantly described, the wave functionals generally fail to carry a representation of the complete spacetime symmetry group of the background, such as the Poincare group in Minkowski spacetime, because spacetime symmetries generally involve distortions or motions of the three-surfaces themselves within that spacetime. In this paper, we show that global spacetime symmetries in the functional Schroedinger picture may be represented by parametrizing the field theory---raising to the status of dynamical variables the embedding variables describing the spacetime location of each three-surface. In particular, we show that the embedding variables provide a connection between the purely geometrical operation of an isometry group on the spacetime and the operation of the usual global symmetry generators (constructed from the energy-momentum tensor) on the wave functionals of the theory. We study the path-integral representation of the wave functionals of the parametrized field theory. We show how to construct, from the path integral, wave functionals that are annihilated by the global symmetry generators, i.e., that are invariant under global spacetime symmetry groups. The invariance of the class of histories summed over in the path integral is identified as the source of the invariance of the wave functionals. We apply this understanding to a study of vacuum states in the de Sitter spacetime. We make mathematically precise a previously given heuristic argument for the de Sitter invariance of the matter wave functionals defined by the no-boundary proposal of Hartle and Hawking
Derivation of the Schroedinger equation from stochastic mechanics
International Nuclear Information System (INIS)
Wallstrom, T.C.
1988-01-01
The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schroedinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time-integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p t (x,y) > cp(y), and this result is applied to show that the set of spin-1/2 diffusions is uniformly ergodic. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp-Haag-Dankel diffusions onto IR 3 converge to a Markovian limit process. This conjecture is proved for the spin-1/2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schroedinger equation
The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests
International Nuclear Information System (INIS)
Dalla Brida, Mattia
2016-03-01
The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.
The Schroedinger functional for Gross-Neveu models
International Nuclear Information System (INIS)
Leder, B.
2007-01-01
Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing betafunction. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed. (orig.)
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
in contrast to a recently found azimuthal instability of spinning doughnut-shaped solitons in the CQ NLS equation, their GL counterparts may be completely stable. On the other hand, a problem of fundamental interest is the possibility of the formation of fully three-dimensional (3D) optical spatiotemporal solitons, also referred ...
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
On symmetry reduction and exact solutions of the linear one-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Barannik, L.L.
1996-01-01
Symmetry reduction of the Schroedinger equation with potential is carried out on subalgebras of the Lie algebra which is the direct sum of the special Galilei algebra and one-dimensional algebra. Some new exact solutions are obtained
New trace formulae for a quadratic pencil of the Schroedinger operator
International Nuclear Information System (INIS)
Yang Chuanfu
2010-01-01
This work deals with the eigenvalue problem for a quadratic pencil of the Schroedinger operator on a finite closed interval with the two-point boundary conditions. We will obtain new regularized trace formulas for this class of differential pencil.
Wave-packet revival for the Schroedinger equation with position-dependent mass
International Nuclear Information System (INIS)
Schmidt, Alexandre G.M.
2006-01-01
We study the temporal evolution of solutions of 1D Schroedinger equation with position-dependent mass inside an infinite well. Revival of wave-packet is shown to exist and partial revivals are different from the usual ones
Localization for off-diagonal disorder and for continuous Schroedinger operators
International Nuclear Information System (INIS)
Delyon, F.; Souillard, B.; Simon, B.
1987-01-01
We extend the proof of localization by Delyon, Levy, and Souillard to accommodate the Anderson model with off-diagonal disorder and the continuous Schroedinger equation with a random potential. (orig.)
International Nuclear Information System (INIS)
Killingbeck, J.
1979-01-01
By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)
Finiteness of the discrete spectrum of the three-particle Schroedinger operator
International Nuclear Information System (INIS)
Abdullaev, Janikul I.; Khalkhujaev, Axmad, M.
2001-08-01
We analyse the spectrum of the three-particle Schroedinger operator with pair contact and three-particle interactions on the neighboring nodes on a three-dimensional lattice. We show that the essential spectrum of this operator is the union of two segments, one of which coincides with the spectrum of an unperturbed operator and the other called two-particle branch. We will prove finiteness of the discrete spectrum of the Schroedinger operator at all parameter values of the problem. (author)
Cathodoluminescence of cubic boron nitride
International Nuclear Information System (INIS)
Tkachev, V.D.; Shipilo, V.B.; Zaitsev, A.M.
1985-01-01
Three types of optically active defect were observed in single-crystal and polycrystalline cubic boron nitride (β-BN). An analysis of the temperature dependences of the intensity, half-width, and energy shift of a narrow zero-phonon line at 1.76 eV (GC-1 center) made it possible to interpret the observed cathodoluminescence spectra as an optical analog of the Moessbauer effect. A comparison of the results obtained in the present study with the available data on diamond single crystals made it possible to identify the observed GC-1 center as a nitrogen vacancy. It was concluded that optical Moessbauer-type spectra can be used to analyze structure defects in the crystal lattice of β-BN
Martensitic cubic → tetragonal transition
International Nuclear Information System (INIS)
Schumann, H.
1983-01-01
Indium-thallium alloys containing 14 to 30% At. Tl have a cubic face-centred beta phase wich changes into a tetragonal face-centred alpha martensite during solidification. The martensite contains twin crystals that are large enough to be seen by means of a light microscope. The phenomenological crystallographic martensite theory was used to calculate Miller's index of the habit plane, the formation of the surface relief, the orientation relations and the critical thickness ratio of the twins. In a beta monocrystal frequently only one of the 24 crystallographic possible habit planes are formed at one end of the sample and migrate through the whole crystal when the temperature drops. Externally applied tension and compression influence in different ways the direction in which the habit plane moves and can even destroy the twinned structure, i.e. they can modify the substructure of the martensite crystal. This induces superelasticity, an effect that has also been described quantitatively. (author)
Nonlinearity without superluminality
International Nuclear Information System (INIS)
Kent, Adrian
2005-01-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality
Scattering of quantized solitary waves in the cubic Schrodinger equation
International Nuclear Information System (INIS)
Dolan, L.
1976-01-01
The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
Gaku Hoshino
2016-01-01
Full Text Available We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.
Cubical local partial orders on cubically subdivided spaces - existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such ...... that the underlying geometry of an HDA may be quite complicated....
Cubical local partial orders on cubically subdivided spaces - Existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2006-01-01
The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...... that the underlying geometry of an HDA may be quite complicated....
Is there a relativistic nonlinear generalization of quantum mechanics?
Energy Technology Data Exchange (ETDEWEB)
Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)
2007-05-15
Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.
Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation
2014-12-01
iΩrotuθ, (2.1) where (·)t = d(·)/dt and (·)θ = d(·)/dθ and (r, θ) are the polar coordinates. Here the potential is assumed as representing a parabolic ... inclusion of dissipation in a Hamiltonian model leads modes of different energy (Krein signature) to move differently, due to their distinct topological...captures the initial stages of the dynamical evolution and the eventual asymptotic behavior may well be different. This can be due to symmetry
Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Infeld, E.
1981-01-01
By limiting attention to the lowest-order Fourier modes we obtain a theory of the Fermi-Pasta-Ulam recurrence that gives excellent agreement with recent numerical results. Both the predicted period of the recurrence and the temporal development of the n = 0 mode are very good fits. The maximum of the n = 1 mode, however, is off by about 30%
On the chirally rotated Schroedinger functional with Wilson fermions
International Nuclear Information System (INIS)
Gonzalez Lopez, Jenifer
2011-01-01
There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional (χSF). We first perform analytical studies of the χSF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed χSF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the χSF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the χSF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the χSF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior of physical
On the chirally rotated Schroedinger functional with Wilson fermions
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Lopez, Jenifer
2011-05-25
There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional ({chi}SF). We first perform analytical studies of the {chi}SF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed {chi}SF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the {chi}SF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the {chi}SF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the {chi}SF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior
Cubical sets as a classifying topos
DEFF Research Database (Denmark)
Spitters, Bas
Coquand’s cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. We show that the underlying cube category is the opposite of the Lawvere theory of De...... Morgan algebras. The topos of cubical sets itself classifies the theory of ‘free De Morgan algebras’. This provides us with a topos with an internal ‘interval’. Using this interval we construct a model of type theory following van den Berg and Garner. We are currently investigating the precise relation...
Generalized Vaidya spacetime for cubic gravity
Ruan, Shan-Ming
2016-03-01
We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.
International Nuclear Information System (INIS)
Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.
2000-01-01
For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)
International Nuclear Information System (INIS)
Dobrev, V. K.; Stoimenov, S.
2010-01-01
The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.
Cubic Pencils and Painlev\\'e Hamiltonians
Kajiwara, Kenji; Masuda, Tetsu; Noumi, Masatoshi; Ohta, Yasuhiro; Yamada, Yasuhiko
2004-01-01
We present a simple heuristic method to derive the Painlev\\'e differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.
Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation
International Nuclear Information System (INIS)
Raptis, A.D.; Cash, J.R.
1987-01-01
A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)
Estimate of the difference between the Kac operator and the Schroedinger semigroup
International Nuclear Information System (INIS)
Ichinose, T.; Satoshi, S.
1997-01-01
An operator norm estimate of the difference between the Kac operator and the Schroedinger semigroup is proved and used to give a variant of the Trotter product formula for Schroedinger operators in the L p operator norm. This extends Helffer's result in the L 2 operator norm to the case in the L p operator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman-Kac a nd Feynman-Kac-Ito formula. (orig.)
International Nuclear Information System (INIS)
Ding Zhonghai; Chen, Goong; Lin, Chang-Shou
2010-01-01
The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.
Energy Technology Data Exchange (ETDEWEB)
Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be
2009-06-19
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -{alpha}r{sup {lambda}}exp(-{beta}r) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential.
International Nuclear Information System (INIS)
Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien
2009-01-01
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -αr λ exp(-βr) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential
International Nuclear Information System (INIS)
Barut, A.O.
1990-06-01
For an arbitrary potential V with classical trajectories x-vector=g-vector(t) we construct localized oscillating three-dimensional wave lumps ψ(x-vector,t,g-vector) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbit g-vector(t) slightly modified due to potential V and ψ(x-vector,t;g-vector) satisfies the Schroedinger equation. The field energy, momentum and angular momentum calculated as integrals over all space are equal to particle energy, momentum and angular momentum. The relation to coherent states and to Schroedinger waves are also discussed. (author). 6 refs
Solving the Schroedinger equation using the finite difference time domain method
International Nuclear Information System (INIS)
Sudiarta, I Wayan; Geldart, D J Wallace
2007-01-01
In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems
International Nuclear Information System (INIS)
Chithiika Ruby, V.; Senthilvelan, M.
2010-01-01
In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schroedinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schroedinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.
A Note on Cubic Convolution Interpolation
Meijering, E.; Unser, M.
2003-01-01
We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.
Cubical version of combinatorial differential forms
DEFF Research Database (Denmark)
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
On the structure of critical energy levels for the cubic focusing NLS on star graphs
International Nuclear Information System (INIS)
Adami, Riccardo; Noja, Diego; Cacciapuoti, Claudio; Finco, Domenico
2012-01-01
We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L 2 -norm. We moreover show that the only stationary state with prescribed L 2 -norm is indeed a saddle point. (fast track communication)
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Cubic AlGaN/GaN structures for device application
Energy Technology Data Exchange (ETDEWEB)
Schoermann, Joerg
2007-05-15
The aim of this work was the growth and the characterization of cubic GaN, cubic AlGaN/GaN heterostructures and cubic AlN/GaN superlattice structures. Reduction of the surface and interface roughness was the key issue to show the potential for the use of cubic nitrides in futur devices. All structures were grown by plasma assisted molecular beam epitaxy on free standing 3C-SiC (001) substrates. In situ reflection high energy electron diffraction was first investigated to determine the Ga coverage of c-GaN during growth. Using the intensity of the electron beam as a probe, optimum growth conditions were found when a 1 monolayer coverage is formed at the surface. GaN samples grown under these conditions reveal excellent structural properties. On top of the c-GaN buffer c-AlGaN/GaN single and multiple quantum wells were deposited. The well widths ranged from 2.5 to 7.5 nm. During growth of Al{sub 0.15}Ga{sub 0.85}N/GaN quantum wells clear reflection high energy electron diffraction oscillations were observed indicating a two dimensional growth mode. We observed strong room-temperature, ultraviolet photoluminescence at about 3.3 eV with a minimum linewidth of 90 meV. The peak energy of the emission versus well width is reproduced by a square-well Poisson- Schroedinger model calculation. We found that piezoelectric effects are absent in c-III nitrides with a (001) growth direction. Intersubband transition in the wavelength range from 1.6 {mu}m to 2.1 {mu}m was systematically investigated in AlN/GaN superlattices (SL), grown on 100 nm thick c-GaN buffer layers. The SLs consisted of 20 periods of GaN wells with a thickness between 1.5 nm and 2.1 nm and AlN barriers with a thickness of 1.35 nm. The first intersubband transitions were observed in metastable cubic III nitride structures in the range between 1.6 {mu}m and 2.1 {mu}m. (orig.)
Spatially localized, temporally quasiperiodic, discrete nonlinear excitations
International Nuclear Information System (INIS)
Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.
1995-01-01
In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
International Nuclear Information System (INIS)
Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.
2010-12-01
A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)
Role of statistical linearization in the solution of nonlinear stochastic equations
International Nuclear Information System (INIS)
Budgor, A.B.
1977-01-01
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables
Intertwining relations and Darboux transformations for Schroedinger equations in (n+1) dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2010-01-01
We evaluate the intertwining relation for Schroedinger equations in (n+1) dimensions. The conditions for the existence of a Darboux transformation are analyzed and compared to their (1+1) dimensional counterparts. A complete solution of the conditions is given for (2+1) dimensions, and a Darboux transformation is constructed.
The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms
International Nuclear Information System (INIS)
Chen Gang
2004-01-01
In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions
Local and non-local Schroedinger cat states in cavity QED
International Nuclear Information System (INIS)
Haroche, S.
2005-01-01
Full text: I will review recent experiments performed on mesoscopic state superpositions of field states in cavity QED. Proposals to extend these studies to Schroedinger cat states delocalized in two cavities will be discussed. New versions of Bell's inequality tests will probe the non-local behavior of these cats and study their sensitivity to decoherence. (author)
Random Schroedinger operators and the theory of disordered systems: some rigorous results
International Nuclear Information System (INIS)
Kunz, H.; Souillard, B.
1981-01-01
The authors report results on a class of finite difference Schroedinger operators with stochastic potentials. The Hamiltonian is then H(V)=-Δ+V; where Δ is the discretized Laplacian and the potential V acts as a multiplication operator. The potential V is random. (Auth.)
Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems
International Nuclear Information System (INIS)
Vanden Berghe, G.; Van Daele, M.; De Meyer, H.
1994-01-01
A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics
1990-03-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).
Bounds on resolvents of dilated Schroedinger operators with non trapping potentials
International Nuclear Information System (INIS)
Duclos, P.; Klein, M.
1985-06-01
We provide bounds on resolvents of dilated Schroedinger operators via an exterior scaling. It is done under a non trapping condition on the potential which has a clear interpretation in classical mechanics. These bounds are a powerful tool to prove absence of resonances due to the tail of the potential in the shape resonance problem
International Nuclear Information System (INIS)
Rezende, J.
1983-01-01
We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)
International Nuclear Information System (INIS)
Zhou Xin
1990-01-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)
Continuous-time random walk as a guide to fractional Schroedinger equation
International Nuclear Information System (INIS)
Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.
2010-01-01
We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.
Quantum corrections for the cubic Galileon in the covariant language
Energy Technology Data Exchange (ETDEWEB)
Saltas, Ippocratis D. [Institute of Astrophysics and Space Sciences, Faculty of Sciences, Campo Grande, PT1749-016 Lisboa (Portugal); Vitagliano, Vincenzo, E-mail: isaltas@fc.ul.pt, E-mail: vincenzo.vitagliano@ist.utl.pt [Multidisciplinary Center for Astrophysics and Department of Physics, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-05-01
We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach in this context is discussed, while all calculations are explicitly presented.
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Linear and nonlinear optical signals in probability and phase-space representations
International Nuclear Information System (INIS)
Man'ko, Margarita A
2006-01-01
Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed
Dipaths and dihomotopies in a cubical complex
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2005-01-01
In the geometric realization of a cubical complex without degeneracies, a $\\Box$-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton...
Some elements go cubic under pressure
Czech Academy of Sciences Publication Activity Database
Legut, Dominik
2007-01-01
Roč. 60, č. 10 (2007), s. 17-17 ISSN 0031-9228 Institutional research plan: CEZ:AV0Z20410507 Keywords : ab initio * polonium * cubic structure Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 5.133, year: 2007
The Exact Limit of Some Cubic Towers
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2017-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as go...
Erwin Schroedinger: Collected papers V. 4. General scientific and popular papers
International Nuclear Information System (INIS)
Schroedinger, E.
1984-01-01
The present volume contains all of Schroedinger's papers, which did not fit naturally into his earlier volumes. It certainly does not contain only popular writings and is perhaps more so than the other volumes a testimony of the spiritual breadth of its author. Schroedinger occupied himself very extensively with the physiological optics. His papers reach from survey articles, where an enormous experimental material is being sifted, to theoretical explorations. A leitmotiv in Schroedinger's thinking, which never left him in peace, was the duality of particle and wave. He looked upon the wave-picture as the one more to the point and in this connection expressed various fruitful thoughts as e.g. that the state of macroscopic bodies would not be eigenstates of the number of particles. He objected against provisional formulations and thus controverted against quantum jumps, which suggest a discontinuous time-development. Schroedinger rejected the radical positivism, which tolerates only directly observable quantities in a theory and he did not look upon the Copenhagen interpretation as the complete solution to the problem. The collection of 59 papers is a goldmine for all pedagogues. Numerous popularizations of Schroedinger's spheres of interest, which go widely beyond his field of exploration prove how simple and clear a topic can be presented. Let it be astronomy or biology, theory of knowledge or Greek mythology, he always discovered the heart of the questions and illustrated it with simple means. He never pretends learning and deepness of thoughts by cryptical remarks and by vague or contradictory formulations. All writings show his way of thinking, which cannot be restricted by authority and objects to any claim of eternal validity. For instance, he analyses various epoche-making arguements of Galileo and finds that his plausible explanation of the tides is wrong. His conceptions on consciousness, free will and human soul are documented in some essays too
International Nuclear Information System (INIS)
Chudnovsky, David; Chudnovsky, G.V.
1978-01-01
The relations between many particle problem with inverse square potential on the line and meromorphic eigenfunctions of Schroedinger operator are presented. This gives new type of Backlund transformations for many particle problem [fr
International Nuclear Information System (INIS)
Meyenn, Karl von
2011-01-01
After Schroedinger has in the beginning of 1926 published his wave mechanics, he has by this opened many new physical views and perspectives, which have decidingly influenced the further development of quantum theory. Also today the Schroedinger equations forms the foundation of the whole microphysics and their far reaching applications. Therefore it is both for the scientist and for the interested layman very attractive to be informed by first hand about the more direct conditions and the problems of their origin. Letters of famous scientists and researchers have also in the past attracted the interest of the public, and many a scientist has been excited to the study by the lecture of such primary sources. The selection of about 300 letters presented here illuminates especially the origin of wave mechanics and their still controverse interpretation. An extensive introduction, comments, remarks, illustrations, and lists establish the physical and historical relations.
Solution of Schroedinger equation for particle moving in two-well potential
International Nuclear Information System (INIS)
Ivanova, O.I.; Sabirov, R.Kh.
2000-01-01
The solution of the Schroedinger equation for the particle, moving in the two-well potential is given on the basis of a single variational method. This potential constitutes the sum of the harmonic potential and the Gaussian addition. The analytical expression for the wave function of the particle basic state is obtained. The dependence of the obtained solutions on the potential barrier height and width is studied. It is shown that the better separation of the potential barrier provides for higher accuracy of the calculations. The values of the two-well potential, whereby good agreement between the calculations and exact numerical solution of the Schroedinger equation may be expected, are presented [ru
Energy Technology Data Exchange (ETDEWEB)
Gaffney, J M
1975-01-01
A reappraisal of electromagnetic field theories is made and an account is given of the radiation gauge, Gupta-Bleuler and Fermi methods of quantitising the electromagnetic fields. The Weyl algebra of the vector potential is constructed and the Fermi method is then related to a certain representation of the algebra. The representation is specified by a generating functional for a state on the algebra. The Weyl algebra of the physical field is then constructed as a factor algebra. The Schroedinger representation of the algebra is then studied and it was found that the Fermi method is just a generalization of this representation to an infinite number of degrees of freedom. The Schroedinger representation of Fermi method is constructed.
International Nuclear Information System (INIS)
Dobrev, V.K.; Doebner, H.D.; Mrugalla, C.
1995-12-01
We give a q-deformation S-perpendicular q of the centrally extended Schroedinger algebra. We construct the lowest weight representations of S-perpendicular q , starting from the Verma modules over S-perpendicular q , finding their singular vectors and factoring the Verma submodules built on the singular vectors. We also give a vector-field realization of S-perpendicular q which provides polynomial realization of the lowest weight representations and an infinite hierarchy of q-difference equations which may be called generalized q-deformed heat equations. We also apply our methods to the on-shell q-Schroedinger algebra proposed by Floreanini and Vinet. (author). 12 refs
Form-preserving Transformations for the Time-dependent Schroedinger Equation in (n + 1) Dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2006-01-01
We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schroedinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L 2 -normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schroedinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one
International Nuclear Information System (INIS)
Ponomarev, L.I.; Puzynin, I.V.; Puzynina, T.P.
1975-01-01
The paper is a part of further development of investigations in which a numerical solution method of the Schroedinger equation for the case of a discrete spectrum has been developed and applied. The suggested algorithm (CAMEN scheme) is generalized and applied to quasistationary solutions of the Schroedinger equation system. Some specific features of the CAMEN scheme realization (such as establishing boundary conditions are observed while calculating quasistationary levels of hydrogen mesic molecules. The calculations have been carried out for energies and wave functions of quasistationary states of hydrogen mesic molecules. The choice of the initial approximation, the accuracy of calculations and characteristics of the convergence of the method have been investigated. The CAMEN algorithm has been realized in the form of the FORTRAN program packet. The CAMEN scheme can be also used for solving scatering problems
Bell's theorem and quantum realism. Reassessment in light of the Schroedinger paradox
International Nuclear Information System (INIS)
Shakur, Asif M.; Hemmick, Douglas L.
2012-01-01
Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: ''There is no quantum world. There is only an abstract mathematical description.'' Among the most significant developments since Bohr's day has been the theorem of John S. Bell. It is important to consider whether Bell's analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schroedinger. Doing so, we see how Bell's theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schroedinger's work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving ''entanglement,'' the link between particles in some quantum systems. (orig.)
High-order nonlinear susceptibilities of He
International Nuclear Information System (INIS)
Liu, W.C.; Clark, C.W.
1996-01-01
High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals
Exact solutions of fractional Schroedinger-like equation with a nonlocal term
International Nuclear Information System (INIS)
Jiang Xiaoyun; Xu Mingyu; Qi Haitao
2011-01-01
We study the time-space fractional Schroedinger equation with a nonlocal potential. By the method of Fourier transform and Laplace transform, the Green function, and hence the wave function, is expressed in terms of H-functions. Graphical analysis demonstrates that the influence of both the space-fractal parameter α and the nonlocal parameter ν on the fractional quantum system is strong. Indeed, the nonlocal potential may act similar to a fractional spatial derivative as well as fractional time derivative.
International Nuclear Information System (INIS)
Carow-Watamura, U.; Schlieker, M.; Watamura, S.
1991-01-01
We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SO q (N) is acting. The differential calculus is required to be manifestly covariant under SO q (N) transformations. Using this calculus, we consider the Schroedinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions. (orig.)
One-dimensional Schroedinger operators with interactions singular on a discrete set
International Nuclear Information System (INIS)
Gesztesy, F.; Kirsch, W.
We study the self-adjointness of Schroedinger operators -d 2 /dx 2 +V(x) on an arbitrary interval, (a,b) with V(x) locally integrable on (a,b)inverse slantX where X is a discrete set. The treatment of quantum mechanical systems describing point interactions or periodic (possibly strongly singular) potentials is thereby included and explicit examples are presented. (orig.)
On a minimization of the eigenvalues of Schroedinger operator relatively domains
International Nuclear Information System (INIS)
Gasymov, Yu.S.; Niftiev, A.A.
2001-01-01
Minimization of the eigenvalues plays an important role in the operators spectral theory. The problem on the minimization of the eigenvalues of the Schroedinger operator by areas is considered in this work. The algorithm, analogous to the conditional gradient method, is proposed for the numerical solution of this problem in the common case. The result is generalized for the case of the positively determined completely continuous operator [ru
International Nuclear Information System (INIS)
Bayramoglu, Mehmet; Tasci, Fatih; Zeynalov, Djafar
2004-01-01
We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schroedinger boundary value problem -Δu+q(x)u=λ 2 u, u vertical bar ∂D =0, with a complex potential q(x) in an angular domain
International Nuclear Information System (INIS)
Amos, K.; Allen, L.J.; Steward, C.; Hodgson, P.E.; Sofianos, S.A.
1995-01-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs
Energy Technology Data Exchange (ETDEWEB)
Amos, K.; Allen, L.J.; Steward, C. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Hodgson, P.E. [Oxford Univ. (United Kingdom). Dept. of Physics; Sofianos, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics
1995-10-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs.
Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schroedinger Equation
Energy Technology Data Exchange (ETDEWEB)
Amor, Sana Hadj, E-mail: sana_hadjamor@yahoo.fr [Ecole Nationale d' Ingenieurs de Monastir (Tunisia)
2012-12-15
Starting from results already obtained for quasi-periodic co-cycles in SL(2, R), we show that the rotation number of the one-dimensional time-continuous Schroedinger equation with Diophantine frequencies and a small analytic potential has the behavior of a 1/2-Hoelder function. We give also a sub-exponential estimate of the length of the gaps which depends on its label given by the gap-labeling theorem.
Quasiseparation of variables in the Schroedinger equation with a magnetic field
International Nuclear Information System (INIS)
Charest, F.; Hudon, C.; Winternitz, P.
2007-01-01
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the separation of variables in the Schroedinger equation. We introduce the concept of 'quasiseparation of variables' and show that in many cases it allows us to reduce the calculation of the energy spectrum and wave functions to linear algebra
International Nuclear Information System (INIS)
Yasuk, F.; Tekin, S.; Boztosun, I.
2010-01-01
In this study, the exact solutions of the d-dimensional Schroedinger equation with a position-dependent mass m(r)=1/(1+ζ 2 r 2 ) is presented for a free particle, V(r)=0, by using the method of point canonical transformations. The energy eigenvalues and corresponding wavefunctions for the effective potential which is to be a generalized Poeschl-Teller potential are obtained within the framework of the asymptotic iteration method.
Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields
International Nuclear Information System (INIS)
Albeverio, S.; Brzezniak, Z.
1994-01-01
We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Todorov, N S [Low Temperature Department of the Institute of Solid State Physics of the Bulgarian Academy of Sciences, Sofia
1981-04-01
It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article rests essentially on the ideology of the preceding articles, in particular article I.
Energy Technology Data Exchange (ETDEWEB)
Todorov, N S
1981-04-01
It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article IV rests essentially on the ideology of the preceding articles, in particular article I.
International Nuclear Information System (INIS)
Morales, J.; Ovando, G.; Pena, J. J.
2010-01-01
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
The discretized Schroedinger equation and simple models for semiconductor quantum wells
International Nuclear Information System (INIS)
Boykin, Timothy B; Klimeck, Gerhard
2004-01-01
The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one
International Nuclear Information System (INIS)
Ziqi Sun
1993-01-01
During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials
Localized excitations in a nonlinearly coupled magnetic drift wave-zonal flow system
International Nuclear Information System (INIS)
Shukla, Nitin; Shukla, P.K.
2010-01-01
We consider the amplitude modulation of the magnetic drift wave (MDW) by zonal flows (ZFs) in a nonuniform magnetoplasma. For this purpose, we use the two-fluid model to derive a nonlinear Schroedinger equation for the amplitude modulated MDWs in the presence of the ZF potential, and an evolution equation for the ZF potential which is reinforced by the nonlinear Lorentz force of the MDWs. Our nonlinearly coupled MDW-ZFs system of equations admits stationary solutions in the form of a localized MDW envelope and a shock-like ZF potential profile.
International Nuclear Information System (INIS)
Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A
2009-01-01
In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed
Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media
El-Dib, Y O
2003-01-01
In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...
Quasiparticle Interference on Cubic Perovskite Oxide Surfaces.
Okada, Yoshinori; Shiau, Shiue-Yuan; Chang, Tay-Rong; Chang, Guoqing; Kobayashi, Masaki; Shimizu, Ryota; Jeng, Horng-Tay; Shiraki, Susumu; Kumigashira, Hiroshi; Bansil, Arun; Lin, Hsin; Hitosugi, Taro
2017-08-25
We report the observation of coherent surface states on cubic perovskite oxide SrVO_{3}(001) thin films through spectroscopic-imaging scanning tunneling microscopy. A direct link between the observed quasiparticle interference patterns and the formation of a d_{xy}-derived surface state is supported by first-principles calculations. We show that the apical oxygens on the topmost VO_{2} plane play a critical role in controlling the coherent surface state via modulating orbital state.
HRTEM studies of dislocations in cubic BN
International Nuclear Information System (INIS)
Nistor, L.C.; Tendeloo, G. van; Dinca, G.
2004-01-01
The atomic structure of dislocations in cubic boron nitride has been investigated by high resolution transmission electron microscopy. Most of the perfect dislocations, screw and 60 edge, are dissociated. A 60 dislocation which was undissociated has been analysed. Computer simulation is performed in an attempt to characterise the core structure. Twinning dislocations and dislocations resulting from the intersection of stacking faults are also revealed. (copyright 2004 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
HRTEM studies of dislocations in cubic BN
Energy Technology Data Exchange (ETDEWEB)
Nistor, L.C. [National Institute for Materials Physics, P.O. Box MG-7 Magurele, 077125 Bucharest (Romania); Tendeloo, G. van [University of Antwerp, EMAT, Groenenborgerlaan 171, 2020 Antwerp (Belgium); Dinca, G. [Dacia Synthetic Diamond Factory, Timisoara av. 5, P.O. Box 58-52, 077350 Bucharest (Romania)
2004-09-01
The atomic structure of dislocations in cubic boron nitride has been investigated by high resolution transmission electron microscopy. Most of the perfect dislocations, screw and 60 edge, are dissociated. A 60 dislocation which was undissociated has been analysed. Computer simulation is performed in an attempt to characterise the core structure. Twinning dislocations and dislocations resulting from the intersection of stacking faults are also revealed. (copyright 2004 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Minimal knotted polygons in cubic lattices
International Nuclear Information System (INIS)
Van Rensburg, E J Janse; Rechnitzer, A
2011-01-01
In this paper we examine numerically the properties of minimal length knotted lattice polygons in the simple cubic, face-centered cubic, and body-centered cubic lattices by sieving minimal length polygons from a data stream of a Monte Carlo algorithm, implemented as described in Aragão de Carvalho and Caracciolo (1983 Phys. Rev. B 27 1635), Aragão de Carvalho et al (1983 Nucl. Phys. B 215 209) and Berg and Foester (1981 Phys. Lett. B 106 323). The entropy, mean writhe, and mean curvature of minimal length polygons are computed (in some cases exactly). While the minimal length and mean curvature are found to be lattice dependent, the mean writhe is found to be only weakly dependent on the lattice type. Comparison of our results to numerical results for the writhe obtained elsewhere (see Janse van Rensburg et al 1999 Contributed to Ideal Knots (Series on Knots and Everything vol 19) ed Stasiak, Katritch and Kauffman (Singapore: World Scientific), Portillo et al 2011 J. Phys. A: Math. Theor. 44 275004) shows that the mean writhe is also insensitive to the length of a knotted polygon. Thus, while these results for the mean writhe and mean absolute writhe at minimal length are not universal, our results demonstrate that these values are quite close the those of long polygons regardless of the underlying lattice and length
Neutrosophic Cubic MCGDM Method Based on Similarity Measure
Directory of Open Access Journals (Sweden)
Surapati Pramanik
2017-06-01
Full Text Available The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials
International Nuclear Information System (INIS)
Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan
2007-01-01
A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models
Cubic-quintic solitons in the checkerboard potential
International Nuclear Information System (INIS)
Driben, Rodislav; Zyss, Joseph; Malomed, Boris A.; Gubeskys, Arthur
2007-01-01
We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ('oblique' and 'straight' ones). Unlike them, compact 'crater-shaped' vortices are unstable, transforming themselves into randomly walking fundamental beams
Quantum-mechanical Green's functions and nonlinear superposition law
International Nuclear Information System (INIS)
Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P. de T.S.
1986-01-01
The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt
Quantum-mechanical Green's function and nonlinear superposition law
International Nuclear Information System (INIS)
Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P.T.S.
1986-01-01
It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field
Complex nonlinear Lagrangian for the Hasegawa-Mima equation
International Nuclear Information System (INIS)
Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.
2005-01-01
The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)
On norm resolvent convergence of Schroedinger operators with δ'-like potentials
International Nuclear Information System (INIS)
Golovaty, Yu D; Hryniv, R O
2010-01-01
For a function V:R→R that is integrable and compactly supported, we prove the norm resolvent convergence, as ε → 0, of a family S ε of one-dimensional Schroedinger operators on the line of the form S ε :=-d 2 /dx 2 + 1/ε 2 V(x/ε). If the potential V satisfies the conditions ∫ R V(ξ)dξ=0, ∫ R ξV(ξ)dξ=-1, then the functions ε -2 V(x/ε) converge in the sense of distributions as ε → 0 to δ'(x), and the limit S 0 of S ε might be considered as a 'physically motivated' interpretation of the one-dimensional Schroedinger operator with a potential δ'. In 1985, Seba claimed that the limit operator S 0 is the direct sum of the free Schroedinger operators on positive and negative semi-axes subject to the Dirichlet condition at x = 0, which suggested that in dimension 1 there is no non-trivial Hamiltonian with the potential δ'. In this paper, we show that in fact S 0 essentially depends on V: although the above results are true generically, in the exceptional (or 'resonant') case, the limit S 0 is non-trivial and is determined by the properties of an auxiliary Sturm-Liouville spectral problem associated with V. We then set V(ξ) = αΨ(ξ) with a fixed Ψ and show that there exists a countable set of resonances {α k } ∞ k=-∞ for which a partial transmission of the wave package occurs for S 0 .
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
International Nuclear Information System (INIS)
Duval, C.; Kuenzle, H.P.
1983-02-01
The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory
Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review
Energy Technology Data Exchange (ETDEWEB)
Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.
1978-10-01
We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.
Quantum scattering via the discretisation of Schroedinger's equation
Energy Technology Data Exchange (ETDEWEB)
Alexopoulos, A. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)]. E-mail: aris.alexopoulos@dsto.defence.gov.au
2007-03-19
We obtain the scattering matrix for particles that encounter a quantum potential by discretising Schroedinger's time independent differential equation without the need to resort to the manipulation of the eigenfunctions directly. The singularities that arise in some solutions by other methods are handled with ease including the effects of resonances while convergence is excellent in all limits with only a small number of orders required to give accurate results. Our method compares the tunnelling probability with that of the WKB theory, exact numerical solutions and the modified Airy function method.
Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach
International Nuclear Information System (INIS)
Nakamura, T.
1997-01-01
A nonstandard path space *-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space endash time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schroedinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a *-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. copyright 1997 American Institute of Physics
Arbitrary l-wave solutions of the Schroedinger equation for the screen Coulomb potential
International Nuclear Information System (INIS)
Dong, Shishan; Sun, Guohua; Dong, Shihai
2013-01-01
Using improved approximate schemes for centrifugal term and the singular factor 1/r appearing in potential itself, we solve the Schroedinger equation with the screen Coulomb potential for arbitrary angular momentum state l. The bound state energy levels are obtained. A closed form of normalization constant of the wave functions is also found. The numerical results show that our results are in good agreement with those obtained by other methods. The key issue is how to treat two singular points in this quantum system. (author)
Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials
International Nuclear Information System (INIS)
Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.
2009-01-01
We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)
Transfer matrix in 1D Schroedinger problems with constant and position-dependent mass
International Nuclear Information System (INIS)
Perez-Alvarez, R.; Rodriguez-Coppola, H.
1987-10-01
We consider the transfer matrix method for obtaining properties of standard wells and barriers in one-dimensional Schroedinger problems with constant and position-dependent mass. We report the formulae for the energy levels of a well and the transmission coefficient of a barrier. We demonstrate the continuity between virtual bound states and bound states in a well of position-dependent mass and the relation between the zero energy gap states of a periodic potential problem with the corresponding energies of the non-periodic ones with transmission coefficient equal to one. The calculations were carried out for a wide class of potential profiles. (author). 30 refs, 2 figs
Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation
International Nuclear Information System (INIS)
Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien
2008-01-01
We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature
Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be
2008-07-11
We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature.
Toward an AdS/cold atoms correspondence: A geometric realization of the Schroedinger symmetry
International Nuclear Information System (INIS)
Son, D. T.
2008-01-01
We discuss a realization of the nonrelativistic conformal group (the Schroedinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.
Exact solution of the Schroedinger equation with the spin-boson Hamiltonian
International Nuclear Information System (INIS)
Gardas, Bartlomiej
2011-01-01
We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (environment). An exact solution of the Schroedinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
International Nuclear Information System (INIS)
Lopez, J. Gonzalez; Jansen, K.; Renner, D.B.; Shindler, A.
2012-01-01
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
International Nuclear Information System (INIS)
Duval, C.; Kuenzle, H.P.
1984-01-01
The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)
Basic properties of the current-current correlation measure for random Schroedinger operators
International Nuclear Information System (INIS)
Hislop, Peter D.; Lenoble, Olivier
2006-01-01
The current-current correlation measure plays a crucial role in the theory of conductivity for disordered systems. We prove a Pastur-Shubin-type formula for the current-current correlation measure expressing it as a thermodynamic limit for random Schroedinger operators on the lattice and the continuum. We prove that the limit is independent of the self-adjoint boundary conditions and independent of a large family of expanding regions. We relate this finite-volume definition to the definition obtained by using the infinite-volume operators and the trace-per-unit volume
International Nuclear Information System (INIS)
Feizi, H.; Rajabi, A.A.; Shojaei, M.R.
2011-01-01
In this work, the three dimensional Woods-Saxon potential is studied within the context of Supersymmetry Quantum Mechanics. We have applied the SUSY method by using the Pekeris approximation to the centrifugal potential l ≠ 0 states. By application of this method, it is possible to solve the Schroedinger equation for this potential. We obtain exactly bound state spectrum and wave function of Woods-Saxon potential for nonzero angular momentum. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. (authors)
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-24
In a previous paper (J. G. Lopez et al.,2012) we have discussed the non-perturbative tuning of the chirally rotated Schroedinger functional ({chi}SF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in this paper we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the {chi}SF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist. (orig.)
International Nuclear Information System (INIS)
Lopez, J. Gonzalez; Jansen, K.; Renner, D.B.; Shindler, A.
2012-01-01
In a previous paper (J. G. Lopez et al.,2012) we have discussed the non-perturbative tuning of the chirally rotated Schroedinger functional (χSF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in this paper we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the χSF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist. (orig.)
A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials
International Nuclear Information System (INIS)
Minelli, T.A.
1976-01-01
A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation
Directory of Open Access Journals (Sweden)
N. N. Rosanov
2015-09-01
Full Text Available Problem statement ill-posedness in the paper by L.S. Konev et al. devoted to formation of backward wave at short laser pulse propagation in nonlinear media or fibers is specified. It is inconceivable in the correct problem statement to consider the radiation field at the medium entrance as a given function of time due to generation of backward wave in the medium, when the backward wave characteristics are target values. The proper evolution variable is time, and it is convenient to use the adopted finite-difference time-domain (FDTD method for backward wave calculation.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
International Nuclear Information System (INIS)
Gosson, Maurice A de
2008-01-01
The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schroedinger's equation when the initial datum is a coherent state. In this paper, we first extend this method to arbitrary squeezed states and thereafter apply our results to the Schroedinger equation in phase space. This adaptation requires the phase-space Weyl calculus developed in previous work of ours. We also study the regularity of the semi-classical solutions from the point of view of the Feichtinger algebra familiar from the theory of modulation spaces
International Nuclear Information System (INIS)
Kravchenko, Viktor G; Kravchenko, Vladislav V
2003-01-01
We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Viktor G [Faculdade de Ciencias y Tecnologia, Universidade do Algarve, Campus de Gambelas, 8000 Faro (Portugal); Kravchenko, Vladislav V [Depto de Telecomunicaciones, SEPI ESIME Zacatenco, Instituto Politecnico Nacional, Av. IPN S/N, Edif. 1 CP 07738, DF (Mexico)
2003-11-07
We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work.
International Nuclear Information System (INIS)
Rasolofoson, N.G.
2014-01-01
The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr
International Nuclear Information System (INIS)
Kavitha, L.; Daniel, M.
2002-07-01
The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)
Black holes in a cubic Galileon universe
Energy Technology Data Exchange (ETDEWEB)
Babichev, E.; Charmousis, C.; Lehébel, A.; Moskalets, T., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr, E-mail: tetiana.moskalets@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)
2016-09-01
We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.
Cubic phase control of ultrashort laser pulses
International Nuclear Information System (INIS)
Mecseki, K.; Erdelyi, M.; Kovacs, A.P.; Szabo, G.
2006-01-01
Complete test of publication follows. The temporal shape of an ultrashort laser pulse may change upon propagating through a linear dispersive medium having a phase shift ψω. The change can be characterized by the Taylor-coefficients of the phase shift which are calculated around the central frequency ω 0 of the pulse. Measurements and independent control of the group delay dispersion (GDD, ψ'(ω 0 )) and the third order dispersion (TOD, ψ'(ω 0 )) are important in several research fields, particularly in the generation of ultrashort laser pulses by chirped pulse amplification (CPA) and pulse shaping for molecular control. The GDD and the TOD of an ideal pulse compressor are equal to the negative of the corresponding dispersion coefficients of the medium. However, in the case of prism-pair and grating-pair compressor is different from the ratio of the coefficients of the medium to be compensated for. Therefore it is necessary to develop so-called cubic compressors that are able to control the TOD of the pulse, yet, do not affect the GDD. In this paper a new cubic compressor setup is investigated theoretically and experimentally, which resembles the set-up proposed by White, however, we control the GDD and the TOD by the position of a birefringent, semi-cylinder crystal place around the focal point of an achromatic lens. For the evaluation of the phase shift introduced by the proposed cubic compressor, a ray tracing program was written. The program allows optimizing the compressor parameters, such as the radius of the crystal, magnification of the lens etc. Calcite was applied because it is a strong birefringent material. Calculations showed that there is a trajectory, along which shifting the crystal the TOD can be tuned independently of the GDD. The value of the TOD changed in a relatively wide range between -3.15 x 10 5 fs 3 and -1.67 x 10 5 fs 3 . Although the defocus also affects the angular dispersion of the pulse leaving the compressor, if does not exceed
Cubic martensite in high carbon steel
Chen, Yulin; Xiao, Wenlong; Jiao, Kun; Ping, Dehai; Xu, Huibin; Zhao, Xinqing; Wang, Yunzhi
2018-05-01
A distinguished structural characteristic of martensite in Fe-C steels is its tetragonality originating from carbon atoms occupying only one set of the three available octahedral interstitial sites in the body-centered-cubic (bcc) Fe lattice. Such a body-centered-tetragonal (bct) structure is believed to be thermodynamically stable because of elastic interactions between the interstitial carbon atoms. For such phase stability, however, there has been a lack of direct experimental evidence despite extensive studies of phase transformations in steels over one century. In this Rapid Communication, we report that the martensite formed in a high carbon Fe-8Ni-1.26C (wt%) steel at room temperature induced by applied stress/strain has actually a bcc rather than a bct crystal structure. This finding not only challenges the existing theories on the stability of bcc vs bct martensite in high carbon steels, but also provides insights into the mechanism for martensitic transformation in ferrous alloys.
Expansion into lattice harmonics in cubic symmetries
Kontrym-Sznajd, G.
2018-05-01
On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
Motion of a Rigid Rod Rocking Back and Forth Cubic-Quintic Duffing Oscillators
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Karimpour, S.
2012-01-01
In this work, we implemented the first-order approximation of the Iteration Perturbation Method (IPM) for approximating the behavior of a rigid rod rocking back and forth on a circular surface without slipping as well as Cubic-Quintic Duffing Oscillators. Comparing the results with the exact...... solution, has led us to significant consequences. The results reveal that the IPM is very effective, simple and convenient to systems of nonlinear equations. It is predicted that IPM can be utilized as a widely applicable approach in engineering....
International Nuclear Information System (INIS)
Hesse, Dirk
2012-01-01
The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.
Finite-time quantum-to-classical transition for a Schroedinger-cat state
International Nuclear Information System (INIS)
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
2011-01-01
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
Energy Technology Data Exchange (ETDEWEB)
Hesse, Dirk
2012-07-13
The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.
Multi-shocks generation and collapsing instabilities induced by competing nonlinearities
Crosta, Matteo; Trillo, Stefano; Fratalocchi, Andrea
2012-01-01
We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.
Oscillating particle-like solutions of nonlinear Klein-Gordon equation
International Nuclear Information System (INIS)
Bogolubsky, I.L.
1976-01-01
A denumerable set of oscillating spherically-symmetric particle-like solutions of the Klein-Gordon equation with cubic nonlinearity is found. Extended particles modelled by them turn out to be slightly radiating and long-lived
Analysis of highly nonlinear oscillation systems using He's max–min ...
Indian Academy of Sciences (India)
Min–max method; nonlinear oscillation; duffing equation; homo- .... where c and ε are the linear and cubic stiffness which do not need to be small in the ..... an easy and direct procedure for determining approximations to the periodic solutions.
Theory of Nonlinear Dispersive Waves and Selection of the Ground State
International Nuclear Information System (INIS)
Soffer, A.; Weinstein, M.I.
2005-01-01
A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides
International Nuclear Information System (INIS)
Cobian, Hector; Schulze-Halberg, Axel
2011-01-01
We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We exhibit an example of a one-dimensional discrete Schroedinger operator with an almost periodic potential for which the steps of the density of states do not belong to the frequency module. This example is suggested by the K-theory
International Nuclear Information System (INIS)
Myrheim, J.
1993-06-01
The thesis deals with the application of different methods to the quantization problem for system of identical particles in one and two dimensions. The standard method is the analytic quantization method due to Schroedinger, which leads to the concept of fractional statistics in one and two dimensions. Two-dimensional particles with fractional statistics are well known by the name of anyons. Two alternative quantization methods are shown by the author, the algebraic method of Heisenberg and the Feynman path integral method. The Feynman method is closely related to the Schroedinger method, whereas the Heisenberg and Schroedinger methods may give different results. The relation between the Heisenberg and Schroedinger methods is discussed. The Heisenberg method is applied to the equations of motion of vortices in superfluid helium, which have the form of Hamiltonian equations for a one-dimensional system. The same method is also discussed more generally for systems of identical particles in one and two dimensions. An application of the Feynman method to the problem of computing the equation of state for a gas of anyons is presented. 104 refs., 4 figs
International Nuclear Information System (INIS)
Inahama, Yuzuru; Shirai, Shin-ichi
2003-01-01
We study the essential spectrum of the magnetic Schroedinger operators on the Poincare upper-half plane and establish a hyperbolic analog of Iwatsuka's result [J. Math. Kyoto Univ. 23(3), 475-480 (1983)] on the stability of the essential spectrum under perturbations from constant magnetic fields
CubiCal - Fast radio interferometric calibration suite exploiting complex optimisation
Kenyon, J. S.; Smirnov, O. M.; Grobler, T. L.; Perkins, S. J.
2018-05-01
It has recently been shown that radio interferometric gain calibration can be expressed succinctly in the language of complex optimisation. In addition to providing an elegant framework for further development, it exposes properties of the calibration problem which can be exploited to accelerate traditional non-linear least squares solvers such as Gauss-Newton and Levenberg-Marquardt. We extend existing derivations to chains of Jones terms: products of several gains which model different aberrant effects. In doing so, we find that the useful properties found in the single term case still hold. We also develop several specialised solvers which deal with complex gains parameterised by real values. The newly developed solvers have been implemented in a Python package called CubiCal, which uses a combination of Cython, multiprocessing and shared memory to leverage the power of modern hardware. We apply CubiCal to both simulated and real data, and perform both direction-independent and direction-dependent self-calibration. Finally, we present the results of some rudimentary profiling to show that CubiCal is competitive with respect to existing calibration tools such as MeqTrees.
International Nuclear Information System (INIS)
Olive, D.
1987-01-01
The centenary of the birth of polymath Erwin Schrodinger was marked by a suitably multidisciplinary conference in April at London's Imperial College, reflecting the impact of the man's work on physics, chemistry, molecular biology and the history and philosophy of science
Energy Technology Data Exchange (ETDEWEB)
Olive, D.
1987-07-15
The centenary of the birth of polymath Erwin Schrodinger was marked by a suitably multidisciplinary conference in April at London's Imperial College, reflecting the impact of the man's work on physics, chemistry, molecular biology and the history and philosophy of science.
Energy Technology Data Exchange (ETDEWEB)
D`Agostino, S. [Rome Univ. (Italy)
1992-12-31
In the 50s, Schroedinger proposed a new conception of a continuous theory of Quantum Mechanics, which remarkably modified his 1926 ideas on ondulatory mechanics. The lack of individuality of the atomic particles presented in the new statistics, and in Heisenberg`s Indeterminacy Relations, was by him considered as an aspect of a more general crisis in the anthology itself of classical atomism. Unlike his 1926 ideas, he proposed now to represent the wave equation in an n-dimensional space and he considered second-quantization technique as the proper mathematical tool for his new physical conception. Although he accepted that space-time discontinuities and casual gaps may appear here and there on the observational level (e.g. in the Indeterminacy Relations), he was convinced that they could be made compatible with a continuous pure theory, provided one accepted a suitable conception of the theory`s epistemiological status. For him, only a continuous theory satisfied the conditions for a complete theory. On these matters, he thought he was somehow orthodox to the ideas of Hertz and Boltzmann, which were also reflected in the teaching of Exner. (author). 69 refs.
Mesostructured germanium with cubic pore symmetry
Energy Technology Data Exchange (ETDEWEB)
Armatas, G S; Kanatzidis, M G [Michigan State Univ., Michigan (United States), Dept. of Chemistry
2006-11-15
Regular mesoporous oxide materials have been widely studied and have a range of potential applications, such as catalysis, absorption and separation. They are not generally considered for their optical and electronic properties. Elemental semiconductors with nanopores running through them represent a different form of framework material with physical characteristics contrasting with those of the more conventional bulk, thin film and nanocrystalline forms. Here we describe cubic meso structured germanium, MSU-Ge-l, with gyroidal channels containing surfactant molecules, separated by amorphous walls that lie on the gyroid (G) minimal surface as in the mesoporous silica MCM-48. Although Ge is a high-meltin covalent semiconductor that is difficult to prepare from solution polymerization, we succeeded in assembling a continuous Ge network using a suitable precursor for Ge{sup 4-} atoms. Our results indicate that elemental semiconductors from group 14 of the periodic table can be made to adopt meso structured forms such as MSU-Ge-1, which features two three-dimensional labyrinthine tunnels obeying la3d space group symmetry and separated by a continuous germanium minimal surface that is otherwise amorphous. A consequence of this new structure for germanium, which has walls only one nanometre thick, is a wider electronic energy bandgap (1.4 eV versus 0.66 eV) than has crystalline or amorphous Ge. Controlled oxidation of MSU-Ge-1 creates a range of germanium suboxides with continuously varying Ge:O ratio and a smoothly increasing energy gap. (author)
Topological Oxide Insulator in Cubic Perovskite Structure
Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.
2013-01-01
The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Bifurcation of limit cycles for cubic reversible systems
Directory of Open Access Journals (Sweden)
Yi Shao
2014-04-01
Full Text Available This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic perturbations
Kinks in systems with cubic and quartic anharmonicity
International Nuclear Information System (INIS)
Kashcheev, V.N.
1988-01-01
For a classical system of interacting particles with on-site cubic or quartic anharmonicity explicit analytic solutions of the d'Alembert equation are obtained in the form of kinks in the presence of dissipation (viscous or Rayleigh) and a constant force. These kinks will be asymptotically stable in the case of quartic anharmonicity and unstable in the case cubic anharmonicity
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is
Analysis of RIA standard curve by log-logistic and cubic log-logit models
International Nuclear Information System (INIS)
Yamada, Hideo; Kuroda, Akira; Yatabe, Tami; Inaba, Taeko; Chiba, Kazuo
1981-01-01
In order to improve goodness-of-fit in RIA standard analysis, programs for computing log-logistic and cubic log-logit were written in BASIC using personal computer P-6060 (Olivetti). Iterative least square method of Taylor series was applied for non-linear estimation of logistic and log-logistic. Hear ''log-logistic'' represents Y = (a - d)/(1 + (log(X)/c)sup(b)) + d As weights either 1, 1/var(Y) or 1/σ 2 were used in logistic or log-logistic and either Y 2 (1 - Y) 2 , Y 2 (1 - Y) 2 /var(Y), or Y 2 (1 - Y) 2 /σ 2 were used in quadratic or cubic log-logit. The term var(Y) represents squares of pure error and σ 2 represents estimated variance calculated using a following equation log(σ 2 + 1) = log(A) + J log(y). As indicators for goodness-of-fit, MSL/S sub(e)sup(2), CMD% and WRV (see text) were used. Better regression was obtained in case of alpha-fetoprotein by log-logistic than by logistic. Cortisol standard curve was much better fitted with cubic log-logit than quadratic log-logit. Predicted precision of AFP standard curve was below 5% in log-logistic in stead of 8% in logistic analysis. Predicted precision obtained using cubic log-logit was about five times lower than that with quadratic log-logit. Importance of selecting good models in RIA data processing was stressed in conjunction with intrinsic precision of radioimmunoassay system indicated by predicted precision. (author)
International Nuclear Information System (INIS)
Leung Shingyu; Qian Jianliang
2010-01-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Schroedinger equation from 0 (h/2π) to o(h/2πinfinity)
International Nuclear Information System (INIS)
Voros, A.
1985-08-01
The Balian and Bloch idea, that the semiclassical treatment of the Schroedinger equation can be carried out exactly to all orders, o(h/2πinfinity), has been explicitly confirmed upon the time-independent equation with a polynomial potential V(q) in one degree of freedom. The global analytic structure of certain functions, which encode the full eigenvalue distribution, has indeed been computed in great detail with the complex WKB method, yielding a structure called a resurgence algebra. In the special case V(q) = q 2 sub(M), this leads to sum rules for the eigenvalues, which have been verified numerically. Inasmuch as the leading order 0(h/2π) of the WKB expansion amounts to the stationary phase evaluation of the Feynman path integral, it is a yet unsolved challenge to reproduce our results by an exact analysis of this path integral using a generalized saddle-point treatment
Antibound states for a class of one-dimensional Schroedinger Operators
Energy Technology Data Exchange (ETDEWEB)
Angeletti, A [Camerino Univ. (Italy). Ist. di Matematica
1980-11-01
Let delta(x) be the Dirac's delta, q(x) element of L/sup 1/(R) L/sup 2/(R) be a real valued function, and lambda, ..mu.. element of R; we will consider the following class of one-dimensional formal Schroedinger operators on L/sup 2/(R) H(lambda,..mu..) = - (d/sup 2//dx/sup 2/) + lambdadelta(x) + ..mu..q(x). It is known that to the formal operator H(lambda, ..mu..) may be associated a selfadjoint operator H(lambda, ..mu..) on L/sup 2/(R). If q is of finite range, for lambda < 0 and /..mu../ is small enough, we prove that H(lambda,..mu..) has an antibound state; that is the resolvent of H(lambda,..mu..) has a pole on the negative real axis on the second Riemann sheet.
Structure and properties of Hughston's stochastic extension of the Schroedinger equation
International Nuclear Information System (INIS)
Adler, Stephen L.; Horwitz, Lawrence P.
2000-01-01
Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics
International Nuclear Information System (INIS)
Dyakin, V.V.; Petrukhnovskii, S.I.
1988-01-01
Three-dimensional periodic Schroedinger operators with potentials that are square integrable on the unit cell (single-electron model of a crystal) are considered. A description is given of the class of rational curves that do not have more than a finite number of common points with any isoenergy surface (in particular, the Fermi surface) of an arbitrary operator of the considered form. A consequence of a theorem proved in the paper is the absence on the isoenergy surfaces of elements of planes, cones, and cylinders with straight generators, and all possible paraboloids and hyperboloids. Another interesting consequence is the following assertion: The topological dimension of an isoenergy manifold does not exceed two, which justifies the use of the word surface. The results generalize the assertion of Thomas's theorem on the absence on isoenergy surfaces of straight edges
Some simple conditions of bound states of Schroedinger operators in dimension d >= 3
International Nuclear Information System (INIS)
Exner, P.
1984-01-01
A necessary condition for existence of bound states below a given energy of a Schroedinger operator H=-Δ+V on L 2 (Rsup(d)), d>=3, together with a lower bound to the ground-state energy of H are derived using the Sobolev inequalities. It generalizes some recent results to the dimensions d>3 and to the potentials that are not necessarily rapidly decreasing. Comparison to other known necessary conditions is given. The examples of the d-dimensional hydrogen-like atom and the d-dimensional harmonic oscillator are discussed. In both of them the bound to the ground-state energy becomes remarkably tight for large values of d
International Nuclear Information System (INIS)
Silverman, J.N.
1983-01-01
A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schroedinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of 10 14 G. The GET results are compared with those obtained by other summing methods
International Nuclear Information System (INIS)
Nordbrock, U.; Kienzler, R.
2007-01-01
Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schroedinger equation is presented. (authors)
International Nuclear Information System (INIS)
Gligoric, G; Hadzievski, Lj; Maluckov, A; Malomed, B A
2009-01-01
A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) with additional terms describing long-range dipole-dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.