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)

Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

Directory of Open Access Journals (Sweden)

Mehmet Pakdemirli

Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

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

Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

Directory of Open Access Journals (Sweden)

Chen Yue

Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated. Keywords: Quintic derivative NLS equation, Solitary wave solutions, Mathematical physics methods, 2000 MR Subject Classification: 35G20, 35Q53, 37K10, 49S05, 76A60

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)

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)

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

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

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

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)

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

Equivalence transformations and differential invariants of a generalized nonlinear Schroedinger equation

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

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)

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

Science.gov (United States)

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.

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...

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

Science.gov (United States)

Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N

2014-09-01

We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.

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.

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.

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

On the quantum inverse problem for a new type of nonlinear Schroedinger equation for Alfven waves in plasma

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

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.

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

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

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

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

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.)

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)

Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

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

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.

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.

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.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

Science.gov (United States)

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.

Symbolic computation and solitons of the nonlinear Schroedinger equation in inhomogeneous optical fiber media

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

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.)

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

From nonlinear Schroedinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

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.

Localized and periodic exact solutions to the nonlinear Schroedinger equation with spatially modulated parameters: Linear and nonlinear lattices

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.

Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

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

A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

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.)

A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

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

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

A relation connecting scale transformation, Galilean transformation and Baecklund transformation for the nonlinear Schroedinger equation

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.)

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.

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

Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

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.

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)

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)

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Science.gov (United States)

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.

Solitary wave solutions as a signature of the instability in the discrete nonlinear Schroedinger equation

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.

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

A comparative analysis of Painleve, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schroedinger equations

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.

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)

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.)

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

Construction of local integro quintic splines

Directory of Open Access Journals (Sweden)

T. Zhanlav

2016-06-01

Full Text Available In this paper, we show that the integro quintic splines can locally be constructed without solving any systems of equations. The new construction does not require any additional end conditions. By virtue of these advantages the proposed algorithm is easy to implement and effective. At the same time, the local integro quintic splines possess as good approximation properties as the integro quintic splines. In this paper, we have proved that our local integro quintic spline has superconvergence properties at the knots for the first and third derivatives. The orders of convergence at the knots are six (not five for the first derivative and four (not three for the third derivative.

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

Stability analysis of embedded solitons in the generalized third-order nonlinear Schroedinger equation

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

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

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.

Linear and nonlinear analogues of the Schroedinger equation in the contextual approach in quantum mechanics

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

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.

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)

Variational method for the derivative nonlinear Schroedinger equation with computational applications

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.

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

Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

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

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

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

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

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.

A General Expression for the Quintic Lovelock Tensor

OpenAIRE

Briggs, C. C.

1996-01-01

A general expression is given for the quintic Lovelock tensor as well as for the coefficient of the quintic Lovelock Lagrangian in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection.

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.)

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

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Science.gov (United States)

Dasanayaka, Sahan; Atai, Javid

2011-08-01

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

The quintic interaction vertex in light-cone gravity

International Nuclear Information System (INIS)

Ananth, Sudarshan

2008-01-01

We consider pure gravity in light-cone gauge and derive the complete quintic interaction vertex. Up to quartic order, the Kawai-Lewellen-Tye (KLT) relations can be made manifest at the level of the Einstein-Hilbert Lagrangian. The quintic interaction vertex represents an essential first step in further extending the off-shell validity of the KLT relations to higher order vertices

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

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

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

On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

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

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

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

Variable-coefficient higher-order nonlinear Schroedinger model in optical fibers: Variable-coefficient bilinear form, Baecklund transformation, brightons and symbolic computation

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

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....

Erwin Schroedinger

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

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

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.

Cubic–quintic long-range interactions with double well potentials

International Nuclear Information System (INIS)

Tsilifis, Panagiotis A; Kevrekidis, Panayotis G; Rothos, Vassilis M

2014-01-01

In the present work, we examine the combined effects of cubic and quintic terms of the long-range type in the dynamics of a double well potential. Employing a two-mode approximation, we systematically develop two cubic–quintic ordinary differential equations and assess the contributions of the long-range interactions in each of the relevant prefactors, gauging how to simplify the ensuing dynamical system. Finally, we obtain a reduced canonical description for the conjugate variables of relative population imbalance and relative phase between the two wells and proceed to a dynamical systems analysis of the resulting pair of ordinary differential equations. While in the case of cubic and quintic interactions of the same kind (e.g. both attractive or both repulsive), only a symmetry-breaking bifurcation can be identified, a remarkable effect that emerges e.g. in the setting of repulsive cubic but attractive quintic interactions is a ‘symmetry-restoring’ bifurcation. Namely, in addition to the supercritical pitchfork that leads to a spontaneous symmetry breaking of the antisymmetric state, there is a subcritical pitchfork that eventually reunites the asymmetric daughter branch with the antisymmetric parent one. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. The model is argued to be of physical relevance, especially so in the context of optical thermal media. (paper)

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.)

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

New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schroedinger equation via ∂-macron-dressing method

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

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

Quintic quasi-topological gravity

Energy Technology Data Exchange (ETDEWEB)

Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)

2017-04-11

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.

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.

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)

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)

A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

Science.gov (United States)

Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

2018-01-01

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

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

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)

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

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.)

Multi-shocks generation and collapsing instabilities induced by competing nonlinearities

KAUST Repository

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.

Global Well-Posedness for Cubic NLS with Nonlinear Damping

KAUST Repository

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.

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.

On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

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

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

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Directory of Open Access Journals (Sweden)

Navnit Jha

2014-04-01

Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schroedinger model

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.)

Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schroedinger model

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.)

Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

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.)

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

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

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

Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schroedinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications

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

Correspondence passed between Einstein and Schroedinger; La correspondance entre Einstein et Schroedinger

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.

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

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.

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

Science.gov (United States)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Soliton-like solutions of a generalized variable-coefficient higher order nonlinear Schroedinger equation from inhomogeneous optical fibers with symbolic computation

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

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

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)

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

Global monodromy modulo 5 of quintic-mirror family

OpenAIRE

Shirakawa, Kennichiro

2011-01-01

The quintic-mirror family is a well-known one-parameter family of Calabi-Yau threefolds. A complete description of the global monodromy group of this family is not yet known. In this paper, we give a presentation of the global monodromy group in the general linear group of degree 4 over the ring of integers modulo 5.

Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

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

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 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

A variable-coefficient unstable nonlinear Schroedinger model for the electron beam plasmas and Rayleigh-Taylor instability in nonuniform plasmas: Solutions and observable effects

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

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

Directory of Open Access Journals (Sweden)

Feng-Tao He

2013-01-01

Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.

Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

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

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)

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

Optical rogue waves generation in a nonlinear metamaterial

Science.gov (United States)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

poincare surface analysis of two coupled quintic oscillators in a ...

African Journals Online (AJOL)

DJFLEX

We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...

Poincare surface analysis of two coupled quintic oscillators in a ...

African Journals Online (AJOL)

We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...

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.)

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.)

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, 2.799nonlinear Schroedinger equation is no longer valid. In this case, another system of equations is derived, which governs both the wave amplitudes involved in this resonance between the fundamental torsional and its second-harmonic longitudinal modes.

A life of Erwin Schroedinger

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.

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

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

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

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

Maximum safe speed estimation using planar quintic Bezier curve with C2 continuity

Science.gov (United States)

Ibrahim, Mohamad Fakharuddin; Misro, Md Yushalify; Ramli, Ahmad; Ali, Jamaludin Md

2017-08-01

This paper describes an alternative way in estimating design speed or the maximum speed allowed for a vehicle to drive safely on a road using curvature information from Bezier curve fitting on a map. We had tested on some route in Tun Sardon Road, Balik Pulau, Penang, Malaysia. We had proposed to use piecewise planar quintic Bezier curve while satisfying the curvature continuity between joined curves in the process of mapping the road. By finding the derivatives of quintic Bezier curve, the value of curvature was calculated and design speed was derived. In this paper, a higher order of Bezier Curve had been used. A higher degree of curve will give more freedom for users to control the shape of the curve compared to curve in lower degree.

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)

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....

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

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 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

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

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

Travelling wave solutions to the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Nickel, J.

2007-01-01

Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by Schuermann to find physical (real and bounded) solutions and to discriminate between periodic and solitary wave solutions are used. The method is shown in detail by evaluating new solutions of the Kuramoto-Sivashinsky equation

Schroedinger's Wave Structure of Matter (WSM)

Science.gov (United States)

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

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

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

Schroedinger fluid

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)

Schroedinger operators and evolutionary strategies; Schroedinger-Operatoren und Evolutionaere Strategien

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 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)

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

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.

Science.gov (United States)

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.

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)

New Efficient Fourth Order Method for Solving Nonlinear Equations

Directory of Open Access Journals (Sweden)

Farooq Ahmad

2013-12-01

Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

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.)

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

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

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.

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

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.

Discrete quintic spline for boundary value problem in plate deflation theory

Science.gov (United States)

Wong, Patricia J. Y.

2017-07-01

We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to illustrate the efficiency of our method as well as to compare with other numerical methods proposed in the literature.

Quasi-periodic Schroedinger operators in one dimension, absolutely continuous spectra, Bloch waves, and integrable Hamiltonian systems

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

Spectral Target Detection using Schroedinger Eigenmaps

Science.gov (United States)

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

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)

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

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.)

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.)

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

Directory of Open Access Journals (Sweden)

Ahmed Bendjeddou

2017-03-01

Full Text Available In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.

The Universe according to Schroedinger and Milo

Science.gov (United States)

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.

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

Monodromy of the matrix Schroedinger equations and Darboux transformations

CERN Document Server

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)

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.)

On the distribution of Weierstrass points on Gorenstein quintic curves

Directory of Open Access Journals (Sweden)

Kamel Alwaleed

2016-07-01

Full Text Available This paper is concerned with developing a technique to compute in a very precise way the distribution of Weierstrass points on the members of any 1-parameter family Ca, a∈C, of Gorenstein quintic curves with respect to the dualizing sheaf KCa. The nicest feature of the procedure is that it gives a way to produce examples of existence of Weierstrass points with prescribed special gap sequences, by looking at plane curves or, more generally, to subcanonical curves embedded in some higher dimensional projective space.

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

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)

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 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)

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

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

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.

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

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

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

Solitons and rogue waves for a higher-order nonlinear Schroedinger-Maxwell-Bloch system in an erbium-doped fiber

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.

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.)

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

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)

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.

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

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.)

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

Science.gov (United States)

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 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

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.)

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

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

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.

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

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.

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

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.

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.)

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

Science.gov (United States)

Meza, L. E. Arroyo; Dutra, A. de Souza; Hott, M. B.; Roy, P.

2015-01-01

By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT )-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.

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

Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors

KAUST Repository

Bartoň, Michael

2017-03-21

We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.

Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors

KAUST Repository

Barton, Michael; Ait-Haddou, Rachid; Calo, Victor Manuel

2017-01-01

We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.

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

Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

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

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)

Nonlinear many-body reaction theories from nuclear mean field approximations

International Nuclear Information System (INIS)

Griffin, J.J.

1983-01-01

Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

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

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

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)

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)

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

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...

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

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

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

Science.gov (United States)

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.

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

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

Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview

Directory of Open Access Journals (Sweden)

Fernando D. Nobre

2017-01-01

Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.

KAM for the non-linear Schroedinger equation

CERN Document Server

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 $...

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

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.)

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.

Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions.

Science.gov (United States)

Soto-Crespo, J M; Grelu, Philippe; Akhmediev, Nail

2006-05-01

We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic Ginzburg-Landau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into "rockets" i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interaction planes.

Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation

CERN Document Server

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.

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

Nonlinear wave propagation in discrete and continuous systems

Science.gov (United States)

Rothos, V. M.

2016-09-01

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

Propagation of dispersion-nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

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 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

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

Nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas

International Nuclear Information System (INIS)

Shukla, P.K.

1993-01-01

The nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas is considered. Stimulated scattering mechanisms involving electromagnetic and acoustic waves in an unmagnetized plasma are investigated. The growth rate and threshold for three-wave decay interactions as well as modulational and filamentation instabilities are presented. Furthermore, the electromagnetic wave modulation theory is generalized for weakly ionized collisional magnetoplasmas. Here, the radiation envelope is generally governed by a nonlinear Schroedinger equation. Accounting for the dependence of the attachment frequency on the radiation intensity, ponderomotive force, as well as the differential Joule heating nonlinearity, the authors derive the equations for the nonthermal electron density and temperature perturbations. The various nonlinear terms in the electron motion are compared. The problems of self-focusing and wave localization are discussed. The relevance of the investigation to ionospheric modification by powerful electromagnetic waves is pointed out

The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

Science.gov (United States)

Djoko, Martin; Kofane, T. C.

2018-06-01

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

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

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

Erwin Schroedinger and the rise of wave mechanics. I. Schroedinger's scientific work before the creation of wave mechanics

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

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.)

Schroedinger's cat

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.

Schroedinger's cat

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)

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.)

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

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

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.)

Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems

KAUST Repository

Trillo, S.

2014-12-03

We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.

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.

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....

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

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)

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

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

Energy Technology Data Exchange (ETDEWEB)

Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

2013-03-15

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

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

Integrability and soliton in a classical one dimensional site dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

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)

An algebraic formulation of quantum electrodynamics. [Fermi method, Schroedinger representation, Weylalgebra

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.

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

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.)

Nonlinear mode conversion with chaotic soliton generation at plasma resonance

International Nuclear Information System (INIS)

Pietsch, H.; Laedke, E.W.; Spatschek, K.H.

1993-01-01

The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations

Investigation of solutions of boundary-value singular perturbated problem for Schroedinger equation of 4th order

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)

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

Singular vectors and invariant equations for the Schroedinger algebra in n ≥ 3 space dimensions. The general case

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.

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

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)

Propagation of optical vortex beams and nucleation of vortex-antivortex pairs in disordered nonlinear photonic lattices

International Nuclear Information System (INIS)

Cho, Yeong-Kwon; Kim, Ki-Hong

2014-01-01

The propagation of optical vortex beams through disordered nonlinear photonic lattices is numerically studied. The vortex beams are generated by using a superposition of several Gaussian laser beams arranged in a radially-symmetric manner. The paraxial nonlinear Schroedinger equation describing the longitudinal propagation of the beam array through nonlinear triangular photonic lattices with two-dimensional disorder is solved numerically by using the split-step Fourier method. We find that due to the spatial disorder, the vortex beam is destabilized after propagating a finite distance and new vortex-antivortex pairs are nucleated at the positions of perfect destructive interference. We also find that in the presence of a self-focusing nonlinearity, the vortex-antivortex pair nucleation is suppressed and the vortex beam becomes more stable, while a self-defocusing nonlinearity enhances the vortex-antivortex pair nucleation.

Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

International Nuclear Information System (INIS)

Plyushchay, Mikhail S.; Nieto, Luis-Miguel

2010-01-01

We study supersymmetry of a self-isospectral one-gap Poeschl-Teller system in the light of a mirror symmetry that is based on spatial and shift reflections. The revealed exotic, partially broken, nonlinear supersymmetry admits seven alternatives for a grading operator. One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, nonperiodic Bogoliubov-de Gennes system. The latter possesses a nonlinear supersymmetric structure, in which any of the three nonlocal generators of a Clifford algebra may be chosen as the grading operator. We find that the supersymmetry generators for both systems are the Darboux-dressed integrals of a free spin-1/2 particle in the Schroedinger picture, or of a free massive Dirac particle. Nonlocal Foldy-Wouthuysen transformations are shown to be involved in the supersymmetric structure.

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

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

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

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)

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)

Mirror quintic vacua: hierarchies and inflation

Energy Technology Data Exchange (ETDEWEB)

Bizet, Nana Cabo [Mandelstam Institute for Theoretical Physics, School of Physics,and NITheP, University of the Witwatersrand, WITS 2050, Johannesburg (South Africa); Departamento de Física, Universidad de Guanajuato,Loma del Bosque 103, CP 37150, León, Guanajuato (Mexico); Loaiza-Brito, Oscar [Departamento de Física, Universidad de Guanajuato,Loma del Bosque 103, CP 37150, León, Guanajuato (Mexico); Zavala, Ivonne [Department of Physics, Swansea University, Singleton Park,Swansea, SA2 8PP (United Kingdom)

2016-10-17

We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in ℙ{sup 4}. We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton τ and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in http://dx.doi.org/10.1103/PhysRevD.66.106006, http://dx.doi.org/10.1007/JHEP03(2011)119. We explore slow-roll inflationary directions of the scalar potential by looking at regions where the multi-field slow-roll parameters ϵ and η are smaller than one. The value of ϵ depends strongly on the approximation of the periods and to achieve a stable value, several orders in the expansion are needed. We do not find realizations of single field axion monodromy inflation. Instead, we find that inflationary regions appear along linear combinations of the four real field directions and for certain configurations of fluxes.

Self-focusing of nonlinear waves in a relativistic plasma with positive and negative ions

International Nuclear Information System (INIS)

Mukherjee, Joydeep; Chowdhury, A.R.

1994-01-01

The phenomenon of self-focusing of nonlinear waves was analysed in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. The effect of the inertia of the relativistic electron is also considered by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schroedinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing. 10 refs., 2 figs

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

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

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Devine, N., E-mail: nnd124@rsphysse.anu.edu.au [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Ankiewicz, A. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Genty, G. [Tampere University of Technology, Optics Laboratory, FI-33101 Tampere (Finland); Dudley, J.M. [Institut FEMTO-ST UMR 6174 CNRS/Universite de Franche-Comte, Besancon (France); Akhmediev, N. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia)

2011-11-07

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

International Nuclear Information System (INIS)

Devine, N.; Ankiewicz, A.; Genty, G.; Dudley, J.M.; Akhmediev, N.

2011-01-01

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

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

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

Single and multiple vibrational resonance in a quintic oscillator with monostable potentials.

Science.gov (United States)

Jeyakumari, S; Chinnathambi, V; Rajasekar, S; Sanjuan, M A F

2009-10-01

We analyze the occurrence of vibrational resonance in a damped quintic oscillator with three cases of single well of the potential V(x)=1/2omega(0)(2)x(2)+1/4betax(4)+1/6gammax(6) driven by both low-frequency force f cos omegat and high-frequency force g cos Omegat with Omega > omega. We restrict our analysis to the parametric choices (i) omega(0)(2), beta, gamma > 0 (single well), (ii) omega(0)(2), gamma > 0, beta 0, beta arbitrary, gamma choice (i) at most one resonance occur while for the other two choices (ii) and (iii) multiple resonance occur. Further, g(VR) is found to be independent of the damping strength d while omega(VR) depends on d. The theoretical predictions are found to be in good agreement with the numerical result. We illustrate that the vibrational resonance can be characterized in terms of width of the orbit also.

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.)

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

Non-Markovian stochastic Schroedinger equations: Generalization to real-valued noise using quantum-measurement theory

International Nuclear Information System (INIS)

Gambetta, Jay; Wiseman, H.M.

2002-01-01

Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction

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.

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

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.

Quantum theory of single events: Localized de Broglie-wavelets, Schroedinger waves and classical trajectories

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

Bound State Eigenvalues of the Schroedinger Eq. in two Spatial Variables.

Science.gov (United States)

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.

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

Kuznetsov-Ma waves train generation in a left-handed material

Science.gov (United States)

Atangana, Jacques; Giscard Onana Essama, Bedel; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Crépin Kofane, Timoléon

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

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.)

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 .

Studies of particles statistics in one and two dimensions, based on the quantization methods of Heisenberg, Schroedinger and Feynman

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

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.

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

... of optical solitons. Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations ... of optical solitons. Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers ... Spinning solitons in cubic-quintic nonlinear media.

An inverse boundary value problem for the Schroedinger operator with vector potentials in two dimensions

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

A q-Schroedinger algebra, its lowest weight representations and generalized q-deformed heat equations

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

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

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

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

Mathematical analysis of the dimensional scaling technique for the Schroedinger equation with power-law potentials

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.

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

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.

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

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

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)

Bouncing dynamics of Bose–Einstein condensates under the effects of gravity

Energy Technology Data Exchange (ETDEWEB)

Sekh, Golam Ali, E-mail: golamali.sekh@ba.infn.it [Department of Physics, University of Kashmir, Hazratbal, Srinagar-190006, J & K (India); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari (Italy)

2017-03-03

Bouncing dynamics of quasi-one dimensional Bose–Einstein condensates (BECs) falling under gravity on delta-function potentials is investigated. First, we consider a single component BEC in the presence of cubic-quintic nonlinearity and study dynamical behavior of different parameters of the system using variational and numerical approaches. We see that the quintic nonlinearity plays a dominant role over cubic nonlinear interaction to extend the bouncing dynamics in the non-linear regime. We find that a matter-wave performs bouncing motion only for certain discrete values of initial position above the reflecting potential. We then consider bouncing dynamics of binary BECs. It is shown that the pair of matter-waves bounces together if inter-species interaction is attractive. However, their pairing breaks down if the inter-species interaction is made repulsive. - Highlights: • Single and coupled BECs • Effects of inter-component interaction and gravity • Periodic and quasi-periodic dynamics • Fermi-type acceleration.

On the construction of coherent states of position dependent mass Schroedinger equation endowed with effective potential

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.

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)

Erwin Schroedinger's views on gravitational physics during his last years at the University of Vienna and some research ensuing from it

International Nuclear Information System (INIS)

Halpern, L.

1987-01-01

The author, who was Schroedinger's assistant during his last years in Vienna, gives an account of Schroedinger's views and activities during that time which lead him to a different approach to research on the relations between gravitation and quantum phenomena. Various features of past research are outlined in nontechnical terms. A heuristic argument is presented for the role of the zero-point energy of massive particles in counteracting gravitational collapse and the formation of horizons. Arguments are presented for the view that progress in describing extreme gravitational phenomena can be achieved by the new outlook obtained from the introduction of the analog of Maxwell's vacuum displacement term with a quasiconstant parameter, rather than from renormalization of special processes, even if this is successful. The results can be expected to be in accord with Schroedinger's conjectures. A physical interpretation for the change of sign of the differential invariant of Karlhede, Lindstroem, and Aman at the horizon is suggested. Some important historical details about Schroedinger are touched upon

The Schroedinger problem

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

On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Energy Technology Data Exchange (ETDEWEB)

Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

2005-01-28

Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

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

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.))

The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

International Nuclear Information System (INIS)

Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

2009-01-01

The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

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.)

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.)

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

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

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.)

Quaternionic factorization of the Schroedinger operator and its applications to some first-order systems of mathematical physics

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

Quaternionic factorization of the Schroedinger operator and its applications to some first-order systems of mathematical physics

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.

Contribution to the establishment and resolution of the Schroedinger equation in a Riemannian manifold with constant curvature

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

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

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)

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.).

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

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.)

Chaotic synchronization of two complex nonlinear oscillators

International Nuclear Information System (INIS)

Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.

2009-01-01

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

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

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

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.

Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices

International Nuclear Information System (INIS)

Rojas-Rojas, S.; Vicencio, R. A.; Molina, M. I.; Abdullaev, F. Kh.

2011-01-01

Modulational instability and discrete matter wave solitons in dipolar BECs, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a dipolar nonlinear lattice is studied and the regions of instability are established. The existence and stability of bulk discrete solitons are analyzed analytically and confirmed by numerical simulations. In marked contrast with the usual discrete nonlinear Schroedinger behavior (no dipolar interactions), we found a region where the two fundamental modes are simultaneously unstable, allowing enhanced mobility across the lattice for large norm values. To study the existence and properties of surface discrete solitons, an analysis of the dimer configuration is performed. The properties of symmetric and antisymmetric modes including stability diagrams and bifurcations are investigated in closed form. For the case of a bulk medium, properties of fundamental on-site and intersite localized modes are analyzed. On-site and intersite surface localized modes are studied, and we find that they do not exist when nonlocal interactions predominate with respect to local ones.

Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations

Energy Technology Data Exchange (ETDEWEB)

Mikaelian, K O

2009-09-28

We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.

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

Stabilization of solitons under competing nonlinearities by external potentials

Energy Technology Data Exchange (ETDEWEB)

Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

2014-12-15

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

Spatiotemporal structure of pulsating solitons in the cubic-quintic Ginzburg-Landau equation: A novel variational formulation

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: smancas@mail.ucf.edu; Roy Choudhury, S. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: choudhur@longwood.cs.ucf.edu

2009-04-15

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic-quintic Ginzburg-Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Next, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the starting formulation

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.)

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.

KAM for the non-linear Schroedinger equation a short presentation

CERN Document Server

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 ...

Semi-classical propagation of wavepackets for the phase space Schroedinger equation: interpretation in terms of the Feichtinger algebra

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

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.

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

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

Science.gov (United States)

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.

Effects of three-body interactions in the parametric and modulational instabilities of Bose–Einstein condensates

International Nuclear Information System (INIS)

Wamba, Etienne; Mohamadou, Alidou; Ekogo, Thierry B.; Atangana, Jacque; Kofane, Timoleon C.

2011-01-01

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic–quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated. -- Highlights: ► The parametric MI for the 1D GPE with a cubic–quintic nonlinearity is analyzed. ► The two- and three-body recombination and time-dependent scattering length is considered. ► We generate bright matter waves soliton through MI.

Numerical method for the nonlinear Fokker-Planck equation

International Nuclear Information System (INIS)

Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

1997-01-01

A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

Continuous analog of Newton's method for determination of quasistationary solutions of the Schroedinger equation

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

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Science.gov (United States)

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.

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

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 instability of nonlinear surface waves in an electrified liquid jet

International Nuclear Information System (INIS)

Moatimid, Galal M

2009-01-01

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schroedinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

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

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.)

Solitons supported by localized nonlinearities in periodic media

International Nuclear Information System (INIS)

Dror, Nir; Malomed, Boris A.

2011-01-01

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single δ function or a combination of two δ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the δ functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single δ function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive δ function in the absence of the periodic potential is completely unstable. In addition, we show that the δ function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single δ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two δ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the δ functions set symmetrically with respect to the minimum or maximum of the underlying potential.

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

Symmetries in Hall-like systems: microwave and nonlinear transport effects

International Nuclear Information System (INIS)

Torres, Manuel; Kunold, Alejandro

2008-01-01

In this work, we present a model to describe the nonlinear response to a dc electrical current of a two-dimensional electron system subjected to magnetic and microwave fields. Considering the separation of the electron coordinates into the non-commuting relative and guiding center coordinates, we obtain a unitary transformation that exactly solves the time-dependent Schroedinger equation in the presence of arbitrarily strong electric, magnetic and microwave fields. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We discuss results related to the recently discovered zero-resistance states and to the microwave-induced resistivity oscillations and the Hall-induced resistivity oscillations

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.

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

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

Recent developments in quantum plasma physics

International Nuclear Information System (INIS)

Shukla, P K; Eliasson, B

2010-01-01

We present a review of recent developments in nonlinear quantum plasma physics involving quantum hydrodynamics and effective nonlinear Schroedinger equation formalisms, for describing collective phenomena in dense quantum plasmas with degenerate electrons. As examples, we discuss simulation studies of the formation and dynamics of dark solitons and quantum vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in dense quantum-electron plasmas with immobile ions. The electron dynamics of dark solitons and quantum vortices is governed by a pair of equations comprising the nonlinear Schroedinger and Poisson system of equations. Both dark solitons and singly charged electron vortices are robust, and the latter tend to form pairs of oppositely charged vortices. The two-dimensional quantum-electron vortex pairs survive during collisions under the change of partners. The dynamics of the CPEM waves is governed by a nonlinear Schroedinger equation, which is nonlinearly coupled with the Schroedinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one-spatial dimension admit stationary solutions in the form of dark solitons. The nonlinear equations also depict trapping of localized CPEM wave envelopes in the electron density holes that are associated with a positive potential profile.

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 ...

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.

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.

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.)

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

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

AUTHOR INDEX

Indian Academy of Sciences (India)

Arumugam M. Optical fiber communication – An overview. 849. Arumugam P ... Spinning solitons in cubic-quintic nonlinear media. 1041. Dang Nguyen Dinh. E1 resonances in .... Measuring the top quark mass in the eµ chan- nel: A study. 689.

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

Supersymmetric quantum mechanics approach to a nonlinear lattice

International Nuclear Information System (INIS)

Ricotta, Regina Maria; Drigo Filho, Elso

2011-01-01

Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)

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.

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.

Impulsive moving mirror model and the stability of Schroedinger equation with impulse effect in a Banach space

International Nuclear Information System (INIS)

Kostadinov, S.I.; Petrov, G.

1992-01-01

From a special class of systems has been used a Schroedinger equation with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studying the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. So the stability of the solution of the Schroedinger evolution equation for the process in the stability of the vacuum of Casimir. 8 refs

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.

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

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.)

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.

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)

Canonical quantization of non-abelian gauge theory in the Schroedinger picture: applications to monopoles and instantons

International Nuclear Information System (INIS)

Wadia, S.R.

1979-01-01

A detailed formulation of the quantum theory of non-abelian gauge fields is presented in the Schroedinger picture. It is applied to the semiclassical quantization of the t'Hoft-Polyakov monopole, with special attention paid to the treatment of boundary conditions and local and global gauge symmetry. The perturbation expansion is then discussed with the aid of standard collective co-ordinates. In the Prasad-Sommerfield limit, all the eigenfunctions of the fluctuation equation are presented, the ground-state wave function is constructed in terms of gauge and translation invariant co-ordinates, and its total angular momentum is computed to be zero. Aspects of instanton phenomena are then examined in the Schroedinger picture; the role of euclidean time is elucidated. The precise relation between boundary conditions, choice of gauge, and the corresponding picture of the semiclassical vacuum is demonstrated

Many particle systems with inverse square potential, Riccatti equation and completely integrable systems connected with Schroedinger operator

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

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

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 density of states for almost periodic Schroedinger operators and the frequency module: a counter-example

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

Radiation from nonlinear coupling of plasma waves

International Nuclear Information System (INIS)

Fung, S.F.

1986-01-01

The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet

A discovery of quite exceptional importance. Schroedinger's correspondence on wave mechanics and on the cat paradoxon

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.

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

Dynamics of wide and snake-like pulses in coupled Schrödinger equations with full-modulated nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu

2016-02-05

We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.

Time-dependent Schroedinger equations with effective mass in (2 + 1) dimensions: intertwining relations and Darboux operators

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).

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

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.

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.

Dynamical barrier for the formation of solitary waves in discrete lattices

International Nuclear Information System (INIS)

Kevrekidis, P.G.; Espinola-Rocha, J.A.; Drossinos, Y.; Stefanov, A.

2008-01-01

We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation

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

Reconstructing a nonlinear dynamical framework for testing quantum mechanics

International Nuclear Information System (INIS)

Jordan, T.F.

1993-01-01

The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs

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.

Inverse spectral results for Schroedinger operators on the unit interval with partial information given on the potentials

International Nuclear Information System (INIS)

Amour, L.; Raoux, T.; Faupin, J.

2009-01-01

We pursue the analysis of the Schroedinger operator on the unit interval in inverse spectral theory initiated in the work of Amour and Raoux [''Inverse spectral results for Schroedinger operators on the unit interval with potentials in Lp spaces,'' Inverse Probl. 23, 2367 (2007)]. While the potentials in the work of Amour and Raoux belong to L 1 with their difference in L p (1≤p k,1 spaces having their difference in W k,p , where 1≤p≤+∞, k(set-membership sign)(0,1,2). It is proved that two potentials in W k,1 ([0,1]) being equal on [a,1] are also equal on [0,1] if their difference belongs to W k,p ([0,a]) and if the number of their common eigenvalues is sufficiently high. Naturally, this number decreases as the parameter a decreases and as the parameters k and p increase

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)

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)

Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

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.)

Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit

International Nuclear Information System (INIS)

Yan Zhanyuan; Zhang Xiaohong; Ma Jinying

2009-01-01

The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoscopic circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schroedinger equation of the system is a four-order difference equation in p-circumflex representation. Using the extended perturbative method, the detail energy spectrum and wave functions are obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopic circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.

On the quantization of a nonlinear oscillator with quasi-harmonic behaviour

International Nuclear Information System (INIS)

Ranada, M.F.; Carinena, J.F.; Satander, M.

2006-01-01

Full text: (author)The quantum version of a non-linear oscillator, depending of a parameter λ, is studied. This λ-dependent system can be considered deformation of the harmonic oscillator in the sense that for λ→0 all the characteristics of the linear oscillator are recovered. This is a problem of quantization of a system with position-dependent mass and with a λ-dependent nonpolynominal rational potential. The quantization problem is solved using existence of a Killing vector, the λ-dependent Schroedinger equation is exactly solved and λ-dependent eigenenergies and eigenfunctions are obtained. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as deformations of the standard Hermite polynomials. In the second part, it is proved the superintegrability of the two-dimensional system

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

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)

Dynamical barrier for the formation of solitary waves in discrete lattices

Energy Technology Data Exchange (ETDEWEB)

Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States)], E-mail: kevrekid@math.umass.edu; Espinola-Rocha, J.A. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See,) (Italy); School of Mechanical and Systems Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523 (United States)

2008-03-24

We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation.

Breaking the hidden symmetry in the Ginzburg-Landau equation

NARCIS (Netherlands)

Doelman, A.

1997-01-01

In this paper we study localised, traveling, solutions to a Ginzburg-Landau equation to which we have added a small, O ( " ), 0 < "? 1, quintic term. We consider this term as a model for the higher order nonlinearities which appear in the derivation of the Ginzburg-Landau equation. By a combination

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.

The essential spectrum of Schroedinger operators with asymptotically constant magnetic fields on the Poincare upper-half plane

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

Nonstationary quantum mechanics. 4. Nonadiabatic properties of the Schroedinger equation in adiabatic processes

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.

Nonstationary quantum mechanics. IV. Nonadiabatic properties of the Schroedinger equation in adiabatic processes

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.

On the discrete spectrum of non-self-adjoint Schroedinger differential equation with an operator coefficient

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

Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

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.).

Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

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.)

SOq(N) covariant differential calculus on quantum space and quantum deformation of Schroedinger equation

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.)

An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

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

An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

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.

Asymptotic iteration method solutions to the d-dimensional Schroedinger equation with position-dependent mass

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.

On quasiclassical approximation in the inverse scattering method

International Nuclear Information System (INIS)

Geogdzhaev, V.V.

1985-01-01

Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem

Spectral transform and solvability of nonlinear evolution equations

International Nuclear Information System (INIS)

Degasperis, A.

1979-01-01

These lectures deal with an exciting development of the last decade, namely the resolving method based on the spectral transform which can be considered as an extension of the Fourier analysis to nonlinear evolution equations. Since many important physical phenomena are modeled by nonlinear partial wave equations this method is certainly a major breakthrough in mathematical physics. We follow the approach, introduced by Calogero, which generalizes the usual Wronskian relations for solutions of a Sturm-Liouville problem. Its application to the multichannel Schroedinger problem will be the subject of these lectures. We will focus upon dynamical systems described at time t by a multicomponent field depending on one space coordinate only. After recalling the Fourier technique for linear evolution equations we introduce the spectral transform method taking the integral equations of potential scattering as an example. The second part contains all the basic functional relationships between the fields and their spectral transforms as derived from the Wronskian approach. In the third part we discuss a particular class of solutions of nonlinear evolution equations, solitons, which are considered by many physicists as a first step towards an elementary particle theory, because of their particle-like behaviour. The effect of the polarization time-dependence on the motion of the soliton is studied by means of the corresponding spectral transform, leading to new concepts such as the 'boomeron' and the 'trappon'. The rich dynamic structure is illustrated by a brief report on the main results of boomeron-boomeron and boomeron-trappon collisions. In the final section we discuss further results concerning important properties of the solutions of basic nonlinear equations. We introduce the Baecklund transform for the special case of scalar fields and demonstrate how it can be used to generate multisoliton solutions and how the conservation laws are obtained. (HJ)

Geon-type solutions of the non-linear Heisenberg-Klein-Gordon equation

International Nuclear Information System (INIS)

Mielke, E.W.; Scherzer, R.

1980-10-01

As a model for a ''unitary'' field theory of extended particles we consider the non-linear Klein-Gordon equation - associated with a ''squared'' Heisenberg-Pauli-Weyl non-linear spinor equation - coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schroedinger type wave functions within the ''scalar geon''. For zero angular momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding ''principal quantum number'' reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particle-like structure of these ''quantized geons''. (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

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

Gauge invariance of the Rayleigh--Schroedinger time-independent perturbation theory

International Nuclear Information System (INIS)

Yang, K.H.

1977-08-01

It is shown that the Rayleigh-Schroedinger time-independent perturbation theory is gauge invariant when the operator concerned is the particle's instantaneous energy operator H/sub B/ = (1/2m)[vector p - (e/c) vector A] 2 + eV 0 . More explicitly, it is shown that the energy perturbation corrections of each individual order of every state is gauge invariant. When the vector potential is curlless, the energy corrections of all orders are shown to vanish identically regardless of the explicit form of the vector potential. The relation between causality and gauge invariance is investigated. It is shown that gauge invariance guarantees conformity with causality and violation of gauge invariance implies violation of causality

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)

On the stability of solitary waves for classical scalar fields

International Nuclear Information System (INIS)

Blanchard, P.; Stubbe, J.; Vazquez, L.

1986-01-01

We study the stability for the bound states of lowest action of certain nonlinear Klein-Gordon and Schroedinger equations by applying the Shatah-Strauss formalism. We extend the range of application of this formalism by using a recent existence theorem for minimum action solutions to a large class of equations including logarithmic Klein-Gordon equation and logarithmic Schroedinger equation and scalar fields with fractional non-linearities. Furthermore we discuss the relation between different stability criteria considered in the literature. (orig.)

Breaking the hidden symmetry in the Ginzburg-Landau equation

NARCIS (Netherlands)

Doelman, A.

1996-01-01

In this paper we study localised, traveling, solutions to a Ginzburg-Landau equation to which we have added a small, O(e), 0 < e << 1, quintic term. We consider this term as a model for the higher order nonlinearities which appear in the derivation of the Ginzburg-Landau equation. By a combination

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

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

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)

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.

Antibound states for a class of one-dimensional Schroedinger Operators

International Nuclear Information System (INIS)

Angeletti, A.

1980-01-01

Let delta(x) be the Dirac's delta, q(x) element of L 1 (R) L 2 (R) be a real valued function, and lambda, μ element of R; we will consider the following class of one-dimensional formal Schroedinger operators on L 2 (R) H(lambda,μ) = - (d 2 /dx 2 ) + lambdadelta(x) + μq(x). It is known that to the formal operator H(lambda, μ) may be associated a selfadjoint operator H(lambda, μ) on L 2 (R). If q is of finite range, for lambda < 0 and /μ/ is small enough, we prove that H(lambda,μ) has an antibound state; that is the resolvent of H(lambda,μ) has a pole on the negative real axis on the second Riemann sheet. (orig.)

Multi-soliton and rogue-wave solutions of the higher-order Hirota system for an erbium-doped nonlinear fiber

Energy Technology Data Exchange (ETDEWEB)

Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics

2014-10-15

The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.

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

Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

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.

Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

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.

A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

International Nuclear Information System (INIS)

Xia Tiecheng; Chen Xiaohong; Chen Dengyuan

2004-01-01

An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations

Self-focusing of electromagnetic waves as a result of relativistic electron-mass variation

International Nuclear Information System (INIS)

Spatschek, K.H.

1977-01-01

Relativistic electron-mass variations due to the presence of intense electromagnetic radiation in the plasma cause a nonlinear refractive index. Using a variational principle the latter is obtained up to fourth order in the electric field amplitude and it is shown that nonlinear effects of the second order lead to self-focusing of a beam of radiation. By nonlinear optics considerations, the self-focusing length of an axially symmetric beam is obtained. Including higher-order dispersive effects it is shown that within the thin-beam approximation the complex electric field envelope obeys a cubic nonlinear Schroedinger equation with an attractive self-consistent potential. The cylindrically symmetric nonlinear Schroedinger equation predicts collapse of the radiation at the self-focusing distance. The nature of the self-focusing singularity is analysed and it is shown that higher-order nonlinearities saturate the amplitude. Then oscillations of the beam radius along the axial direction occur. (author)

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.)

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.

Computation of a long-time evolution in a Schroedinger system

International Nuclear Information System (INIS)

Girard, R.; Kroeger, H.; Labelle, P.; Bajzer, Z.

1988-01-01

We compare different techniques for the computation of a long-time evolution and the S matrix in a Schroedinger system. As an application we consider a two-nucleon system interacting via the Yamaguchi potential. We suggest computation of the time evolution for a very short time using Pade approximants, the long-time evolution being obtained by iterative squaring. Within the technique of strong approximation of Moller wave operators (SAM) we compare our calculation with computation of the time evolution in the eigenrepresentation of the Hamiltonian and with the standard Lippmann-Schwinger solution for the S matrix. We find numerical agreement between these alternative methods for time-evolution computation up to half the number of digits of internal machine precision, and fairly rapid convergence of both techniques towards the Lippmann-Schwinger solution

Capriccio For Strings: Collision-Mediated Parallel Transport in Curved Landscapes and Conifold-Enhanced Hierarchies among Mirror Quintic Flux Vacua

Science.gov (United States)

Eckerle, Kate

theories that arise from the low energy limit of flux vacua built on type IIb string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution of Taylor coefficients in a polynomial expansion of each model's scalar potential to fourth order. We provide an analytic explanation of the proncounced hierarchies exhibited by the random sample of masses and couplings generated numerically. The analytic argument is based on the structure of masses in no scale supergravity and the divergence of the Yukawa coupling at the conifold point in the moduli space of the mirror quintic. Our results cast the superpotential vev as a random element whose capacity to cloud structure vanishes as the conifold is approached.

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.

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Use of time-dependent Schroedinger equation to analyze effect of collectivization of valence neutrons on near-barrier nuclear fusion enhancement

International Nuclear Information System (INIS)

Zagrebaev, V.I.; ); Samarin, V.V.

2006-01-01

Fusion of heavy nuclei was analyzed on the basis of the numerical solution of the Schroedinger three-body and three-dimensional nonstationary equations. One revealed the increase of fuss ion probability in 66 He + 2O Pb reaction caused by transfer and collectivization of valent neutrons [ru

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.

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

Nonlinear rolling of a biased ship in a regular beam wave under external and parametric excitations

Energy Technology Data Exchange (ETDEWEB)

El-Bassiouny, A.F. [Mathematics Dept., Benha Univ., Benha (Egypt)

2007-10-15

We consider a nonlinear oscillator simultaneously excited by external and parametric functions. The oscillator has a bias parameter that breaks the symmetry of the motion. The example that we use to illustrate the problem is the rolling oscillation of a biased ship in longitudinal waves, but many mechanical systems display similar features. The analysis took into consideration linear, quadratic, cubic, quintic, and seven terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. Two methods (the averaging and the multiple time scales) are used to investigate the first-order approximate analytical solution. The modulation equations of the amplitudes and phases are obtained. These equations are used to obtain the stationary state. The stability of the proposed solution is determined applying Liapunov's first method. Effects of different parameters on the system behaviour are investigated numerically. Results are presented graphically and discussed. The results obtained by two methods are in excellent agreement. (orig.)

Continuity and completeness in physical theory: Schroedinger`s return to the wave interpretation of quantum mechanics in the 1950`s

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.

Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

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.

Supersymmetric Solution of the Schroedinger Equation for Woods-Saxon Potential by Using the Pekeris Approximation

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)

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

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

A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Applications

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.)

A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Applications

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.)

Supra-transmission and bistability in nonlinear media with a photonic and electronic forbidden band gap; Supratransmission et bistabilite nonlineaire dans les milieux a bandes interdites photoniques et electroniques

Energy Technology Data Exchange (ETDEWEB)

Chevriaux, D

2007-06-15

We study wave scattering in different nonlinear media possessing a natural forbidden band gap. In particular, we show the existence of a bistable behavior in media governed by the sine-Gordon equation (short pendular chain, Josephson junction array, quantum Hall bilayer), or the nonlinear Schroedinger equation (Kerr and Bragg media), in discrete and continuous models. These different media are submitted to periodic boundary conditions with a frequency in the forbidden band gap and an amplitude that determines their stability states. Indeed, for a sufficient amplitude (supra-transmission), the medium switches from reflector to transmitter, hence allowing the output signal to jump from evanescent to large values. We give a complete analytical description of the bistability that allows to understand the different stationary states observed and to predict the switch of one state to the other. (author)

Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.

1991-01-01

A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs

Comment on: Path integral solution of the Schroedinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310 endash 4319 (1996)

International Nuclear Information System (INIS)

Wurm, A.; LaChapelle, J.

1997-01-01

The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schroedinger equation for the case of n-dimensional spherical coordinates

Solitary wave dynamics in time-dependent potentials

International Nuclear Information System (INIS)

Abou Salem, Walid K.

2008-01-01

The long time dynamics of solitary wave solutions of the nonlinear Schroedinger equation in time-dependent external potentials is rigorously studied. To set the stage, the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schroedinger equation with time-dependent nonlinearities and potential is established. Afterward, the dynamics of NLS solitary waves in time-dependent potentials is studied. It is shown that in the space-adiabatic regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. Finally, two physical applications are discussed: the first is adiabatic transportation of solitons and the second is the Mathieu instability of trapped solitons due to time-periodic perturbations

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

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

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

Science.gov (United States)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Born series for (2 cluster) → (2 cluster) scattering of two, three, and four particle Schroedinger operators

International Nuclear Information System (INIS)

Hagedorn, G.A.

1979-01-01

We investigate elastic and inelastic (2 cluster)→(2 cluster)scattering for classes of two, three, and four body Schroedinger operators H=H 0 +ΣVij. Formulas are derived for those generalized eigenfunctions of H which correspond asymptotically in the past to two freely moving clusters. With these eigenfunctions, we establish a formula for the (2 cluster)→(2 cluster) T-matrix and prove the convergence of a Born series for the T-matrix at high energy. (orig.) [de

One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions

International Nuclear Information System (INIS)

Cardoso, W. B.; Avelar, A. T.; Bazeia, D.

2011-01-01

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

International Nuclear Information System (INIS)

Anastassi, Z. A.; Simos, T. E.

2010-01-01

We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

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.)

A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

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.)

On the solution of the inverse scattering problem for the quadratic bundle of the one-dimensional Schroedinger operators of the whole axis

International Nuclear Information System (INIS)

Maksudov, F.G.; Gusejnov, G.Sh.

1986-01-01

Inverse scattering problem for the quadratic bundle of the Schroedinger one-dimensional operators in the whole axis is solved. The problem solution is given on the assumption of the discrete spectrum absence. In the discrete spectrum presence the inverse scattering problem solution is known for the Shroedinger differential equation considered

The Schroedinger-Poisson equations as the large-N limit of the Newtonian N-body system. Applications to the large scale dark matter dynamics

Energy Technology Data Exchange (ETDEWEB)

Briscese, Fabio [Northumbria University, Department of Mathematics, Physics and Electrical Engineering, Newcastle upon Tyne (United Kingdom); Citta Universitaria, Istituto Nazionale di Alta Matematica Francesco Severi, Gruppo Nazionale di Fisica Matematica, Rome (Italy)

2017-09-15

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schroedinger-Poisson equations in the large N limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as ℎ ∝ M{sup 5/3}G{sup 1/2}(N/ left angle ρ right angle){sup 1/6}, where is G the gravitational constant, N and M are the number and the mass of the bodies, and left angle ρ right angle is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schroedinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales. (orig.)

Recent additions to fundament aspects of quantum mechanics

International Nuclear Information System (INIS)

Flamm, D.

1991-01-01

Problems like those of Schroedinger's can comprise quantum systems as classical systems, the measurement process and reality. After a reviewing the history of interpretation of quantum mechanics it is shown how a generalized algebraic quantum theory (e.g. G.G. Emch 1986) can tackle these problems and paradoxes. This theory treats systems with infinite degrees of freedom and open systems. It is applicable both to quantum as to classical systems and thus to the measurement process with its irreversibility. The usual linear Schroedinger equation is replaced by a non-linear one where the nonlinear terms reflect the interaction of the system with its environment or with the measuring apparatus. (Quittner) To appear also in 'Naturwissenschaft und Weltbild', 1992

On the stability of soliton solution in NLS-type general field model

International Nuclear Information System (INIS)

Chakrabarti, S.; Nayyar, A.H.

1982-08-01

A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)

A particular inverse problem for Schroedinger discrete equation in two and higher dimensions under apriori information of wave functions

International Nuclear Information System (INIS)

Pavlus, M.

1997-01-01

The entire potential and the rest of wave functions are determined in parallelepiped domain if the entire discrete spectrum and the apriori information about the wave functions on one side of parallelepiped are given. Formulation for solving the Schroedinger discrete equation in two and higher dimensions is proposed and new formulas are derived for their solution. Two examples for a 2D case and one example for a 3D case are demonstrated

Variational principles for collective motion: Relation between invariance principle of the Schroedinger equation and the trace variational principle

International Nuclear Information System (INIS)

Klein, A.; Tanabe, K.

1984-01-01

The invariance principle of the Schroedinger equation provides a basis for theories of collective motion with the help of the time-dependent variational principle. It is formulated here with maximum generality, requiring only the motion of intrinsic state in the collective space. Special cases arise when the trial vector is a generalized coherent state and when it is a uniform superposition of collective eigenstates. The latter example yields variational principles uncovered previously only within the framework of the equations of motion method. (orig.)