consistency between adiabatic and non adiabatic geometric phases for non self adjoint hamiltonians we show that the adiabatic approximation for non self adjoint hamiltonians seems to induce two non equal expressions for the geometric phase the first one is related to the spectral projector involved in the adiabatic theorem and the other one is the adiabatic limit of the non adiabatic geometric phase this apparent inconsistency is resolved by observing that the difference between the two expressions is compensated by a small deviation in the dynamical phases

elementary exponential error estimates for the adiabatic approximation we present an elementary proof that the quantum adiabatic approximation is correct up to exponentially small errors for hamiltonians that depend analytically on the time variable our proof uses optimal truncation of a straightforward asymptotic expansion we estimate the terms of the expansion with standard cauchy estimates

adiabatic passage for a lossy two level quantum system by a complex time method using a complex time method with the formalism of stokes lines we establish a generalization of the davis dykhne pechukas formula which gives in the adiabatic limit the transition probability of a lossy two state system driven by an external frequency chirped pulse shaped field the conditions that allow this generalization are derived we illustrate the result with the dissipative allen eberly and rosen zener models

solution of the epidemic model by homotopy perturbation method in this article the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered he s homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear ordinary differential equations governing on the problem the results are compared with the results obtained by adomian decomposition method some plots are presented to show the reliability and simplicity of the method

general adiabatic evolution with a gap condition we consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity away from the rest of the spectrum the restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable

numerical solutions of the nonlinear integro differential equations wavelet galerkin method and homotopy perturbation method this paper compares the homotopy perturbation method with the wavelet galerkin method for solving nonlinear integro differential equations from the computational viewpoint the homotopy perturbation method is more efficient and easy to use

on the adiabatic theorem for nonself adjoint hamiltonians the authors consider the evolution of a two level system driven by a nonself adjoint hamiltonian h in t and treat the adiabatic limit in to 0 while adiabatic theorem like results do not hold true in general for this case they prove that they are still valid for the subspace corresponding to the eigenvalue having the largest imaginary part least dissipative eigenvalue the theory gives the full asymptotic expansion of the evolution restricted to this subspace the first correction beyond berry s phase is to their best knowledge given explicitly for the first time

homotopy perturbation method for solving hyperbolic partial differential equations this paper applies the homotopy perturbation method proposed by ji huan he to obtain approximate analytic solutions of hyperbolic partial differential equations the procedure of the method is systematically illustrated to give an extensive account of the method some examples are provided the results derived by this method will be compared with the results of characteristics method the results of homotopy perturbation method are of high accuracy verifying that the method is very effective and promising

exponentially small adiabatic invariant for the schrodinger equation we study an adiabatic invariant for the time dependent schrfdinger equation which gives the transition probability across a gap from time t to time t when the hamiltonian depends analytically on time and t oo t oo we give sufficient conditions so that this adiabatic invariant tends to zero exponentially fast in the adiabatic limit

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

an improvement to homotopy perturbation method for solving system of linear equations in this paper we present an efficient numerical algorithm to find exact solutions for the system of linear equations based on homotopy perturbation method hpm a reliable modification is proposed and the modified method is employed to solve the system of linear equations the results are compared with those obtained by the original homotopy perturbation method two examples are given to illustrate the ability and reliability of the modified method the results reveal that the modified method is very simple and effective

on the homotopy perturbation method for boussinesq like equations abstract we comment on some analytical solutions to a class of boussinesq like equations derived recently by means of the homotopy perturbation method hpm we show that one may obtain exactly the same result by means of the taylor series in the time variable we derive more general results by means of traveling waves and argue that a curious superposition principle proposed by the author may not be of any mathematical or physical significance

superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum during the last years several theoretical and experimental works have been devoted to different aspects of the adiabatic regime of quantum dynamics we consider here two aspects of this physically important regime the construction of approximate evolutions of the schriidinger equation called superadiabatic evolutions and the explicit computation of the probability of a transition between two nondegenerate energy levels isolated in the spectrum of the hamiltonian from the mathematical point of view the adiabatic limit for time dependent systems is of the same kind as the semiclassical limit for stationary systems it is a singular limit which cannot be tackled by usual perturbation methods recently a mathematical theory of the two considered aspects has been developed when the time dependent hamiltonian is analytic in time the transition probability for two level systems has been studied in refs l 3 and was shown to be exponentially small in the adiabaticity parameter for general systems in ref 4 on the other hand the existence of superadiabatic evolutions has been shown in ref 5 however no general formula for the transition probability between isolated levels in the adiabatic limit can be found in the literature it is the goal of this paper to establish such a formula for general unbounded hamiltonians the paper is divided into two parts we first construct a superadiabatic evolution which approximates the true evolution of the schrijdinger equation up to exponentially small correction terms with respect to the parameter controlling the adiabatic regime once the superadiabatic evolution is defined we show that the computation of the transition probability of the initial problem reduces to an effective two dimensional problem which we analyze as in ref 1 the concept of superadiabatic evolution can be traced back up to a paper of garrido 6 who considered evolutions different from the usual adiabatic evolution which he used to obtain higher order corrections to the adiabatic theorem of quantum mechanics but it is berry7v8 who emphasized the importance of such evolutions in the present problem and introduced the

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

histories of adiabatic quantum transitions the way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation for a 2 state quantum system by transforming to a series of superadiabatic bases clinging ever closer to the exact evolving state it is shown that transition histories renormalize onto a universal one in which the amplitude grows to its final value as an error function rather than via large oscillations as in the ordinary adiabatic basis the time for the universal transition is of order surd hslash delta where delta is the small adiabatic slowness parameter in perturbation theory the pre exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value textstyle frac 1 3 pi for the ordinary adiabatic basis to the correct value unity the various histories could be observed in spin experiments

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

linear adiabatic theory exponential estimates a general adiabatic expansion is written down the basic result is that under appropriate smoothness conditions the adiabatic estimations can be pushed up to exponential order the results imply exponential estimates not only for hamiltonians analytic in a neighbourhood of the real axis but also for hamiltonians which in an appropriate sense beong to gevrey classes

the role of the geometric phases in adiabatic population tracking for non hermitian hamiltonians the definition of instantaneous eigenstate populations for a dynamical non self adjoint system is not obvious the nadirect extension of the definition used for the self adjoint case leads to inconsistencies the resulting artifacts can induce a false inversion of population or a false adiabaticity we show that the inconsistency can be avoided by introducing geometric phases in another possible definition of populations an example is given which demonstrates both the anomalous effects and their removal by our approach

determination of natural frequencies of fluid conveying pipes using homotopy perturbation method in the present paper the natural frequencies of fluid conveying pipes with pinned pinned boundary condition are derived explicitly in a systematical and straightforward way with the help of homotopy perturbation method numerical results are presented for two cases and the effect of fluid flow velocity on the natural frequencies is discussed good agreement with their experimental and fem counterparts is found numerically over ranges of practical interest

travelling wave solutions of two nonlinear evolution equations by using the g g expansion method abstract by using the g g expansion method proposed recently we give the exact travelling wave solutions of two different types of nonlinear evolution equations in this paper the travelling wave solutions are expressed by three types of functions the computation for the method appears to be easier and faster by general mathematical software

some observations on the spectra of positive operators on finite dimensional c algebras abstract the classical theorems of o perron and g frobenius about spectral properties of matrices with positive entries have been studied and generalized by various authors in the book of a berman and r j plemmons 3 the finite dimensional aspects of this theory are described whereas in the two monographs of h h schaefer 20 21 the infinite dimensional theory is developed our purpose is to continue these extensions to finite dimensional c algebras obtaining a complete description of the spectrum of positive irreducible operators on such ordered vector spaces

the travelling wave solutions for non linear initial value problems using the homotopy perturbation method in this article we have used the homotopy perturbation method hpm to find the travelling wave solutions for some non linear initial value problems in the mathematical physics these problems consist of the burgers fisher equation the kuramoto sivashinsky equation the coupled schordinger kdv equations and the long short wave resonance equations together with initial conditions the results of these problems reveal that the hpm is very powerful effective convenient and quite accurate to the systems of non linear equations it is predicted that this method can be found widely applicable in engineering and physics

a new perturbative approach to nonlinear problems a recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the lagrangian such as 4 by 2 1 and then treating as a small parameter it is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the lane emden thomas fermi blasius and duffing equations

application of he s methods to nonlinear chemistry problems in this paper he s variational iteration method vim and homotopy perturbation method hpm are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications in both methods the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions the solution procedure is of utter simplicity and the obtained solution is of high accuracy

almost quantum adiabatic dynamics and generalized time dependent wave operators we consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit to treat these systems we introduce a generalization of the time dependent wave operator theory which is usually used to treat dynamics which do not escape too far from an initial subspace called the active space our generalization is based on a time dependent adiabatic deformation of the active space the geometric phases associated with the almost adiabatic representation are also derived we use this formalism to study the adiabaticity of a dynamics surrounding an exceptional point of a non hermitian hamiltonian we show that the generalized time dependent wave operator can be used to correct easily the adiabatic approximation which is very imperfect in this situation

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method