Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Deriving Energy-Gap of Some Nonlinear Hamiltonians by Invariant Eigen-operator Method

By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value wy2 - wx2 due to the existence of the saddle potential.

An iterative Wiener filtering method based on the gravity gradient invariants

How to deal with colored noises of GOCE （Gravity field and steady - state Ocean Circulation Explorer） satellite has been the key to data processing. This paper focused on colored noises of GOCE gradient data and the frequency spectrum analysis. According to the analysis results, gravity field model of the optima] degrees 90-240 is given, which is recovered by COCE gradient data. This paper presents an iterative Wiener filtering method based on the gravity gradient invariants. By this method a degree-220 model was calculated from GOCE SGG （Satellite Gravity Gradient） data. The degrees above 90 of ITG2010 were taken as the prior gravity field model, replacing the low degree gravity field model calculated by GOCE orbit data. GOCE gradient colored noises was processed by Wiener filtering. Finally by Wiener filtering iterative calculation, the gravity field model was restored by space-wise harmonic analysis method. The results show that the model＇s accuracy matched well with the ESA＇s （European Space Agency） results by using the same data,

Second-order nonlinear differential operators possessing invariant subspaces of submaximal dimension

The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.

Energy Level of Three-Mode Harmonic Oscillator for Coordinate Operators Satisfying Cyclic Commutative Relations Obtained by IEO Method

Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.

Method for array gain and phase uncertainties calibration based on ISM and ESPRIT

A new method for array calibration of array gain and phase uncertainties, which severely degrade the performance of spatial spectrum estimation, is presented. The method is based on the idea of the instrumental sensors method （ISM）, two well-calibrated sensors are added into the original array. By applying the principle of estimation of signal parameters via rotational invariance techniques （ESPRIT）, the direction-of-arrivals （DOAs） and uncertainties can be estimated simultaneously through eigen-decomposition. Compared with the conventional ones, this new method has less computational complexity while has higher estimation precision, what＇s more, it can overcome the problem of ambiguity. Both theoretical analysis and computer simulations show the effectiveness of the proposed method.

Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.

Existence and Concentration of Sign-Changing Solutions of Quasilinear Choquard Equation

In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on RN × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, Iα is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .

Exact solution for the thermo Jaynes Cummings model

Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes Cummings system.

Exact Solution for Jaynes-Cummings Model with Bosonic Field Nonlinearity and Strong Boson-Fermion Coupling

We use Lewis Riesenfeld invariant approach to treat the modified Jaynes-Cummings models involving any forms of nonlinearty of the bosonic field when strong boson-fermion couplings are nilpotent Grassmann valued. The general state functions, time evolution operator and the time-evolution expressions for both the bosonic number and the fermionic number are presented.

Quantum Light and Coherent States in Conducting Media

We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.

Wave Functions for Time-Dependent Morse Potentials

The one dimensional Schrodinger equation associated with a time-dependent Morse potentials is studied. We use the invariant operator method （Lewis and Riesenfeld） to obtain approximate solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the Morse potentials.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.

Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature.The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures,and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions.Three critical magnetic field intensities H_(CB),H_(CE)and H_(CS) were obtained,in which the H_(CB) and H_(CE)correspond to the appearance and disappearance of the 1/3 magnetization plateau,respectively,and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system.The energies of elementary excitation hω_(σ,k)(σ=1,2,3)present the extrema of zero at the three critical magnetic fields at 0 K,i.e.,[hω_(3,k)(H_(CB)]_(min)=0,[hω_(2,k)(H_(CE)]_(max)=0 and[hω_(2,k)(H_(CS)]_(min)=0,and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships.According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities,the magnetic field-temperature phase diagram was drawn.It was observed that if the magnetic phase diagram shows a three-phase critical point,which is intersected by the ferrimagnetic phase,the ferrimagnetic plateau phase,and the Luttinger liquid phase,the disappearance of the 1/3 magnetization plateau would inevitably occur.However,the 1/3 magnetization plateau would not disappear without the three-phase critical point.The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.

Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.

Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation

In this research,invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method,and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles.The governing equations are classified and transformed into a system of ordinary differential equations,and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations.The method gives logarithmic,polynomial,exponential,and trigonometric solutions for equations.The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinarydifferential equations.