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Real eigenvalues determined by recursion of eigenstates
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作者 刘通 王友国 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期196-200,共5页
Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the syste... Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations. 展开更多
关键词 real eigenvalues NON-HERMITIAN QUASIPERIODIC
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Efficient method to calculate the eigenvalues of the Zakharov–Shabat system
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作者 崔世坤 王振 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期243-249,共7页
A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential ... A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems. 展开更多
关键词 Zakharov–Shabat system EIGENVALUE numerical method Chebyshev polynomials
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On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media
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作者 Shaotong Wang Laiyu Lu 《Earthquake Science》 2024年第1期13-35,共23页
Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.I... Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth. 展开更多
关键词 dispersion curve EIGENVALUE generalized reflection and transmission coefficient surface wave guide wave
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Petrochemical eigenvalues and diagrams for the identification of metamorphic rocks'protolith,taking the host rocks of Dashuigou tellurium deposit in China as an example 被引量:1
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作者 Jianzhao Yin Shoupu Xiang +2 位作者 Yuhong Chao Yuhan Yin Hongyun Shi 《Acta Geochimica》 EI CAS CSCD 2023年第1期103-124,共22页
The Dashuigou tellurium deposit is the world’s only known independent tellurium deposit.By restoring metamorphic rocks’protolith,we seek to understand not only the development and evolution trajectory of the region ... The Dashuigou tellurium deposit is the world’s only known independent tellurium deposit.By restoring metamorphic rocks’protolith,we seek to understand not only the development and evolution trajectory of the region but also the origin of the relevant deposits.While there are many ways to restore metamorphic rocks’protolith,we take the host metamorphic rocks of Dashuigou tellurium deposit and leverage various petrochemical eigenvalues and related diagrams previously proposed to reveal the deposit’s host metamorphic rocks’protolith.The petrochemical eigenvalues include molecular number,Niggli’s value,REE parity ratio,CaO/Al_(2)O_(3)ratio,Fe^(3+) /(Fe^(3+) -+Fe^(2+) )ratio,chondrite-normalized REE value,logarithmic REE value,various REE eigenvalues including scandium,Eu/Sm ratio,total REE amount,light and heavy REEs,δEu,Eu anomaly,Sm/Nd ratio,and silicon isotope δ^(30) SiNBS-29‰,etc.The petrochemical plots include ACMs,100 mg-c-(al+alk),SiO_(2)-(Na_(2)O+K_(2)O),(al+fm)-(c+alk)versus Si,FeO+Fe_(2)O^(3+) TiO)-Al_(2)O_(3)-MgO,c-mg,Al_(2)O_(3)-(Na_(2)O+K_(2)O),chondrite-normalized REE model,La/Yb-REE,and Sm/Nd ratio,etc.On the basis of these comprehensive analyses,the following conclusions are drawn,starting from the many mantle-derived types of basalt developed in the study area of different geological ages,combined with the previously published research results on the deposit s fluid inclusions and sulfur and lead isotopes.The deposit is formed by mantle degassing in the form of a mantle plume in the late Yanshanian orogeny.The degassed fluids are rich in nano-sc ale substances including Fe,Te,S,As,Bi,Au,Se,H_(2),CO_(2),N_(2),H_(2)O,and CH_(4),which are enriched by nano-effect,and then rise to a certain part of the crust in the form of mantle plume along the lithospheric fault to form the deposit.The ultimate power for tellurium mineralization was from H_(2)flow with high energy,which was produced through radiation from the melted iron of the Earth’s outer core.The H,flow results in the Earth’s degassing,as well as the mantle and crust’s uplift. 展开更多
关键词 Petrochemical diagrams and eigenvalue PROTOLITH Metamorphic rock Independent tellurium deposit Host rock The mantle plume
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LARGE DEVIATIONS FOR TOP EIGENVALUES OFβ-JACOBI ENSEMBLES AT SCALING TEMPERATURES
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作者 雷良贞 马宇韬 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1767-1780,共14页
Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ<1.We offer the large deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the... Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ<1.We offer the large deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,whenγ=0. 展开更多
关键词 β-Jacobi ensemble large deviation Wachter law extremal eigenvalue
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Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems
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作者 SUN Fu LI Kun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期100-110,共11页
The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation... The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues. 展开更多
关键词 Sturm-Liouville problem nonlocal potential complex valued coefficient non-real eigenvalue
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There Is a Way to Comprise Half-Integer Eigenvalues for Photon Spin
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作者 ShaoXu Ren 《Journal of Modern Physics》 2016年第11期1364-1374,共12页
In this article, an attempt based on Spin Topological Space, STS, to give areasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in ... In this article, an attempt based on Spin Topological Space, STS, to give areasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in quantum mechanics, which can be used to account for where the unconventional half-integer spin eigenvalues phenomenon of light photon comes from. We suggest to dectect the possible existence of photonic one-third-spinization phenomenon of light photon, by using three beams of light photon in interference experiment. 展开更多
关键词 Spin Topological Space STS Non-Hermitian matrix Casimir operator photonic fermionization phenomena half-integer spin eigenvalues one third one fourth spin eigenvalues of photon spin
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ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS 被引量:11
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作者 O.Sh.Mukhtarov Department of Mathematics, Science and Arts Faculty, Gaziosmanpasa University, Tokat, TurkeyMustafa Kandemir Department of Mathematics, Faculty of A mas y a Education, Ondokuz Mayis University, Amasya, Turkey 《Acta Mathematica Scientia》 SCIE CSCD 2002年第3期335-345,共11页
In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered in... In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found. 展开更多
关键词 Asymptotic behaviour of eigenvalues boundary-value problems functional-conditions discontinuous coefficients
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LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS 被引量:2
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作者 陈化 陈洪葛 +1 位作者 段忆芮 胡鑫 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1653-1664,共12页
Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =(X1,X2,... ,Xm) be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmande... Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =(X1,X2,... ,Xm) be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander's condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω. 展开更多
关键词 Dirichlet eigenvalues finitely degenerate elliptic operators HSrmander's con-dition sub-elliptic estimate Grushin type operator
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Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems 被引量:1
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作者 解惠青 戴华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第6期837-845,共9页
A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the s... A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system. 展开更多
关键词 eigenvalue derivatives eigenvector derivatives sensitivity analysis damped systems repeated eigenvalues
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Bounding the sum of powers of the Laplacian eigenvaluesof graphs 被引量:1
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作者 CHEN Xiao-dan QIAN Jian-guo 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第2期142-150,共9页
For a non-zero real number α, let sα(G) denote the sum of the αth power of thenon-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection betweensα(G) and the first Zagreb index in wh... For a non-zero real number α, let sα(G) denote the sum of the αth power of thenon-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection betweensα(G) and the first Zagreb index in which the H¨older’s inequality plays a key role. By usingthis result, we present a lot of bounds of sα(G) for a connected (molecular) graph G in terms ofits number of vertices (atoms) and edges (bonds). We also present other two bounds for sα(G)in terms of connectivity and chromatic number respectively, which generalize those results ofZhou and Trinajsti′c for the Kirchho? index [B Zhou, N Trinajsti′c. A note on Kirchho? index,Chem. Phys. Lett., 2008, 455: 120-123]. 展开更多
关键词 Laplacian eigenvalues the first Zagreb index Kirchhoff index CONNECTIVITY chromatic number.
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A NEW METHOD FOR ESTIMATING BOUNDS OF EIGENVALUES 被引量:1
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作者 Yang Xiaowei Chen Suhuan +1 位作者 Lian Huadong Yang Guang 《Acta Mechanica Solida Sinica》 SCIE EI 2001年第3期242-250,共9页
A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To... A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To illustrate that the present method can beapplied to structures which cannot be treated by non-negativedecomposition, a plane frame with 202 nodes and 357 beam elements isgiven. The results show that the present method is effective forestimating the bounds of eigenvalues and is more common than Qiu's. 展开更多
关键词 bounds of eigenvalues non-negative decomposition eigenvalue inclusiontheorem
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Edge detection using directional eigenvalues of potential field gradient tensor data 被引量:2
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作者 ZHOU Shuai HUANG Danian 《Global Geology》 2015年第3期188-195,共8页
Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We ... Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We purposed new edge detection methods based on directional eigenvalues of potential field gradient tensor for the causative sources. In order to balance strong and weak amplitude anomalies simultaneously,we present one normalization method using different orders of vertical derivatives to improve the new filters. The presented filters were tested on synthetic and real potential field data to verify its feasibility. All of the results have shown that the new edge detection methods can not only display the sources edges precisely and clearly,but also bring out more geological subtle details. 展开更多
关键词 directional eigenvalues edge detection potential field
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THE UNCERTAIN EIGENVALUES ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS 被引量:1
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作者 Guo Xuedong Xie Jun Chen Suhuan 《Acta Mechanica Solida Sinica》 SCIE EI 2000年第3期230-236,共7页
This paper presents a method for estimating the upper and lowerbounds of eigenvalues of structures with uncertainties. The uncertainparameters re described by the convex model. A numerical ex- ample ofthe frame struct... This paper presents a method for estimating the upper and lowerbounds of eigenvalues of structures with uncertainties. The uncertainparameters re described by the convex model. A numerical ex- ample ofthe frame structure is given to illustrate the efficiency of themethod. 展开更多
关键词 structures with uncertainties upper and lower bound of eigenvalues
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Computation of the Eigenvalues of 3<i>D</i>“Charged” Integral Equations 被引量:1
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作者 Diego Caratelli Pierpaolo Natalini Paolo E. Ricci 《Journal of Applied Mathematics and Physics》 2017年第10期2051-2071,共21页
The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures... The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures. Some applications are shown, relevant to the problem of computing the eigenvalues of a body charged by a finite number of masses concentrated on points, curves or surfaces lying in. 展开更多
关键词 3D Fredholm-Stieltjes Integral Equations eigenvalues Rayleigh-Ritz METHOD Inverse Iteration METHOD
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A Construction of Multi-Sender Authentication Codes from Eigenvalues and Eigenvectors of the Matrix Over Finite Fields
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作者 Xiuli Wang Lina Wang Yakun Hao 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2019年第1期51-60,共10页
We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful atta... We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message. 展开更多
关键词 multi-sender AUTHENTICATION codes NONSINGULAR symmetric matrix eigenvalues EIGENVECTORS finite fields
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Analysis of Eigenvalues for Molecular Structures
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作者 Muhammad Haroon Aftab Kamel Jebreen +1 位作者 Mohammad Issa Sowaity Muhammad Hussain 《Computers, Materials & Continua》 SCIE EI 2022年第10期1225-1236,共12页
In this article,we study different molecular structures such as Polythiophene network,PLY(n)for n=1,2,and 3,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cycli... In this article,we study different molecular structures such as Polythiophene network,PLY(n)for n=1,2,and 3,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 for their cardinalities,chromatic numbers,graph variations,eigenvalues obtained from the adjacency matrices which are square matrices in order and their corresponding characteristics polynomials.We convert the general structures of these chemical networks in to mathematical graphical structures.We transform the molecular structures of these chemical networks which are mentioned above,into a simple and undirected planar graph and sketch them with various techniques of mathematics.The matrices obtained from these simple undirected graphs are symmetric.We also label the molecular structures by assigning different colors.Their graphs have also been studied for analysis.For a connected graph,the eigenvalue that shows its peak point(largest value)obtained from the adjacency matrix has multiplicity 1.Therefore,the gap between the largest and its smallest eigenvalues is interlinked with some form of“connectivity measurement of the structural graph”.We also note that the chemical structures,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 generally have two same eigenvalues.Adjacency matrices have great importance in the field of computer science. 展开更多
关键词 Vertex degree EDGES eigenvalues characteristics polynomials adjacency matrices graphical model GENETICS POLYTHIOPHENE SILICATES
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Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear
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作者 WANG Huai-Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期931-937,共7页
In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. W... In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful. 展开更多
关键词 spectral theorem many-body Green's functions correlation functions complex eigenvalues
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Energy eigenvalues from an analytical transfer matrix method
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作者 何英 张凡明 +1 位作者 杨艳芳 李春芳 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期50-55,共6页
A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c... A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable. 展开更多
关键词 analytical transfer matrix method energy eigenvalues bound state one-dimensional potential
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SIGN PATTERNS REQUIRING ALL DISTINCT EIGENVALUES
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作者 Harris Laura 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2000年第S1期15-17,共3页
A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs... A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs indicated by the corresponding entries of A.We say that a sign pattern matrix A requires a matrix property P if every real matrix in Q(A)has the property P.A matrix with all distinct eigenvalues has many nice 展开更多
关键词 LENGTH CYCLE SIGN PATTERNS REQUIRING ALL DISTINCT eigenvalues DE REAL
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