The Experts below are selected from a list of 35250 Experts worldwide ranked by ideXlab platform
David K Hoffman - One of the best experts on this subject based on the ideXlab platform.
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direct approach to density functional theory iterative treatment using a Polynomial Representation of the heaviside step function operator
Chemical Physics Letters, 1995Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A new approach to density functional theory is presented. The ground state electronic density and energy of a many-electron system are obtained directly using a Polynomial Representation of the Heaviside step operator acting on a trial wavefunction. A radial coordinate extension of the distributed approximating functional (DAF) is developed to treat Coulomb singularities and cusps accurately. Examples of electronic structure for the He and Ne atomic systems are presented.
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general energy separable faber Polynomial Representation of operator functions theory and application in quantum scattering
Journal of Chemical Physics, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:A general, uniformly convergent series Representation of operator‐valued functions in terms of Faber Polynomials is presented. The method can be used to evaluate the action of any operator‐valued function which is analytic in a simply connected region enclosed by a curve, Lγ. The three most important examples include the time‐independent Green’s operator, G+(E)=1/[E−(H−ie)], where H may be Hermitian or may also contain a negative imaginary absorbing potential, the time‐dependent Green’s or evolution operator, exp(−iHt/ℏ), and the generalized collision operator from nonequilibrium statistical mechanics, 1/[E−(L−ie)], where L is the Liouvillian operator for the Hamiltonian. The particular uniformly convergent Faber Polynomial expansion employed is determined by the conformal mapping between the simply connected region external to the curve Lγ, which encloses the spectrum of H−ie (or L−ie), and the region external to a disk of radius γ. A locally smoothed conformal mapping is introduced containing a finite n...
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a general energy separable Polynomial Representation of the time independent full green operator with application to time independent wavepacket forms of schrodinger and lippmann schwinger equations
Chemical Physics Letters, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A general, energy-separable Faber Polynomial Representation of the full time-independent Green operator is presented. Non-Hermitian Hamiltonians are included, allowing treatment of negative imaginary absorbing potentials. A connection between the Faber Polynomial expansion and our earlier Chebychev Polynomial expansion (Chem. Phys. Letters 206 (1993) 96) is established, thereby generalizing the Chebychev expansion to the complex energy plane. The method is applied to collinear H + H2 reactive scattering.
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analytic continuation of the Polynomial Representation of the full interacting time independent green function
Chemical Physics Letters, 1993Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract We present an analytic continuation of a Polynomial Representation of the full, interacting time-independent Green function, thereby enabling the use of negative, imaginary absorbing potentials to shorten the grid necessary to treat scattering problems. The approach retains the clean separation of the energy and Hamiltonian dependences characteristic of our earlier orthogonal Polynomial Representation of the operator ( E - H +i0 + ) −1 . This treatment, combined with our time-independent wavepacket Lippmann-Schwinger equation method, leads to a computational approach in which all of the energy dependence resides in known analytical expansion coefficients. The Hamiltonian operator appears as the argument of other orthogonal Polynomials. These act solely on an initial wavepacket which provides a “universal source” of scattered waves, independent of the particular energies of interest. This energy independence, combined with highly truncated grids, results in an extremely efficient procedure for scattering calculations.
Hsiaochuan Wang - One of the best experts on this subject based on the ideXlab platform.
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a segmental probabilistic model of speech using an orthogonal Polynomial Representation application to text independent speaker verification
Speech Communication, 1996Co-Authors: Hsiaochuan WangAbstract:Abstract A segmental probabilistic model based on an orthogonal Polynomial Representation of speech signals is proposed. Unlike the conventional frame based probabilistic model, this segment based model concatenates the similar acoustic characteristics of consecutive frames into an acoustic segment and represents the segment by an orthogonal Polynomial function. An iterative algorithm that performs recognition and segmentation processes is proposed for estimating the segment model. This segment model is applied in the text independent speaker verification. Tests were carried out on a 20-speaker database. With the best version of the model, an equal error rate of 0.59% can be reached, for test utterances of 10 digits. This corresponds to a relative error rate reduction of more than 50%, compared to the conventional frame based probabilistic model.
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an orthogonal Polynomial Representation of speech signals and its probabilistic model for text independent speaker verification
International Conference on Acoustics Speech and Signal Processing, 1995Co-Authors: Hsiaochuan Wang, F K Soong, Chaoshih HuangAbstract:A segmental probabilistic model based on an orthogonal Polynomial Representation of speech signals is proposed. Unlike the conventional frame based probabilistic model, this segment based model concatenates the similar acoustic characteristics of consecutive frames into an acoustic segment and represents the segment by an orthogonal Polynomial function. An algorithm which iteratively performs recognition and segmentation processes is proposed for estimating the parameters of the segment model. This segment model is applied in the text independent speaker verification. For a 20-speaker database, the experimental results show that the performance by using segment models is better than that by using the conventional frame based probabilistic model. The equal error rate can be reduced by 3.6% when the models are represented by 64-mixture density functions.
Dominika Zgid - One of the best experts on this subject based on the ideXlab platform.
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chebyshev Polynomial Representation of imaginary time response functions
Physical Review B, 2018Co-Authors: Emanuel Gull, Sergei Iskakov, Igor Krivenko, Alexander A Rusakov, Dominika ZgidAbstract:Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise Representation of these functions. In this paper, we explore the Representation of Green's functions and self-energies in terms of a series of Chebyshev Polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev Representation for realistic systems with the uniform-power grid Representation, which is most commonly used in this context.
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chebyshev Polynomial Representation of imaginary time response functions
Physical Review B, 2018Co-Authors: Emanuel Gull, Sergei Iskakov, Igor Krivenko, Alexander A Rusakov, Dominika ZgidAbstract:Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise Representation of these functions. In this paper, we explore the Representation of Green's functions and self-energies in terms of a series of Chebyshev Polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev Representation for realistic systems with the uniform-power grid Representation, which is most commonly used in this context.
Youhong Huang - One of the best experts on this subject based on the ideXlab platform.
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direct approach to density functional theory iterative treatment using a Polynomial Representation of the heaviside step function operator
Chemical Physics Letters, 1995Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A new approach to density functional theory is presented. The ground state electronic density and energy of a many-electron system are obtained directly using a Polynomial Representation of the Heaviside step operator acting on a trial wavefunction. A radial coordinate extension of the distributed approximating functional (DAF) is developed to treat Coulomb singularities and cusps accurately. Examples of electronic structure for the He and Ne atomic systems are presented.
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general energy separable faber Polynomial Representation of operator functions theory and application in quantum scattering
Journal of Chemical Physics, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:A general, uniformly convergent series Representation of operator‐valued functions in terms of Faber Polynomials is presented. The method can be used to evaluate the action of any operator‐valued function which is analytic in a simply connected region enclosed by a curve, Lγ. The three most important examples include the time‐independent Green’s operator, G+(E)=1/[E−(H−ie)], where H may be Hermitian or may also contain a negative imaginary absorbing potential, the time‐dependent Green’s or evolution operator, exp(−iHt/ℏ), and the generalized collision operator from nonequilibrium statistical mechanics, 1/[E−(L−ie)], where L is the Liouvillian operator for the Hamiltonian. The particular uniformly convergent Faber Polynomial expansion employed is determined by the conformal mapping between the simply connected region external to the curve Lγ, which encloses the spectrum of H−ie (or L−ie), and the region external to a disk of radius γ. A locally smoothed conformal mapping is introduced containing a finite n...
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a general energy separable Polynomial Representation of the time independent full green operator with application to time independent wavepacket forms of schrodinger and lippmann schwinger equations
Chemical Physics Letters, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract A general, energy-separable Faber Polynomial Representation of the full time-independent Green operator is presented. Non-Hermitian Hamiltonians are included, allowing treatment of negative imaginary absorbing potentials. A connection between the Faber Polynomial expansion and our earlier Chebychev Polynomial expansion (Chem. Phys. Letters 206 (1993) 96) is established, thereby generalizing the Chebychev expansion to the complex energy plane. The method is applied to collinear H + H2 reactive scattering.
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analytic continuation of the Polynomial Representation of the full interacting time independent green function
Chemical Physics Letters, 1993Co-Authors: Youhong Huang, Donald J Kouri, David K HoffmanAbstract:Abstract We present an analytic continuation of a Polynomial Representation of the full, interacting time-independent Green function, thereby enabling the use of negative, imaginary absorbing potentials to shorten the grid necessary to treat scattering problems. The approach retains the clean separation of the energy and Hamiltonian dependences characteristic of our earlier orthogonal Polynomial Representation of the operator ( E - H +i0 + ) −1 . This treatment, combined with our time-independent wavepacket Lippmann-Schwinger equation method, leads to a computational approach in which all of the energy dependence resides in known analytical expansion coefficients. The Hamiltonian operator appears as the argument of other orthogonal Polynomials. These act solely on an initial wavepacket which provides a “universal source” of scattered waves, independent of the particular energies of interest. This energy independence, combined with highly truncated grids, results in an extremely efficient procedure for scattering calculations.
Chaoshih Huang - One of the best experts on this subject based on the ideXlab platform.
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an orthogonal Polynomial Representation of speech signals and its probabilistic model for text independent speaker verification
International Conference on Acoustics Speech and Signal Processing, 1995Co-Authors: Hsiaochuan Wang, F K Soong, Chaoshih HuangAbstract:A segmental probabilistic model based on an orthogonal Polynomial Representation of speech signals is proposed. Unlike the conventional frame based probabilistic model, this segment based model concatenates the similar acoustic characteristics of consecutive frames into an acoustic segment and represents the segment by an orthogonal Polynomial function. An algorithm which iteratively performs recognition and segmentation processes is proposed for estimating the parameters of the segment model. This segment model is applied in the text independent speaker verification. For a 20-speaker database, the experimental results show that the performance by using segment models is better than that by using the conventional frame based probabilistic model. The equal error rate can be reduced by 3.6% when the models are represented by 64-mixture density functions.