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I V Tokatly - One of the best experts on this subject based on the ideXlab platform.
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continuum mechanics for quantum many body systems linear response regime
Physical Review B, 2010Co-Authors: Xianlong Gao, Jianmin Tao, Giovanni Vignale, I V TokatlyAbstract:We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.
Xianlong Gao - One of the best experts on this subject based on the ideXlab platform.
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continuum mechanics for quantum many body systems linear response regime
Physical Review B, 2010Co-Authors: Xianlong Gao, Jianmin Tao, Giovanni Vignale, I V TokatlyAbstract:We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.
Tokatly I. - One of the best experts on this subject based on the ideXlab platform.
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Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime
'American Physical Society (APS)', 2010Co-Authors: Gao Xianlong, Tao Jianmin, Vignale G., Tokatly I.Abstract:We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009
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Continuum mechanics for quantum many-body systems: Linear response regime
'American Physical Society (APS)', 2010Co-Authors: Vignale G., Tokatly I.Abstract:22 páginas, 4 figuras, 1 tabla.-- PACS number(s): 71.15.Mb, 31.15.ag.-- et al.We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.This work was supported by DOE under Grant Nos. DEFG02- 05ER46203 (G.V.) and DE-AC52-06NA25396 (J.T.) and by the IKERBASQUE Foundation. G.X. was supported by NSF of China under Grant Nos. 10704066 and 10974181. I.V.T. acknowledges funding by the Spanish MEC (Grant No. FIS2007-65702-C02-01), “Grupos Consolidados UPV/ EHU del Gobierno Vasco” (Grant No. IT-319-07), and the European Community through e-I3 ETSF project (Contract No. 211956).Peer reviewe
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Continuum mechanics for quantum many-body systems: Linear response regime
'American Physical Society (APS)', 2010Co-Authors: Gao Xianlong, Tao Jianmin, Vignale, Giovanni 1957-, Tokatly I.Abstract:URL:http://link.aps.org/doi/10.1103/PhysRevB.81.195106 DOI:10.1103/PhysRevB.81.195106We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high- frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.This work was supported by DOE under Grant Nos. DEFG02-05ER46203 G.V. and DE-AC52-06NA25396 J.T. and by the IKERBASQUE Foundation. G.X. was supported by NSF of China under Grant Nos. 10704066 and 10974181. I.V.T. acknowledges funding by the Spanish MEC Grant No. FIS2007-65702-C02-01 , “Grupos Consolidados UPV/EHU del Gobierno Vasco” Grant No. IT-319-07 , and the European Community through e-I3 ETSF project Contract No. 211956 . G.V. gratefully acknowledges the kind hospitality of the ETSF in San Sebastian where this work was completed
Jianmin Tao - One of the best experts on this subject based on the ideXlab platform.
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continuum mechanics for quantum many body systems linear response regime
Physical Review B, 2010Co-Authors: Xianlong Gao, Jianmin Tao, Giovanni Vignale, I V TokatlyAbstract:We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.
Giovanni Vignale - One of the best experts on this subject based on the ideXlab platform.
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continuum mechanics for quantum many body systems linear response regime
Physical Review B, 2010Co-Authors: Xianlong Gao, Jianmin Tao, Giovanni Vignale, I V TokatlyAbstract:We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of Orthonormal Eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.
