Semiclassical limits in quantum-transport theory

Lill, James; Haftel, M. I.; Herling, G. H.

doi:10.1103/physreva.39.5832

Cited by 17 publications

(27 citation statements)

References 24 publications

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“…Similar hydrodynamic expansions have been carried out in literature for a onedimensional case [3,35,42]. Analogously, in the recent past, the derivation of three-dimensional QHD models, obtained by first-moments expansion [11,23,24] of the Wigner equation, has attracted considerable attention for the growing field of nanotechnology applications.…”

Section: Development Of the Quantum Hydrodynamic System In Powermentioning

confidence: 52%

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Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

Trovato

Reggiani

2011

Phys. Rev. E

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By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of h(2). In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when h → 0.

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Section: Development Of the Quantum Hydrodynamic System In Powermentioning

confidence: 52%

“…With this approach, for the Fermi and Bose gases we obtain the classic relations [1,7] (42). Analogously, by considering the successive term of the expansion (A66) we obtain…”

Section: Explicit First-order Quantum Correction For the Fermi And Bomentioning

confidence: 87%

Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

Trovato

Reggiani

2011

Phys. Rev. E

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“…Particular cases exist, like a general Gaussian density, for which the hierarchy does break off at a finite order, here, the third order. 9,27 Otherwise, suitable truncation schemes must be found to cut the hierarchy at a given order. The following two aspects then need to be considered: first, the correct representation of the initial state in terms of a finite number of moments, and second, the appropriate treatment of the dynamical coupling to higher-order moments of the hierarchy.…”

Section: ͑2͒mentioning

confidence: 99%

“…While these and related works focus on the description of wave functions, or pure quantum states, a parallel development took place from the late 1940s onwards, which concerned phase-space distributions and their moments. [6][7][8][9][10][11] By formulating ''kinetic'' equations of motion for these moments, the latter investigations also led to a hydrodynamic theory. Here, the case of mixed quantum states, or statistical mixtures, is naturally included.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics for dissipative systems: A hydrodynamic perspective

Burghardt

Møller

2002

The Journal of Chemical Physics

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“…[34][35][36][37][38] The moments come from a Taylor expansion of the one-particle density matrix with respect to the offdiagonal variable. [34][35][36][37][38] The moments come from a Taylor expansion of the one-particle density matrix with respect to the offdiagonal variable.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic tensor density functional theory with correct susceptibility

Овчинников

Bartell

Neuhauser

2007

The Journal of Chemical Physics

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In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.

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Semiclassical limits in quantum-transport theory

Cited by 17 publications

References 24 publications

Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

Quantum dynamics for dissipative systems: A hydrodynamic perspective

Hydrodynamic tensor density functional theory with correct susceptibility

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