Analytic continuation average spectrum method for transport in quantum liquids

Kletenik-Edelman, Orly; Rabani, Eran; Reichman, David R.

doi:10.1016/j.chemphys.2010.01.012

Cited by 6 publications

(3 citation statements)

References 65 publications

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“…Boltzmann particles). It has been shown by Rabani et al, 41,42 Hone et al, 43,44 and Miller III 45 that approximate methods of quantum dynamics generate similar values of self-diffusion constants for simple quantum fluids at finite temperatures.…”

Section: Introductionmentioning

confidence: 94%

Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubes

Kowalczyk

Gauden²,

Terzyk³

et al. 2011

Phys. Chem. Chem. Phys.

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Quantum fluctuations significantly increase the self-diffusive motion of para-hydrogen adsorbed in narrow carbon nanotubes at 30 K comparing to its classical counterpart. Rigorous Feynman's path integral calculations reveal that self-diffusive motion of para-hydrogen in a narrow (6,6) carbon nanotube at 30 K and pore densities below ∼29 mmol cm(-3) is one order of magnitude faster than the classical counterpart. We find that the zero-point energy and tunneling significantly smoothed out the free energy landscape of para-hydrogen molecules adsorbed in a narrow (6,6) carbon nanotube. This promotes a delocalization of the confined para-hydrogen at 30 K (i.e., population of unclassical paths due to quantum effects). Contrary the self-diffusive motion of classical para-hydrogen molecules in a narrow (6,6) carbon nanotube at 30 K is very slow. This is because classical para-hydrogen molecules undergo highly correlated movement when their collision diameter approached the carbon nanotube size (i.e., anomalous diffusion in quasi-one dimensional pores). On the basis of current results we predict that narrow single-walled carbon nanotubes are promising nanoporous molecular sieves being able to separate para-hydrogen molecules from mixtures of classical particles at cryogenic temperatures.

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Section: Introductionmentioning

confidence: 94%

Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubes

Kowalczyk

Gauden²,

Terzyk³

et al. 2011

Phys. Chem. Chem. Phys.

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“…Such approach is called stochastic analytical continuation method or average spectrum methods (ASM). [24][25][26][27] Recent application of the ASM and MaxEnt approaches argued that the ASM should be superior to the MaxEnt at least in its ability to resolve sharp spectral features. 28,29 Examples included the calculation of the dynamical density fluctuations in liquid para-hydrogen and ortho-deuterium 29 as well as spin dynamics in anti ferromagnetic Heisenberg spin chain.…”

Section: Introductionmentioning

confidence: 99%

Analytical continuation approaches to electronic transport: The resonant level model

Wilner

Levy

Rabani

2012

The Journal of Chemical Physics

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The analytical continuation average spectrum method (ASM) and maximum entropy (MaxEnt) method are applied to the dynamic response of a noninteracting resonant level model within the framework of the Kubo formula for electric conductivity. The frequency dependent conductivity is inferred from the imaginary time current-current correlation function for a wide range of temperatures, gate voltages, and spectral densities representing the leads, and compared with exact results. We find that the MaxEnt provides more accurate results compared to the ASM over the full spectral range.

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“…Since its original formulation in 1948, Feynman’s path integral representation of time-dependent quantum mechanics has provided a powerful tool for studying many-body problems at finite temperatures without introducing uncontrolled approximations. − While computing equilibrium properties at finite temperatures via path integrals has become routine, the calculation of dynamical properties from path integrals remains one of the most challenging problems in computational chemistry and physics. This is because path integral calculations in imaginary time converge on time scales similar to those of classical calculations.…”

Section: Introductionmentioning

confidence: 99%

Cryogenic Helium Adsorbed in Zeolite Rho: Inside Localization Controlled Self-Diffusion of Confined Quantum Particles

Kowalczyk

Gauden²,

Terzyk³

et al. 2011

J. Phys. Chem. C

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Applying Feynman's treatment of quantum mechanics at finite temperatures via path integrals and the numerical analytic continuation method developed recently (Kowalczyk, P.; Gauden, P. A.; Terzyk, A. P.; Furmaniak, Sylwester, J. Chem. Theory Comput. 2009, 5, 1990À1996), we study the mobility of 4 He atoms adsorbed in zeolite rho at 40 K. At studied temperature, the self-diffusive motion of 4 He atoms in zeolite rho is strongly concentration-dependent. At low pore concentrations, 4 He atoms are adsorbed in high-energetic adsorption centers of the zeolite. Due to strong localization in the solidÀfluid potential well, an average kinetic energy of 4 He atoms at infinite dilution reaches ∼120 K (i.e., twice of the classical kinetic energy at 40 K, E class = 60 K), whereas the self-diffusion constant drops up to ∼0.001 Å 2 ps À1 . Increasing pore concentration of 4 He leads to the rapid increase in mobility of adsorbed 4 He atoms. We show that ∼8 mmol cm À3 , self-diffusive motion of confined 4 He atoms increases up to ∼1 Å 2 ps À1 . Variation of the kinetic energy, potential energy, and enthalpy of 4 He adsorption with pore concentration indicates that highenergetic adsorption sites in studied zeolite sample are saturated at low pore densities. The remaining adsorption sites are characterized by weaker solidÀfluid potential, which allows higher delocalization of adsorbed 4 He atoms. The reported novel phenomenon of localization controlled self-diffusion of confined 4 He seems to be promising for smart designing of nanoporous quantum molecular sieves and storage nanovessels. Understanding of 4 He cryogenic adsorption in the smallest pores enriches our knowledge that is crucial for precise analysis of ultramicropore sizes.

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Analytic continuation average spectrum method for transport in quantum liquids

Cited by 6 publications

References 65 publications

Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubes

Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubes

Analytical continuation approaches to electronic transport: The resonant level model

Cryogenic Helium Adsorbed in Zeolite Rho: Inside Localization Controlled Self-Diffusion of Confined Quantum Particles

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