Quantum Theory of Hydrodynamic Currents

Yee, D. D. H.

doi:10.1103/physrev.184.196

Cited by 10 publications

(7 citation statements)

References 7 publications

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“…Since we assume a constant density, ρ = ρ 0 , we can not see an apparent role for the above commutation relation. To make further development of the BMM, we naturally arrive at the idea of the expansion of ρ around ρ 0 , i.e., ρ = ρ 0 +ρ ′ [43,18,19,21]. Lastly, we prove the gauge invariance of the velocity operator v expressed in terms of the Clebsch parameters as v=−∇φ− 1 ρ π∇ψ, i.e., (2.1) where we have used the relation π=−ρλ.…”

Section: Discussion and Further Outlookmentioning

confidence: 98%

A possible quantum fluid-dynamical approach to vortex motion in nuclei

Nishiyama

Providência

2017

Int. J. Mod. Phys. E

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The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\nabla \phi(x) + \lambda(x) \nabla \psi(x) (\phi ; velocity potential, \lambda and \psi: Clebsch parameters) is very powerful and has an advantage deriving equations of fluid motion from a Lagransian. Making the best use of the advantage, Kronig-Thellung, Ziman and Ito obtained a Hamiltonian including the internal rotational motion, the vortex motion, through the term \lambda(x) \nabla \psi(x). Going to quantum fluid dynamics, Ziman and Thellung finally derived a roton spectrum of liquid Helium II postulated by Landau. Is it possible to apply such the manner to a description of the collective vortex motion in nuclei? The description of such a collective motion has never been treated in the Bohr-Mottelson model (BMM) for a long time. In this paper, we will investigate a possibility of describing the vortex motion in nuclei basing on the theories of Ziman and Ito together with Marumori's work.Comment: 23 pages, no figures, Publication versio

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Section: Discussion and Further Outlookmentioning

confidence: 98%

A possible quantum fluid-dynamical approach to vortex motion in nuclei

Nishiyama

Providência

2017

Int. J. Mod. Phys. E

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“…To be consistent with (11), it is easily seen that a proper functional representation for i.,l would be…”

Section: Functional Representation Of the Commutation Relationsmentioning

confidence: 94%

Density and Current Density as Coordinates for a System of Interacting Bosons at Absolute Zero

Chang

1971

Journal of Mathematical Physics

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The quantum field Hamiltonian expressed in terms of density and current density variables has been employed together with the equal-time commutation relations among these variables to find the ground state energy and the density fluctuation excitation spectrum of a system of interacting bosons at T = 0 oK. The approximation involved consists in assuming that the density fluctuation in space is small compared with the average density. The results easily obtained in the lowest-order approximation agree with those of Bogoliubov. However, in our treatment no condensation of particles in zero-momentum state is assumed or apparent. A connection between the present treatment and the quantum hydrodynamic approach to the irrotational flow of a Bose liquid has been made.

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“…In particular, they pointed out that the use of currents had long been established in classical non-relativistic field theories such as hydrodynamics. Since the fundamental variables in hydrodynamics were density and velocity, as advocated by Landau, rather than density and current, Yee [21] extended the hydrodynamic current approach to density and velocity fields so that many of the concepts and interpretations of classical hydrodynamic theory might be exploited to guide and interpret the results and developments of the quantum theory as Landau did in developing his theory of superfluidity.…”

Section: §2 Introductionmentioning

confidence: 99%

“…The formalism presented by Yee [21] begins from first principles in the second quantization formalism with the typical density and current operators…”

Section: §2 Introductionmentioning

confidence: 99%

“…From the commutation relations (3.2) which define the current algebra, we may establish the commutation relations between the velocity operator and the canonical variables, ρ and J. The determination of these relations, particularly the velocity-velocity relation, is presented by Yee in [21] and result the quantized version of the Clebsch formula [9] for the velocity operator. That is,…”

Section: §2 Introductionmentioning

confidence: 99%

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Second Quantized Landau Variables in the Case of Dilute Bose-Einstein Condensates

Yee,

Myers

2017

Preprint

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Landau was the first to advance hydrodynamic concepts such as density and velocity to describe the superfluidity of liquid He 4 . Due to the recent spectacular success of experiments demonstrating Bose Einstein condensation in dilute Bose atomic gases, interest has been revitalized in the theoretical description of Bose Einstein condensates. Many of the properties of these gases were obtained by using the Gross-Pitaevskii equation (GPE) to derive the hydrodynamic equations for the gases. However, it is interesting to apply the hydrodynamic equations obtained by Yee for bosons. Many of the properties obtained for the dilute Bose gases are also consequences of Yee's hydrodynamic equations, which derive from a formalism distinct from that of the GPE.

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Quantum Theory of Hydrodynamic Currents

Cited by 10 publications

References 7 publications

A possible quantum fluid-dynamical approach to vortex motion in nuclei

A possible quantum fluid-dynamical approach to vortex motion in nuclei

Density and Current Density as Coordinates for a System of Interacting Bosons at Absolute Zero

Second Quantized Landau Variables in the Case of Dilute Bose-Einstein Condensates

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