Plain nuclear vortex

Kartavenko, V. G.

doi:10.1088/0954-3899/19/5/001

Cited by 13 publications

(39 citation statements)

References 2 publications

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“…Furthermore, in the framework of a nonlocal quantum theory, the generalization of the corresponding Lagrange multipliers is also an open problem. On the other hand, the rigorous formulation of quantum HD (QHD) closed models is a demanding issue for many kinds of problems in quantum systems, like interacting fermionic and bosonic gases [12], quantum turbulence [13], quantum fluids [14], quantized vortices [15], nuclear physics [16], confined carrier transport in semiconductor heterostrucures [17], phonon and electron transport in nanostructures [18,19], and nanowires and thin layers [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Trovato

Reggiani

2011

Phys. Rev. E

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“…review [4] and [5][6][7][8] for the recent refs.). However any extension of nonlinear dynamics from 1+1 to 2+1 and 3+1 dimensions meets principal difficulties.…”

Section: Motivationmentioning

confidence: 99%

Nonlinear evolution of the axisymmetric nuclear surface

2002

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We consider an uniformly charged incompressible nuclear fluid bounded by a closed surface. It is shown that an evolution of an axisymmetric surface Γ(r, t) ≡ σ − Σ(z, t) = 0, r = (σ, φ, z) can be approximately reduced to a motion of a curve in the (σ, z)-plane. A nonlinear integro-diffrerential equation for the contour Σ(z, t) is derived. It is pointed on a direct correspondence between Σ(z, t) and a local curvature, that gives possibility to use methods of differential geometry to analyze an evolution of an axisymmetric nuclear surface. I. MOTIVATIONNonlinear dynamics of a nuclear surface is an object of special interest due to the following reasons. First, nuclear density falls considerably in the surface region, where the density fluctuations and clustering may be important. Second, different types of instability may be developed in the surface region and lead to fragmentation processes at low (fission, nucleon transfer) and high (multifragmentation, break-up etc.) energies. Finally, the liquid drop concept [1] for over a century are intensively used in macro-[2] and micro-physics [3]. Nonlinear dynamics of shapes in any complicated systems enevitably leads to mathematical problem of describing global geometric quantities such as surface and enclosed volume in different dimensions (polymers, cell membranes, 3D droplets).An application of a soliton concept to nonlinear nuclear hydrodynamics has given yet new possibilities in this field (See e.g. review [4] and [5][6][7][8] for the recent refs.). However any extension of nonlinear dynamics from 1+1 to 2+1 and 3+1 dimensions meets principal difficulties. The crucial point is to reduce the dimension of a problem. In paper [9] we considered the simplest two-dimensional nonlinear liquid objects. It was shown that 2D pure vortical motion of inviscid nuclear liquid can be reduced to 1D evolution of the contour bounding this drop. In the next paper [10] the extension to semi-3D geometry was done. The equations of motion describing localized vortex on a spherical nuclear surface -a bounded region of constant vorticity, surrounded by irrotational flux -were reduced to 1D nonlinear evolution of the boundary.In this short report we consider an uniformly charged incompressible nuclear 3D fluid bounded by a closed surface. It is shown that evolution of an axisymmetric surface Γ(r, t) ≡ σ − Σ(z, t) = 0, r = (σ, φ, z) can be approximately reduced to a motion of a curve in the (σ, z)-plane. II. FRAMEWORKThe evolution of one-body Wigner phase-space distribution function is analyzed instead of a full many-body wave function. Integrating the kinetic equationover the momentum space with different polynomial weighting functions of the p-variable one comes to an infinite chain of equations for local collective observables including the density, collective velocity, pressure and an infinite set of tensorial functions of the time and space coordinates, which are defined as moments of the distribution function in the momentum space: -the particle n(r, t) ≡ g dp f (r, p, t), and the mas...

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“…gave yet the possibility to derive for nuclear physics unexpected collective modes, which can not be obtained by traditional methods of perturbation theory near some equilibrium state (see e.g. review 27 and 28 for the recent refs.). The most important reason is that the fragmentation and clusterization is a very general phenomenon.…”

Section: The Frameworkmentioning

confidence: 99%

On Scission Configuration in Ternary Fission

Kartavenko¹,

Greiner²,

District³

et al. 2001

Fusion Dynamics at the Extremes

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A static scission configuration in cold ternary fission has been considered in the framework of two mean field approaches. The virial theorems has been suggested to investigate correlations in the phase space, starting from a kinetic equation. The inverse mean field method is applied to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximation of reflectless single-particle potentials.

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Plain nuclear vortex

Cited by 13 publications

References 2 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

Nonlinear evolution of the axisymmetric nuclear surface

On Scission Configuration in Ternary Fission

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