Comment on “Dynamics of nuclear fluid. VIII. Time-dependent Hartree-Fock approximation from a classical point of view”

Krivoruchenko, M. I.; Martemyanov, B. V.; Fuchs, Christian

doi:10.1103/physrevc.76.059801

Cited by 6 publications

(4 citation statements)

References 24 publications

(21 reference statements)

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“…It is seen that the canonical equation of motion ∂ P/∂t = −∇ r U is obtained only in the limit of s → 0. It was also commented that the above method solves the evolution of the Wigner function to the first order in the time increment only [85]. The above discussions are valid for a momentum-independent mean-field potential.…”

Section: Boltzmann-uehling-uhlenbeck Approachmentioning

confidence: 97%

Transport approaches for the description of intermediate-energy heavy-ion collisions

2019

Progress in Particle and Nuclear Physics

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The transport approach is a useful tool to study dynamics of non-equilibrium systems. For heavy-ion collisions at intermediate energies, where both the smooth nucleon potential and the hard-core nucleon-nucleon collision are important, the dynamics are properly described by two families of transport models, i.e., the Boltzmann-Uehling-Uhlenbeck approach and the quantum molecular dynamics approach. These transport models have been extensively used to extract valuable information of the nuclear equation of state, the nuclear symmetry energy, and microscopic nuclear interactions from intermediate-energy heavy-ion collision experiments. On the other hand, there do exist deviations on the predications and conclusions from different transport models. Efforts on the transport code evaluation project are devoted in order to understand the model dependence of transport simulations and well control the main ingredients, such as the initialization, the mean-field potential, the nucleon-nucleon collision, etc. A new era of accurately extracting nuclear interactions from transport model studies is foreseen. 2 from 50 MeV to 2 GeV, where the nucleon degree of freedom dominates the dynamics, and both the smooth nuclear potential and the hard-core nucleon-nucleon collisions become important. The central purpose of intermediate-energy heavy-ion collisions is to extract the equation of state (EOS) of the hot and dense nuclear matter formed during the collisions, while the uncertainties mostly come from the isospin-dependent part, i.e., the nuclear symmetry energy.In order to describe properly the dynamics of intermediate-energy heavy-ion collisions, transport approaches at this energy regime are mostly developed along two directions: the Boltzmann-Uehling-Uhlenbeck (BUU) approach and quantum molecular dynamics (QMD) approach. The BUU approach basically models the time evolution of the one-body phase-space distribution based on the BUU equation numerically using the test-particle method, and the QMD approach models the time evolution of nucleons under a many-body Hamiltonian with the wave function of each nucleon represented by a Gaussian wave packet. Both approaches can be derived from many-body theories with various approximations. Without nucleon-nucleon collisions, the BUU approach reduces to the Vlasov approach, which is similar to the TDHF approach. On the other hand, it is difficult to solve exactly the extended TDHF approach, which incorporates the collision contribution into the TDHF approach [3]. Both the BUU approach and the QMD approach include mainly three ingredients: the initialization of projectile and target nuclei, the mean-field potential for each nucleon, and the nucleon-nucleon collision in the dynamical evolution. The mean-field potential can be obtained from effective in-medium nucleon-nucleon interactions based on the Hartree or Hartree-Fock method, and in this way the microscopic nuclear interaction is related to the macroscopic nuclear EOS through the energy-density functional form.So far both the BUU appr...

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Section: Boltzmann-uehling-uhlenbeck Approachmentioning

confidence: 97%

Transport approaches for the description of intermediate-energy heavy-ion collisions

2019

Progress in Particle and Nuclear Physics

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“…[19] and comments in Ref. [40]). Applying the test-particle approach to solving the spin-dependent BUU equation for the first time, we found that the EOMs of nucleon test particles are similar to those for electrons obtained within Method I described above, albeit with different forms of interactions.…”

Section: Introductionmentioning

confidence: 92%

“…We then fix n = ŷ in Eqs. (40) and (41) and set n i = ±ŷ in Eqs. ( 45), (47), and (49) depending on whether the ith particle is spin-up or spin-down with respect to the y axis.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

Xia

et al. 2016

Physics Letters B

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A consistent derivation of the equations of motion (EOMs) of test particles for solving the spindependent Boltzmann-Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.

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“…This important fact is not appreciated by all: a number of incorrect schemes to model quantum dynamics using phase space trajectories have been devised [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], leading to confusion [17][18][19][20][21][22][23][24]. The schemes' failures have, in some quarters, given phase space representations of quantum mechanics an undeservedly poor standing [25].…”

Section: Introductionmentioning

confidence: 99%

Anharmonic quantum mechanical systems do not feature phase space trajectories

Oliva¹,

Kakofengitis²,

Steuernagel³

2018

Physica A: Statistical Mechanics and its Applications

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Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

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Comment on “Dynamics of nuclear fluid. VIII. Time-dependent Hartree-Fock approximation from a classical point of view”

Cited by 6 publications

References 24 publications

Transport approaches for the description of intermediate-energy heavy-ion collisions

Transport approaches for the description of intermediate-energy heavy-ion collisions

Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

Anharmonic quantum mechanical systems do not feature phase space trajectories

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