A nonperturbative transport approach including particle collisions and density fluctuations

Cassing, W.; Peter, Andreas; Pfitzner, A.

doi:10.1016/0375-9474(93)90169-x

Cited by 10 publications

(12 citation statements)

References 26 publications

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“…Toward this end we apply the Kerman-Klein factorization method [113]. In this method, the evaluation of matrix elements of the Hamiltonian of the type n|H|n ′ is predicated on the following factorization of the two-body density matrix (summation convention) 116) which is assumed to be valid when pairing correlations are neglected. The simplest qualitative arguments in favor of this approximate factorization are: (i) it satisfies the Pauli principle; (ii) by suitable choice of the states |n , it leads to equations that preserve the symmetries broken by standard Hartree-Fock theory, namely, translation and rotation invariance; (iii) it reduces to Hartree-Fock theory in the appropriate limit.…”

Section: Relation Of the Effective Hamiltonian To Matrix Elements Of mentioning

confidence: 99%

“…We have already alluded to the theoretical and practical advances that have been made in the study of the problem of the collision term [115][116][117][118][119][120]. Our purposes are best served by reference to the treatment of Ayik [122].…”

Section: Basic Dynamical Equationsmentioning

confidence: 99%

“…Here we use the explicit form 116) and with the specification that the width, ω 0 , is the same for all the distributions, we also introduce constants A 12 and A 22 . We thus encounter integrals of the form (subscripts understood)…”

Section: Dissipative Equations Of Motionmentioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Section: Relation Of the Effective Hamiltonian To Matrix Elements Of mentioning

confidence: 99%

Section: Basic Dynamical Equationsmentioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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“…Neglecting c 3 in (2.15) and inserting the truncated cluster expansions into the equations of motion (2.11) and (2.12), we arrive at a closed system of coupled nonlinear differential equations for ρ and c 2 . In order to compactify these lengthy equations (in close analogy to fermionic correlation dynamics [3,4]) we introduce the following abbreviations:…”

Section: )mentioning

confidence: 99%

Two-body correlations in pionic systems

1995

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In close analogy to fermionic many-body theory the truncation of the bosonic BBGKY density matrix hierarchy on the two-body level leads to a coupled set of nonlinear equations of motion for the one-body density matrix and the two-body correlation function. These equations provide a nonperturbative description of the nonequilibrium time evolution of particle number conserving bosonic many-body systems including the dynamical resummation of parquet-like diagrams. Within this framework we study the properties of a pionic system as a function of temperature and density with focus on two-body quantities. For each temperature we find a related pion density for which the relative strength of the two-body correlation function assumes a maximum and the pionic system is far from the mean-field limit. Since these correlated phases up to T =200 MeV only appear at rather low pion density, the hot and dense pion gas as generated in ultrarelativistic nucleusnucleus collisions should be well described within mean-field theory; i.e. the HBT analysis of pion sources from π − π correlations should remain valid even in the case of strongly interacting pions. * supported by DFG, BMFT, GSI Darmstadt and KFA Jülich

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“…In the last decades many non-perturbative approaches were developed such as variational methods [1,2], Dyson-Schwinger-calculations [3,4] or the coupled cluster expansion [5,6]. Among the approaches that are based on techniques known from many-particle physics is the method of correlation dynamics, which was successfully applied to the nonrelativistic nuclear many-particle problem [7,8,9] and for the description of interacting boson systems [10]. Within a formulation in terms of connected equal-time Green functions the problem of ground-state symmetry breaking was studied in detail for Φ 4 -theory in 1 + 1 and 2 + 1 space-time dimensions [11,12] as well as the convergence properties of the truncation scheme applied [13].…”

Section: Introductionmentioning

confidence: 99%

Correlation dynamics of Yukawa-theory in 1+1 dimensions

Juchem

Cassing

Hauser

1998

EPJ A

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Using the method of correlation dynamics we investigate the properties of a field-theory for fermions and scalar bosons coupled via a Yukawa interaction. Within this approach, which consists in an expansion of full equal-time Green functions into connected equal-time Green functions and a corresponding truncation of the hierarchy of equations of motion we carry out calculations up to 4th order in the connected Green functions and evaluate the effective potential of the theory in 1+1 dimensions on a torus. Comparing the different approximations we find a strong influence of the connected 4-point functions on the properties of the system. * supported by DFG, GSI Darmstadt

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A nonperturbative transport approach including particle collisions and density fluctuations

Cited by 10 publications

References 26 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Two-body correlations in pionic systems

Correlation dynamics of Yukawa-theory in 1+1 dimensions

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