arXiv subjects

Helmut Hofmann

Publications and source records attributed to Helmut Hofmann.

10 recordsLinked to original sources

arXiv2005

A variational approach to the partition function of an interacting many body system

For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational approach quantum effects can be treated even at very low temperatures. In order to test its accuracy the novel approach is applied to the exactly solvable Lipkin-Meshkov-Glick model (LMGM). For thermodynamic properties and level densities good agreement with the exact calculations is found.

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arXiv2005

Damped collective motion of many body systems: A variational approach to the quantal decay rate

We address the problem of collective motion across a barrier like encountered in fission. A formula for the quantal decay rate is derived which bases on a recently developed variational approach for functional integrals. This formula can be applied to low temperatures that have not been accessible within the former PSPA type approach. To account for damping of collective motion one particle Green functions are dressed with appropriate self-energies.

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arXiv2004

Damped collective motion of isolated many body systems within a variational approach to functional integrals

Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational approach quantum effects can be treated even at very low temperatures. A method is proposed of how to include collisional damping. Finally, our approach is applied to the calculation of the decay rate of metastable systems.

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arXiv2004

Nuclear quantum transport for barrier problems

A method is presented which allows one to introduce collective coordinates self-consistently, in distinction to the Caldeira-Leggett model. It is demonstrated how the partition function Z for the total nuclear system can be calculated to deduce information both on its level density as well as on the decay rate of unstable modes. For the evaluation of Z different approximations are discussed. A recently developed variational approach turns out superior to the conventional methods that include quantum effects on the level of local RPA. Dissipation is taken into account by applying energy smearing, simulating in this way the coupling to more complicated states. In principle, such a coupling must depend on temperature. Previous calculations along another microscopic approach show this fact to imply an intriguing variation of the transport coefficients of collective motion with T. The relevance of this feature is demonstrated for the thermal fission rate and for the formation probability of super-heavy elements.

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arXiv2003

Influence of microscopic transport coefficients on the formation probabilities for super-heavy elements

The formation probability is shown to increase by a few orders of magnitude if microscopic transport coefficients are used rather than those of the common macroscopic pictures. Quantum effects in collective dynamics are taken into account through the fluctuating force, as exhibited in diffusion coefficients for a Gaussian process. In the range of temperatures considered here, they turn out to be of lesser importance.

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arXiv1997

Variation of transport coefficients for average fission dynamics with temperature and shape

We study slow collective motion at finite thermal excitations on the basis of linear response theory applied to the locally harmonic approximation. The transport coefficients for average motion, friction γ, inertia M and the local stiffness C are computed along a fission path of Th-224 within a quasi-static picture. The inverse relaxation time β=γ/M and the effective damping rate η=γ/(2\sqrt{M|C|}) are found to increase with temperature, but do not change much with the collective variable. The values found for ηand βas well as their behavior with temperature are in accord with experimental findings.

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arXiv1995

On the nature of nuclear dissipation, as a hallmark for collective dynamics at finite excitation

We study slow collective motion of isoscalar type at finite excitation. The collective variable is parameterized as a shape degree of freedom and the mean field is approximated by a deformed shell model potential. We concentrate on situations of slow motion, as guaranteed, for instance, by the presence of a strong friction force, which allows us to apply linear response theory. The prediction for nuclear dissipation of some models of internal motion are contrasted. They encompass such opposing cases as that of pure independent particle motion and the one of "collisional dominance". For the former the wall formula appears as the macroscopic limit, which is here simulated through Strutinsky smoothing procedures. It is argued that this limit hardly applies to the actual nuclear situation. The reason is found in large collisional damping present for nucleonic dynamics at finite temperature $T$. The level structure of the mean field as well as the $T$-dependence of collisional damping determine the $T$-dependence of friction. Two contributions are isolated, one coming from real transitions, the other being associated to what for infinite matter is called the "heat pole". The importance of the latter depends strongly on the level spectrum of internal motion, and thus is very different for "adiabatic" and "diabatic" situations, both belonging to different degrees of "ergodicity".

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arXiv1994

On the Macroscopic Limit of Nuclear Dissipation

The Landau-Vlasov equation is applied to a slab of width $L$. This geometry is introduced to simulate somehow the finiteness of real nuclei but to allow for analytical solutions, nevertheless. We focus on the damping of low frequency surface modes and discuss their friction coefficient. For this quantity we study the macroscopic limit as defined by $L\to \infty$. We demonstrate that the same result can be obtained for finite $L$ by applying an appropriate frequency smoothing, if only the smearing interval is sufficiently large. The apparent, but important consequences are discussed which this result will have for the understanding of the nature of dissipation in real nuclei.

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arXiv1994

Quantum Effects in the Stochastic Behaviour of Nuclear Matter at Finite Excitations\FOOTNOTE

We examine the dynamics of statistical fluctuations in nuclear matter. Linear response functions for the average phase space density are derived within Landau theory. Properties of the stochastic forces are deduced from the quantal fluctuation dissipation theorem, with a suitable generalization to unstable modes. Sizable quantum effects are found both inside and outside the spinodal regime.

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arXiv1993

Fission Decay Rates Determined from a Quantal Transport Equation

The decay of a metastable system is described by extending Kramers' method to the quantal regime. For temperatures above twice the crossover value we recover the result known from applying Euclidean path integrals to solvable models. Our derivation is not restricted to a linearly coupled heat bath of oscillators, and thus applicable to nuclear systems.

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