Functional integral mean field expansions for nuclear many fermion systems

Kerman, A.K.; Levit, Shimon; Troudet, T.

doi:10.1016/0003-4916(83)90246-4

Cited by 62 publications

(46 citation statements)

References 20 publications

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“…Since each evolution can be solved with numerical techniques used in mean field theories, SSE offer a chance to solve exactly the dynamics of strongly interacting fermionic systems. This property has already been noted in several pioneering works [16,17,18]. A very similar conclusion has been reached for the description of interacting bosons using MonteCarlo wave function techniques [21].…”

Section: B Functional Integrals and Stochastic Many-body Dynamicssupporting

confidence: 81%

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Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Lacroix

2005

Phys. Rev. C

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We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D ab = |Φa Φ b |, where each state evolves according to the Stochastic Schrödinger Equation (SSE) given in ref. [1]. A stochastic Liouville-von Neumann equation is derived as well as the associated Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

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Section: B Functional Integrals and Stochastic Many-body Dynamicssupporting

confidence: 81%

“…Functional integrals methods applied to quantum fermionic systems in interaction [16,17] lead to general stochastic formulations of the quantum many-body problem. They however also lead to specific difficulties.…”

Section: B Functional Integrals and Stochastic Many-body Dynamicsmentioning

confidence: 99%

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Lacroix

2005

Phys. Rev. C

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“…It is known that the standard HS transformation does not yield a Hartree Fock mean-field state and cannot capture both Hartree and the exchange fluctuations 13 . Kerman, Levit, and Troudet have presented a generalization of the HS transformation which overcomes these limitations 14 . To establish our notation (which differs from that of Kerman et al), we briefly review the previous work which describes an approach for obtaining systematic corrections to Hartree-Fock mean-field approximations for the grand potential.…”

Section: Auxiliary Field Functional Integral Approachmentioning

confidence: 99%

Microscopic functional integral theory of quantum fluctuations in double-layer quantum Hall ferromagnets

Joglekar

MacDonald

2001

Phys. Rev. B

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We present a microscopic theory of zero-temperature order parameter and pseudospin stiffness reduction due to quantum fluctuations in the ground state of double-layer quantum Hall ferromagnets. Collective excitations in this systems are properly described only when interactions in both direct and exchange particle-hole channels are included. We employ a functional integral approach which is able to account for both, and comment on its relation to diagrammatic perturbation theory. We also discuss its relation to Gaussian fluctuation approximations based on Hubbard-Stratonovichtransformation representations of interactions in ferromagnets and superconductors. We derive remarkably simple analytical expressions for the correlation energy, renormalized order parameter and renormalized pseudospin stiffness.

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“…It has been shown that the one-body evolution operator (the last exponent in Eq. (II.1) can be chosen to have an arbitrary form [26] and that this arbitrariness is resolved only when one goes beyond the stationary phase approximation and includes the quadratic fluctuations of the auxiliary field σ αβ (k).…”

Section: A Real-time Functional Integral Approach and Some Of Its LImentioning

confidence: 99%

The long journey fromab initiocalculations to density functional theory for nuclear large amplitude collective motion

Bulgac

2010

J. Phys. G: Nucl. Part. Phys.

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At present there are two vastly different ab initio approaches to the description of the the manybody dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented exactly, the DFT approach can allow in principle the exact evaluation of arbitrary one-body observable. However, when applied to Large Amplitude Collective Motion (LACM) this approach needs to be extended in order to accommodate the phenomenon of surface-hoping, when adiabaticity is strongly violated and the description of a system using a single (generalized) Slater determinant is not valid anymore. The functional integral approach on the other hand does not appear to have such restrictions, but its implementation does not appear to be straightforward endeavor. However, within a functional integral approach one seems to be able to evaluate in principle any kind of observables, such as the fragment mass and energy distributions in nuclear fission. These two radically approaches can likely be brought brought together by formulating a stochastic time-dependent DFT approach to many-body dynamics. We know a great deal by now about interactions between nucleons, although one might rightly argue that the link to quarks and gluons through the more fundamental theory Quantum Chromodynamics has not yet been fully established. It will still be a long time until this goal will be reached with the needed degree of accuracy and sophistication. In this respect the nuclear many-body theory is at a great disadvantage when compared to condensed matter and atomic theories or chemistry, where the dominant role of the Coulomb interaction and the link to Quantum Electrodynamics were clarified a long time ago. There is a general consensus by now however, that in order to describe nuclear many-body systems one probably can get away with the use of one set or another of reasonably well established two-and three-nucleon potentials (if only one would manage to use them in a convincing implementation) and that a non-relativistic approach is likely sufficient for now. The best example we have so far that such an ab initio approach can be brought to fruition is the Green Function Monte-Carlo (GFMC) approach implemented so successfully by V.R. Pandharipande and his many students and collaborators J. Carlson (truly the author of GFMC), S.C. Pieper, R. Schiavilla, K.E. Schmidt, R.B. Wiringa, and many others [1]. One of the most frustrating limitations of the GFMC approach is the relatively low particle number this method can deal with. Presently one cannot envision the study of nuclei heavier than oxygen within a GFMC framework. The Coupled-Cluster (CC) method [2] looks very promising in this respect, as it might be applied to medium size closed shell nuclei in the near future. The No-Core-Shell Model (NCSM) [3] will likely be successfully applied to light and medium size nuclei in the foreseeable future with a reasonable degree of accuracy.Heavy-nuclei seem out of reach from a direct frontal ab initio attack and th...

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Functional integral mean field expansions for nuclear many fermion systems

Cited by 62 publications

References 20 publications

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Microscopic functional integral theory of quantum fluctuations in double-layer quantum Hall ferromagnets

The long journey fromab initiocalculations to density functional theory for nuclear large amplitude collective motion

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