Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics E

A STOCHASTIC PARAMETRISATION OF THE SPECTRA OF THE NUCLEAR PAIRING HAMILTONIAN

HERVÉ MOLIQUE, J. Dudek

Published Feb 1, 2004• 0 citations
Publisher

Abstract

In this article we present a method to parametrise the exact solutions to the nuclear pairing problem, for realistic large-scale many-body spaces. This new approach allows for rapid and quite accurate estimates of the pairing influence on the excitation energies of the nucleus, treated in the standard mean-field approximation.
DOI
10.1142/s0218301304002004

Related papers

NUCLEAR PAIRING AS RANDOM WALK OF COOPER PAIRS

J. Dudek, Jean Baptiste Faes

We develop a stochastic approach to obtain the energies and wave functions of the full spectrum of the nuclear pairing Hamiltonian (i.e. not only the ground-state but also the excited states of the nuclear many-body systems). We assume that nuclear Cooper pairs may spontaneously jump from one energy configuration to another, the mechanism resembling that of the random walk on a mesh of non-equidistant points. A probability distribution associated with such a random walk is modelled and the resulting solutions tested using an exact quantum algorithm. We use the Hamiltonian parameters characteristic for the nuclear scale: at present an agreement between the quantum and stochastic treatment is of the order of a few permille in terms of eigen-energies.

International Journal of Modern Physics E•Feb 1, 2004•0 citations

Exact solutions for the mean field plus state-dependent pairing Hamiltonian

Feng Pan, Jerry Paul Draayer, Lu Guo

The nuclear mean field plus state-dependent pairing problem is studied by using the Bethe ansatz method. It is shown that the Hamiltonian can be expanded in terms of generators of the infinite-dimensional Lie algebra without central extension. Exact solutions for excited energies and the corresponding eigenstates of the nuclear pairing problem are derived through the Bethe ansatz equations.

Journal of Physics A Mathematical and General•Feb 22, 2000•8 citations

New approach to large-scale nuclear structure calculations

J. Dukelsky, Stuart Pittel

A new approach to large-scale nuclear structure calculations, based on the density matrix renormalization group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in a single large-$j$ shell and interacting via a pairing plus quadrupole interaction. In cases in which exact diagonalization of the Hamiltonian is possible, the method is able to reproduce the exact results for the ground-state energy and the energies of low-lying excited states with extreme precision. Results are also presented for a model problem in which exact solution is not feasible.

arXiv:nucl-th/0101048•Physical Review C•May 2, 2001•27 citations

Nuclear pairing within a configuration-space Monte Carlo approach

Mark Lingle, Alexander Volya

Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.

Physical Review C•Jun 8, 2015•8 citations

Study of nuclear pairing with Configuration-Space Monte-Carlo approach

Mark Lingle, Alexander Volya

Pairing correlations in nuclei play a decisive role in determining nuclear drip-lines, binding energies, and many collective properties. In this work a new Configuration-Space Monte-Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte-Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control, are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with non-constant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.

arXiv:1503.06179•Mar 20, 2015•0 citations

Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian

Yiheng Qiu, Thomas M. Henderson, T. Duguet +1 more

A many-body formalism is developed to consistently combine particle-number projection techniques with Bogoliubov coupled-cluster theory. Applied to the Richardson pairing Hamiltonian, the method produces highly accurate solutions over the complete range of pairing strengths (from weak to strong correlations). The next step will be to apply the method to realistic nuclear Hamiltonians and treat similarly the angular-momentum breaking and restoration.

arXiv:1810.11245•Physical Review C•Apr 1, 2019•58 citations
We develop a stochastic approach to obtain the energies and wave functions of the full spectrum of the nuclear pairing Hamiltonian (i.e. not only the ground-state but also the excited states of the nuclear many-body systems). We assume that nuclear Cooper pairs may spontaneously jump from one energy configuration to another, the mechanism resembling that of the random walk on a mesh of non-equidistant points. A probability distribution associated with such a random walk is modelled and the resulting solutions tested using an exact quantum algorithm. We use the Hamiltonian parameters characteristic for the nuclear scale: at present an agreement between the quantum and stochastic treatment is of the order of a few permille in terms of eigen-energies.
A new approach to large-scale nuclear structure calculations, based on the density matrix renormalization group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in a single large-jjj shell and interacting via a pairing plus quadrupole interaction. In cases in which exact diagonalization of the Hamiltonian is possible, the method is able to reproduce the exact results for the ground-state energy and the energies of low-lying excited states with extreme precision. Results are also presented for a model problem in which exact solution is not feasible.
Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.
Pairing correlations in nuclei play a decisive role in determining nuclear drip-lines, binding energies, and many collective properties. In this work a new Configuration-Space Monte-Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte-Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control, are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with non-constant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.