arXiv subjects

Niels R. Walet

Publications and source records attributed to Niels R. Walet.

At least 55 records · Page 3Linked to original sources

arXiv2004

Description of resonances in light nuclei using a microscopic cluster model

We investigate resonances in light halo nuclei using a fully microscopic cluster model and the complex scaling method. We make use of the hermitian representation of the complex scaling method. The general structure of the cluster model is that of a correlation operator acting on a starting function that describes a number of neutrons relative to an alpha-particle. The correlation operator is expanded in terms of a small non-orthogonal set of Gaussian basis states and we make use of a simplified, central but state-dependent, interaction. The many-body integrals required for the computation are evaluated by a variational Monte-Carlo algorithm. We show how to obtain resonant states for both $^5$He and $^6$He.

nucl-th↗

arXiv2004

Baryon structure in a quark-confining non-local NJL model

We study the nucleon and diquarks in a non-local Nambu-Jona-Lasinio model. For certain parameters the model exhibits quark confinement, in the form of a propagator without real poles. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states is solved in the covariant diquark-quark picture. The dependence of the nucleon mass on diquark masses is studied in detail. We find parameters that lead to a simultaneous reasonable description of pions and nucleons. Both the diquarks contribute attractively to the nucleon mass. Axial-vector diquark correlations are seen to be important, especially in the confining phase of the model. We study the possible implications of quark confinement for the description of the diquarks and the nucleon. In particular, we find that it leads to a more compact nucleon.

hep-ph↗

arXiv2004

Pairing in Many-Fermion Systems: An Exact Renormalisation Group Treatment

We study the application of the exact renormalisation group to a many-fermion system with a short-range attractive force. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The initial conditions are obtained by renormalising the interaction to fit the scattering length in vacuum. At some critical value of the running scale, the numerical solutions show a phase transition to a gapped phase. Standard results are recovered if we omit the boson loops. When boson fluctuations are included, we find that their contributions are significant only in the small-gap regime.

hep-ph↗

arXiv2004

Variational Monte Carlo for Microscopic Cluster Models

We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyse the required steps for a reliable application of the VMC in the case of a complicated many-body problem such as the direct solution of the nuclear hamiltonian with realistic interactions. We also examine the possibility of variance reduction through the `zero variance principle', paying particular attention to the complexity of the many-body problem.

nucl-th↗

arXiv2004

Oblate-prolate shape coexistence at finite angular momentum

We investigate shape coexistence in a rotating nucleus. We concentrate on the interesting case of 72-Kr which exhibits an interesting interplay between prolate and oblate states as a function of angular momentum. The calculation uses the local harmonic version of the method of self-consistent adiabatic large-amplitude collective motion. We find that the collective behaviour of the system changes with angular momentum and we focus on the role of non-axial shapes.

nucl-th↗

arXiv2003

Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach

Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to renormalization, we show that a powerful and elegant method exist to solve such problems. The method is in principle non-perturbative, and is not necessarily unitary.

hep-ph↗

arXiv2003

Towards a practical approach for self-consistent large amplitude collective motion

We investigate the use of an operatorial basis in a self-consistent theory of large amplitude collective motion. For the example of the pairing-plus-quadrupole model, which has been studied previously at equilibrium, we show that a small set of carefully chosen state-dependent basis operators is sufficient to approximate the exact solution of the problem accuratly. This approximation is used to study the interplay of quadrupole and pairing degrees of freedom along the collective path for realistic examples of nuclei. We show how this leads to a viable calculational scheme for studying nuclear structure, and discuss the surprising role of pairing collapse.

nucl-th↗

arXiv2003

Coupled-cluster renormalization group

The coupled cluster method (CCM) is one of the most successful and universally applicable techniques in quantum many-body theory. The intrinsic nonlinear and non-perturbative nature of the method is considered to be one of its advantages. We present here a combination of CCM with the Wilsonian renormalization group which leads to a powerful framework for construction of effective Hamiltonian field theories. As a toy example we obtain the two-loop renormalized $ϕ^{4}$ theory.

hep-th↗

arXiv2003

Relativistic Faddeev approach to a non-local NJL model

The diquark and nucleon are studied in a non-local NJL model. We solve the relativistic Faddeev equation and compare the results with the ordinary NJL model. Although the model is quark confining, it is not diquark confining in the rainbow-ladder approximation. We show that the off-shell contribution to the diquark $T$ matrix is crucial for the structure of the nucleon: without its inclusion the attraction in the scalar channel is too weak to form a three-body bound state.

hep-ph↗

arXiv2003

The unreasonable accuracy of the Jastrow approach in many-body physics

We investigate in a simple model whether a Jastrow-based approach for a many-body system containing two-body interactions can be exact. By comparison with recent assertions to the contrary, we find that in general the exact wave function is \emph{not} purely two-body correlated. Nonetheless, we show that the energy estimate obtained from the calculations is as accurate as it can possibly be, suggesting why Jastrow wave functions are such a good choice.

physics.chem-ph↗

arXiv2003

Linked-cluster Tamm-Dancoff Field Theory

To solve the relativistic bound-state problem one needs to systematically and simultaneously decouple the high-energy from the low-energy modes and the many-body from the few-particle states using a consistent renormalization scheme. In a recent paper we have shown that one such approach can be a combination of the coupled cluster method as used in many-body theory and the Wilsonian exact renormalization group. Even though the method is intrinsically non-perturbative, one can easily implement a loop expansion within it. In this letter we provide further support for this aspect of our formalism by obtaining results for the two-loop renormalized $ϕ^{4}$ theory. We show that the non-unitary representation inherent in our method leads to an economic computation and does not produce any non-hermiticity in the relevant terms.

hep-th↗

arXiv2002

Off-shell effects and consistency of many-body treatments of dense matter

Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyse this issue in the context of many-body approaches to nuclear matter, where it should be possible to shift the contributions of lowest order in purely off-shell two-body interactions into three-body forces. We show that none of the commonly used truncations of the two-body scattering amplitude such as the ladder, Brueckner-Hartree-Fock or parquet approximations respect this requirement.

nucl-th↗

arXiv2002

Soliton Systems at Finite Temperatures and Finite Densities

The finite-density and finite-temperature phase portraits of the baby-Skyrme and Skyrme models are investigated. Both grand-canonical and canonical approaches are employed. The grand-canonical approach can be used to find the ``natural'' crystal structure of the baby-Skyrme model and it is shown to have triangular symmetry. The phase portraits include solid, liquid and phase-coexistence between solids and vacuum states. Furthermore, a chiral phase transition can be observed for both models. The phase portrait of the Skyrme model is compared with that expected of strongly interacting matter, and we also contrast our results to other models.

hep-ph↗

arXiv2001

Colour superconductivity in finite systems

In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems.

hep-ph↗

arXiv2001

Full 2D Numerical Study of the Quantum Hall Skyrme Crystal

Spin textures arise in the effective action approach to the quantum Hall effect. Up to now these textures, also called Skyrmions, have been mainly studied using approximations. Studies of its finite density form, the crystal, have been limited to a given symmetry and tend ignore Skyrmion deformation. Using a simulated annealing technique, adapted to problems with a long-range interaction, we are able to present the first full 2D study of quantum Hall Skyrmions and the corresponding crystals. Our results show that only the Skyrmions with topological charge one and two are bound and that the Skyrme crystal is probably a triangular lattice made of charge-two Skyrmions.

cond-mat.mes-hall↗

arXiv2001

Towards a phase diagram of the 2D Skyrme model

We discuss calculations of the phase diagram of the baby-Skyrme model, a two-dimensional version of the model that has been so successful in the description of baryons. Contact is made with the sine Gordon model in 1D, and relations with the Skyrme model used in the quantum-Hall effect are pointed out. It is shown that at finite temperature the phase diagram is dominated by a liquid, and not the crystal that plays a role for zero temperature.

hep-ph↗

arXiv1999

Nucleons or diquarks? Competition between clustering and color superconductivity in quark matter

We study the instabilities of quark matter in the framework of a generalized Nambu--Jona-Lasinio model, in order to explore possible competition between three-quark clustering to form nucleons and diquark formation leading to color superconductivity. Nucleon and $Δ$ solutions are obtained for the relativistic Faddeev equation at finite density and their binding energies are compared with those for the scalar and axial-vector diquarks found from the Bethe-Salpeter equation. In a model with interactions in both scalar and axial diquark channels, bound nucleons exist up to nuclear matter density. However, except at densities below about a quarter of that of nuclear matter, we find that scalar diquark formation is energetically favored. This raises the question of whether a realistic phase diagram of baryonic matter can be obtained from any model which does not incorporate color confinement.

hep-ph↗

arXiv1999

Local harmonic approaches with approximate cranking operators

Methods of large amplitude collective motion in the adiabatic limit are examined with a special emphasis on conservation laws. We show that the restriction to point transformations, which is a usual assumption of the adiabatic time-dependent mean-field theory, needs to be lifted. In order to facilitate the application of large amplitude collective motion techniques, we examine the possibility of representing the RPA normal-mode coordinates by linear combinations of a limited number of one-body operators. We study the pairing-plus-quadrupole model of Baranger and Kumar as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner.

nucl-th↗