Brane cosmology in an arbitrary number of dimensions

Chatillon, N.; Macesanu, Cosmin; Trodden, Mark

doi:10.1103/physrevd.74.124004

Cited by 18 publications

(26 citation statements)

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“…The study of the fission of the neutron-deficient Thorium isotopes, which are analyzed in this paper, has been motivated by the experimental data obtained during the 2012 SOFIA campaign at GSI Darmstadt [58,59]. The measurements concern the thorium isotopes 230 Th, 229 Th, 226 Th, 225 Th, 223 Th, 222 Th and 221 Th.…”

Section: Resultsmentioning

confidence: 99%

“…The tensor interaction rearranges the position of the single particle orbitals changing the shell effects responsible for many of the properties of the quantities relevant to fission. In fact, it could be the missing ingredient required to explain a symmetric bimodal fission mode recently found in some neutron-deficient thorium isotopes [56][57][58][59]. Recent experimental data provided by the experiments of the SOFIA collaboration have revealed the existence of such a symmetric bimodal mode, composed of the standard super-long mode and a new compact mode.…”

Section: Introductionmentioning

confidence: 95%

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Description of the asymmetric to symmetric fission transition in the neutron-deficient thorium isotopes: Role of the tensor force

et al. 2020

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In the present study, we have investigated the impact of the tensor force on fission paths, in particular the symmetric and asymmetric barriers in 230 Th, 226 Th, 222 Th and 216 Th isotopes which display an asymmetric to symmetric fission transition. This analysis has been performed within the HFB approach with (Q20,Q30,Q40) as collective variable constraints, using the D1ST2a Gogny+tensor term interaction and comparing to the standard D1S Gogny interaction results. The effects from the tensor term on the potential energy surface landscape, and especially on barrier heights and its topology by opening a new valley in agreement with experimental data, are found to be crucial in the description of exotic actinide fission. We conclude that a tensor term should be integrated to the long range part of the effective interaction for a better description of the fission.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Description of the asymmetric to symmetric fission transition in the neutron-deficient thorium isotopes: Role of the tensor force

et al. 2020

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“…The equilibrium points are then given by (z a = 0, y = y o ). The nature as well as the stability of these equilibrium points can be obtained by linearising equations (9) and studying the eigenvalues of the corresponding Jacobian matrix about the equilibrium points. In this case this is a 2n × 2n matrix given by…”

Section: Motion Of Massive Particles In the Neighbourhood Of The Submmentioning

confidence: 99%

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

et al. 2008

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We study the classical geodesic motions of nonzero rest mass test particles and photons in (3 + 1 + n)-dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3+1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3 + 1)-spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.

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“…Consequently, it is necessary to review the development of the relativity and gravity in higher dimensional wave equations for completeness. These contributions can be summarized as follows: the brane models [119], scalar field contribution to rotating black hole entropy [120], brane cosmology [121], N -dimensional Vaidya metric with a cosmological constant in double-null coordinates [122], the spherical gravitational collapse in N dimensions [123], the motion of a dipole in a cosmic string background [124], repulsive Casimir effect from extra dimensions and Robin boundary conditions [125], extremal black hole/CFT correspondence in gauged supergravity [126], massive fermion emission from higher dimensional black holes [127], magnetic and electric black holes [128], fermion families from two layer warped extra dimensions [129], quasinormal behavior of the D-dimensional Schwarzschild black hole [130], the study of the Schrödinger-Newton equations in D dimensions [131], rotating Einstein-Maxwell-Dilaton black holes in D dimensions [132], the Kaluza-Klein theory in the limit of large number of extra dimensions [133], gauge invariance of the one-loop effective potential in (d + 1)-dimensional Kaluza-Klein theory [134] and the multicentered solution for maximally charged dilaton black holes in arbitrary dimensions [135]. Such method was also generalized to quantum modes of the scalar field on AdS d+1 space-time [117] as well as geometric models of the (d + 1)-dimensional relativistic rotating oscillators [118].…”

Section: Introduction 1 Basic Reviewmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

224

153

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No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. PrefaceThis work will introduce the wave equations in higher dimensions at an advanced level addressing students of physics, mathematics and chemistry. The aim is to put the mathematical and physical concepts and techniques like the wave equations, group theory, generalized hypervirial theorem, the Levinson theorem, exact and proper quantization rules related to the higher dimensions at the reader's disposal. For this purpose, we attempt to provide a comprehensive description of the wave equations including the non-relativistic Schrödinger equation, relativistic Dirac and Klein-Gordon equations in higher dimensions and their wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this field are the quantum mechanics and group theory. In fact, the author's driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the wave equations in higher dimensions drawn from the teaching and research experience of the author since the literature is inundated with scattered articles in this field and to pave the reader's way into this territory as rapidly as possible. We have made the effort to present the clear and understandable derivations and include the necessary mathematical steps so that the intelligent and diligent reader is able to follow the text with relative ease, in particular, when mathematically difficult material is presented. The author also embraces enthusiastically the potential of the LaTeX typesetting language to enrich the presentation of the formulas as to make the logical pattern behind the mathematics more transparent. In addition, any suggestions and criticism to improve the text are most welcome. It should be pointed out that the main effort to follow the text and master the material is left to the reader even though this book makes an effort to serve the reader as much as was possible for the author. This book starts out in Chap. 1 with a comprehensive review for the wave equations in higher dimensions and builds on this to introduce in Chap. 2 the fundamental theory about the SO(N ) group to be used in the successive Chaps. 3-5 including the non-relativistic Schrödinger equation, relativistic Dirac and Klein-Gordon equations. As important applications in non-relativistic quantum mechanics, from Chap. 6 to Chap. 12, we shall apply the theories proposed in Part II to study some vii viii Preface important quantum systems such as the harmonic oscillator, Coulomb potential, the Levinson theorem, generalized hypervirial theorem, exact and proper...

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Brane cosmology in an arbitrary number of dimensions

Cited by 18 publications

References 60 publications

Description of the asymmetric to symmetric fission transition in the neutron-deficient thorium isotopes: Role of the tensor force

Description of the asymmetric to symmetric fission transition in the neutron-deficient thorium isotopes: Role of the tensor force

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

Wave Equations in Higher Dimensions

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