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Fri, 04 May 2001 00:00:00 +0200Fri, 04 May 2001 00:00:00 +0200Holographic Trace Anomaly and Cocycle of Weyl Group
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1190
Abstract: The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.R. Manvelyan; R. Mkrtchyan; H. J. W. Müller-Kirstenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1190Thu, 05 Apr 2001 00:00:00 +0200Periodic Bounce for Nucleation Rate at Finite Temperature in Minisuperspace Models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1182
Abstract: The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy considered here we observe that the period of the bounce increases with energy monotonically. The periodic bounces do not have bifurcations and make no contribution to the nucleation rate except the one with zero energy. The sharp first order phase transition from quantum tunneling to thermal activation is verified with the general criterions.J.-Q. Liang; H. J. W. Müller-Kirsten; Y.-B. Zhang; A.V. Shurgaia; S.-P Kou; D.K. Parkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1182Fri, 16 Feb 2001 00:00:00 +0100Universality or Non-Universality of Absorption Cross Sections for Extended Objects
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1175
Abstract: The calculation of absorption cross sections for minimal scalars in supergravity backgrounds is an important aspect of the investigation of AdS/CFT correspondence and requires a matching of appropriate wave functions. The low energy case has attracted particular attention. In the following the dependence of the cross section on the matching point is investigated. It is shown that the low energy limit is independent of the matching point and hence exhibits universality. In the high energy limit the independence is not maintained, but the result is believed to possess the correct energy dependence.D.K. Park; H. J. W. Müller-Kirstenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1175Fri, 16 Feb 2001 00:00:00 +0100Instanton-Sphaleron transition in the d = 2 Abelian-Higgs model on a Circle
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1176
Abstract: The transition from the instanton-dominated quantum regime to the sphaleron-dominated classical regime is studied in the d = 2 abelian-Higgs model when the spatial coordinate is compactified to S1. Contrary to the noncompactified case, this model allows both sharp first-order and smooth second-order transitions depending on the size of the circle. This finding may make the model a useful toy model for the analysis of baryon number violating processes.D.K. Park; H. J. W. Müller-Kirsten; J.-Q. Liang; A. V. Shurgaiapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1176Fri, 16 Feb 2001 00:00:00 +0100Quantum Phase Interference for Quantum Tunneling in Spin Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1179
Abstract: The point-particle-like Hamiltonian of a biaxial spin particle with external magnetic field along the hard axis is obtained in terms of the potential field description of spin systems with exact spin-coordinate correspondence. The Zeeman energy term turns out to be an effective gauge potential which leads to a nonintegrable phase of the Euclidean Feynman propagator. The phase interference between clockwise and anticlockwise under barrier propagations is recognized explicitly as the Aharonov-Bohm effect. An additional phase which is significant for quantum phase interference is discovered with the quantum theory of spin systems besides the known phase obtained with the semiclassical treatment of spin. We also show the energy dependence of the effect and obtain the tunneling splitting at excited states with the help of periodic instantons.J.-Q. Liang; H. J. W. Müller-Kirsten; D. K. Park; F.-C. Pupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1179Fri, 16 Feb 2001 00:00:00 +0100Absorption Cross Section of Scalar Field in Supergravity Background
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1155
Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.R. Manvelyan; H. J. W. Müller-Kirsten; J.-Q. Liang; Yunbo Zhangpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1155Fri, 09 Feb 2001 00:00:00 +0100Finite Temperature Tunneling and Phase Transitions in SU(2)-Gauge Theory
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1151
A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field confiurations are found, which interpolate between the vacuum and sphaleron field configurations. It is shown by explicit calculation that only smooth second order transitions occur for all permissible values of the parameter A introduced with the quartic term. The theory is one of the rare cases which canbe handled analytically.A.V. Shurgaia; H. J. W. Müller-Kirsten; J.-Q. Liang; D.K. Parkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1151Mon, 22 Jan 2001 00:00:00 +0100Nucleation at Finite Temperature Beyond the Superminispace Model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1152
Abstract: The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O (3) nonlinear o-model, the transition is seen to be only of the first order. PACS numbers: 11.15.Kc, 03.65Sq, 05.70.Fh, 98.80.CqJ.-Q. Liang; H. J. W. Müller-Kirsten; D.K. Park; A. V. Shurgaiapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1152Mon, 22 Jan 2001 00:00:00 +0100BRST-Invariant Approach to Quantum Mechanical Tunneling
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/883
A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path- integral calculation of quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the Sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhoupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/883Mon, 03 Apr 2000 00:00:00 +0200Periodic Instantons and Quantum-Classical Transitions in Spin Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/896
The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.Jiu-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; D.K. Parkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/896Mon, 03 Apr 2000 00:00:00 +0200Light-Cone Formulation of Super D2-Brane
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/900
The light-cone Hamiltonian approach is applied to the super D2- brane, and the equivalent area-preserving and U(1) gauge-invariant effective Lagrangian, which is quadratic in the U(1) gauge field, is derived. The latter is recognised to be that of the three- dimensional U(1) gauge theory, interacting with matter supermultiplets, in a special external induced supergravity metric and the gravitino field, depending on matter fields. The duality between this theory and 11d supermembrane theory is demonstrated in the light-cone gauge.Ruben Manvelyan; H. J. W. Müller-Kirsten; A. Melikyan; R. Mkrtchyanpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/900Mon, 03 Apr 2000 00:00:00 +0200A new look at the RST model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/885
The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field 1 in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors TSigma Sigma are recovered to be true tensor quantities. Especially, the part of the stress tensors for the hidden dynamical field 1 gives the precise expression for tSigma . At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field 1, the fact that the semi-classical static soluti on of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhoupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/885Mon, 03 Apr 2000 00:00:00 +0200Skyrme Sphalerons of an O(3)-oe Model and the Calculation of Transition Rates at Finite Temperature
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/892
The reduced O(3)-oe model with an O(3) ! O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i. e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the fluctuation path integrals which is therefore evaluated using a measure-modified Fourier-Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme-less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.H. J. W. Müller-Kirsten; D.H. Tschrakian; F. Zimmerschiedpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/892Mon, 03 Apr 2000 00:00:00 +0200Significance of zero modes in path-integral quantization of solitonic theories with BRST invariance
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/886
The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1 + 2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to -the one-loop approximation.Jui-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Jiang-Ge Zhou; D. H. Tchrakianapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/886Mon, 03 Apr 2000 00:00:00 +0200Quantisation of 2D-gravity with Weyl and area-preserving diffeomorphism invariances
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/887
The constraint structure of the induced 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called "quasi-light-cone" gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. This observation indicates that the claimed correspondence between the SL(2,R) residual symmetry and the area-preserving diffeomorphism invariance in both regularisation approaches does not hold. The string-like approach is then applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained, which means that the area-preserving diffeomorphism invariance can be maintained at the quantum level.J.-Q. Liang; H. J. W. Müller-Kirsten; Zhenjiu Zhang; J.-G. Zhou; Y.-G. Miaopreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/887Mon, 03 Apr 2000 00:00:00 +0200Instanton Induced Tunneling Amplitude At Excited States With The LSZ Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/889
Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory and may be of importance in the study of macroscopic quantum phenomena in magnetic systems.H. J. W. Müller-Kirsten; Jiu-Qing Liang; J.-G. Zhou; J. Burzlaffpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/889Mon, 03 Apr 2000 00:00:00 +0200Application of Instatons: Quenching Of Macroscopic Quantum Coherence And Macroscopic Fermi-Particle Configurations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/890
Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels E = ffl0 Gamma 24ffl cos(s + ,)ss of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of cos(s + ,)ss in disagreement with the suppression of tunneling (i.e. 4ffl = 0) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunne- ling rate ( 24fflss ) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.H. J. W. Müller-Kirsten; Jiu-Qing Liang; Jian-Ge Zhoupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/890Mon, 03 Apr 2000 00:00:00 +0200Simple Calculation of Quantum Spin Tunneling Effects
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/891
The level splitting formulae much discussed in the study of spin tunneling in macroscopic ferromagnetic particles and previously derived only by complicated pseudoparticle methods for the ground state, are derived from those of eigenvalues of periodic equations and extended to excited states.Jiu-Qing Liang; H. J. W. Müller-Kirsten; J. M. Singh Ranapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/891Mon, 03 Apr 2000 00:00:00 +0200Enhancement of Quantum Tunneling for Excited States in Ferromagnetic Particles
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/894
A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual(vacuum) instanton is recovered.The observation made with our new result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.Jiu-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; Y.-B. Zhang; Jian-Ge Zhou; F.-C. Pupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/894Mon, 03 Apr 2000 00:00:00 +0200Calculation of Spin Tunneling Effects in the Presence of an Applied Magnetic Field
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/895
The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.Jiu-Qing Liang; H. J. W. Müller-Kirsten; F. Zimmerschied; A.V. Shurgaiapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/895Mon, 03 Apr 2000 00:00:00 +0200Quantum Tunneling and Phase Transitions in Spin Systems with an Applied Magnetic Field
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/897
Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first- or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.S.-Y. Lee; H. J. W. Müller-Kirsten; F. Zimmerschied; D.K. Parkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/897Mon, 03 Apr 2000 00:00:00 +0200Dilute Instanton Gas of an O(3)Skyrme Model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/901
The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.H. J. W. Müller-Kirsten; S.-N. Tamariana; D.H. Tchrakian; Frank Zimmerschiedpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/901Mon, 03 Apr 2000 00:00:00 +02002D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/902
The ADM and Bondi mass for the RST model have been first discussed from Hawking and Horowitz's argument. Since there is a nonlocal term in the RST model, the RST lagrangian has to be localized so that Hawking and Horowitz's proposal can be carried out. Expressing the localized RST action in terms of the ADM formulation, the RST Hamiltonian can be derived, meanwhile keeping track of all boundary terms. Then the total boundary terms can be taken as the total energy for the RST model. Our result shows that the previous expression for the ADM and Bondi mass actually needs to be modified at quantum level, but at classical level, our mass formula can be reduced to that given by Bilal and Kogan [5] and de Alwis [6]. It has been found that there is a new contribution to the ADM and Bondi mass from the RST boundary due to the existence of the hidden dynamical field. The ADM and Bondi mass with and without the RST boundary for the static and dynamical solutions have been discussed respectively in detail, and some new properties have been found. The thunderpop of the RST model has also been encountered in our new Bondi mass formula.H. J. W. Müller-Kirsten; Jian-Ge Zhou; Yan-Gang Miao; Jiu-Qing Liangpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/902Mon, 03 Apr 2000 00:00:00 +0200A condition for first order phase transitions in quantum mechanical tunneling models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1070
H. J. W. Müller-Kirsten; D.K. Park; J.M.S. Ranapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1070Fri, 10 Mar 2000 00:00:00 +0100The Wess-Zumino term and quantum tunneling
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1071
J.-Q. Liang; L. Maharana; H. J. W. Müller-Kirstenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1071Fri, 10 Mar 2000 00:00:00 +0100