Multiresonance modes in sine–Gordon brane models

In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine–Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine–Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.     

Decoherence effects in Bose–Einstein condensate interferometry I. General theory

The present paper outlines a basic theoretical treatment of decoherence and dephasing effects in interferometry based on single component Bose–Einstein condensates in double potential wells, where two condensate modes may be involved. Results for both two mode condensates and the simpler single mode condensate case are presented. The approach involves a hybrid phase space distribution functional method where the condensate modes are described via a truncated Wigner representation, whilst the basically unoccupied non-condensate modes are described via a positive P representation. The Hamiltonian for the system is described in terms of quantum field operators for the condensate and non-condensate modes. The functional Fokker–Planck equation for the double phase space distribution functional is derived. Equivalent Ito stochastic equations for the condensate and non-condensate fields that replace the field operators are obtained, and stochastic averages of products of these fields give the quantum correlation functions that can be used to interpret interferometry experiments. The stochastic field equations are the sum of a deterministic term obtained from the drift vector in the functional Fokker–Planck equation, and a noise field whose stochastic properties are determined from the diffusion matrix in the functional Fokker–Planck equation. The stochastic properties of the noise field terms are similar to those for Gaussian–Markov processes in that the stochastic averages of odd numbers of noise fields are zero and those for even numbers of noise field terms are the sums of products of stochastic averages associated with pairs of noise fields. However each pair is represented by an element of the diffusion matrix rather than products of the noise fields themselves, as in the case of Gaussian–Markov processes. The treatment starts from a generalised mean field theory for two condensate modes, where generalised coupled Gross–Pitaevskii equations are obtained for the modes and matrix mechanics equations are derived for the amplitudes describing possible fragmentations of the condensate between the two modes. These self-consistent sets of equations are derived via the Dirac–Frenkel variational principle. Numerical studies for interferometry experiments would involve using the solutions from the generalised mean field theory in calculations for the stochastic fields from the Ito stochastic field equations.     

Brane bounce-type configurations in a string-like scenario

Brane world six-dimensional scenario with string-like metric has been proposed to alleviate the problem of field localization. However, these models have been suffering from some drawbacks related with energy conditions as well as from difficulties to find analytical solutions. In this work, we propose a model where a brane is made of a scalar field with bounce-type configurations and embedded in a bulk with a string-like metric. This model produces a sound AdS scenario where none of the important physical quantities is infinite. Among these quantities are the components of the energy–momentum tensor, which have its positivity ensured by a suitable choice of the bounce configurations. Another advantage of this model is that the warp factor can be obtained analytically from the equations of motion for the scalar field, obtaining as a result a thick brane configuration, in a six-dimensional context. Moreover, the study of the scalar field localization in this scenario is done.     

Unified field theories of bags and strings

Within our models of temporary quark confinement in field theoretical bags, we exhibit, in the tree approximation, string-like solutions. We argue that the bag-like and dual string-like pictures complement each other with the former describing the low-lying hadronic states and the latter the excited states of large angular momentum. When certain quantum fluctuation effects are included, we find Regge trajectories, in a certain dynamical regime, to always approach straight lines in a (J, E²) plane.     

WKB analysis of relativistic Stern–Gerlach measurements

Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern–Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern–Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern–Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle we show that the +1 and −1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern–Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern–Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered.     

Massive CP theory from a microscopic model for doped antiferromagnets

A path-integral for the t–J$t\text{–}J$ model in two dimensions is constructed based on Dirac quantization, with an action found originally by Wiegmann [P. Wiegmann, Phys. Rev. Lett. 60 (1988) 821; P. Wiegmann, Nucl. Phys. B 323 (1989) 311]. Concentrating on the low doping limit, we assume short range antiferromagnetic order of the spin degrees of freedom. Going over to a local spin quantization axis of the dopant fermions, that follows the spin degree of freedom, staggered CP¹ fields result and the constraint against double occupancy can be resolved. The staggered CP¹ fields are split into slow and fast modes, such that after a gradient expansion, and after integrating out the fast modes and the dopant fermions, a CP¹ field-theory with a massive gauge field is obtained that describes generically incommensurate coplanar magnetic structures, as discussed previously in the context of frustrated quantum antiferromagnets. Hence, the possibility of deconfined spinons is opened by doping a colinear antiferromagnet.     

Quantum contour field equations

The renormalization procedure for fields on a contour is considered. It is shown that in a quantum string-like equation for a non-abelian contour field the mass term has the correct sign.     

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.     

K-essential covariant holography

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.     

Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Schwinger mechanism enhanced by the Nielsen–Olesen instability

We discuss gluon production by the Schwinger mechanism in collinear color-electric and magnetic fields which may be realized in pre-equilibrium stages of ultra-relativistic heavy-ion collisions. Fluctuations of non-Abelian gauge fields around a purely color-magnetic field contain exponentially growing unstable modes in a longitudinally soft momentum region, which is known as the Nielsen–Olesen instability. With a color-electric field imposed parallelly to the color-magnetic field, we can formulate this instability as the Schwinger mechanism. This is because soft unstable modes are accelerated by the electric fields to escape from the instability condition. Effects of instability remain in the transverse spectrum of particle modes, leading to an anomalously intense Schwinger particle production.     

Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations

The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collective coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center-of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) σ-model.     

SIM(2)-invariant modifications of electrodynamic theory

In the Cohen–Glashow Very Special Relativity we exhibit possible modifications to the Maxwell theory and to the quantum electrodynamics Lagrangian in some generality, and discuss characteristic features depending on the modifications. Modified gauge transformations in SIM(2)-invariant theories are introduced and the related gauge fields, with two polarization states, can have nonzero mass. Also considered are SIM(2)-covariant modifications to the Proca-type field equations for a massive spin-1 particle.     

Confluent Heun functions and the physics of black holes: Resonant frequencies,Hawking radiation and scattering of scalar waves

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.     

Creation of vector bosons by an electric field in curved spacetime

We investigate the creation rate of massive spin-1 bosons in the de Sitter universe by a time-dependent electric field via the Duffin–Kemmer–Petiau (DKP) equation. Complete solutions are given by the Whittaker functions and particle creation rate is computed by using the Bogoliubov transformation technique. We analyze the influence of the electric field on the particle creation rate for the strong and vanishing electric fields. We show that the electric field amplifies the creation rate of charged, massive spin-1 particles. This effect is analyzed by considering similar calculations performed for scalar and spin-1/2$1/2$ particles.     

Analytic solutions in the dyon black hole with a cosmic string: Scalar fields,Hawking radiation and energy flux

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.     

Extended entanglement to quantum networks

Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms–fields entanglement to atoms–atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.     

The phase and critical point of quantum Einstein–Cartan gravity

By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D 82 (2010) 064039] the quantum Einstein–Cartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein–Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein–Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.