Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

The full spectrum of two‐dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of graphene, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in graphene. Here, only one Lorentz‐violating parameter is considered, belonging to the scalar sector. The analytical methods developed in the context of 1+1 field theories are extended to explore the effect of the Lorentz symmetry breaking in the charge carrier density of two‐dimensional materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. These findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.     

The Mixmaster Universe in Five Dimensions

We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this result within the context of induced matter theory.     

Energy and Relativistic Clock Rates in Five Dimensions

In the framework of a Kaluza-Klein-like scheme, based on a five-dimensional Riemannian space in which energy plays the role of the fifth dimension, we discuss a class of solutions of the five-dimensional Einstein equations in vacuum, which allows us to recover the energy-dependent phenomenological metric for gravitation, recently derived from the analysis of some experimental data concerning the slowing down of clock rates in the gravitational field of Earth.     

Seiberg--Witten Monopoles in Three Dimensions

Dimensional reduction of the Seiberg--Witten equations leads to the equations of motion of a U(1) Chern--Simons theory coupled to a massless spinorial field. A topological quantum field theory is constructed for the moduli space of gauge equivalence classes of solutions of these equations. The Euler characteristic of the moduli space is obtained as the partition function which yields an analogue of Casson's invariant.A mathematically rigorous definition of the invariant isdeveloped for homology spheres using the theory of spectral flow ofself-adjoint Fredholm operators.     

Deuteron Disintegration in Three Dimensions

We compare results from traditional partial wave treatment of deuteron electro-disintegration with a new approach that uses three-dimensional formalism. The new framework for the two-nucleon (2N) system using a complete set of isospin–spin states made it possible to construct simple implementations that employ a very general operator form of the current operator and 2N states.     

Large Bipolarons in Two and Three Dimensions

The large bipolaron in two and three dimensions is investigated by combining the reasonable asymptotic relative wavefunctions and the Lee-Low-Pines-Huybrechts (LLP-H) variational method. The values of the critical coupling constant α_C above which bipolarons may exist and the critical ratio of dielectric constants η_c below which bipolarons may exist are evaluated, which are very close to the recent results obtained within totally different variational approaches. It is also found that low-dimensional materials are more favorable for the formation of bipolarons.     

Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three-dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described in both superfield and component field forms. The relationship between these models and similar models in four-dimensional Minkowski space is described.     

The Wulff Construction in Three and More Dimensions

In this paper we prove the Wulff construction in three and more dimensions for an Ising model with nearest neighbor interaction. Received: 5 January 1999 / Accepted: 27 April 1999     

Properties of an Accelerating Gauss-Bonnet Vacuum in Five Dimensions

The causal structure of a five-dimensional C-metric like vacuum solution of Gauss-Bonnet gravity is analyzed in detail, the Gauss-Bonnet parameter make it more complex than that of a C-metric like solution of Einstein gravity. The acceleration of the observer fixed at a spatial position is calculated, the effect of the Gauss-Bonnet parameter comes in, but the acceleration of the origin is not affected by the parameter. The geodesics of the test particles in the spacetime are investigated, it is found that objects accelerate to go to the horizon in the accelerating spacetime.     

Excitation of Complicated Shapes in Three Dimensions

We experimentally verified a recently proposed technique for the excitation of a complicated three-dimensional profile (CARVE,completelyarbitraryregionalvolumeexcitation). CARVE is based on a generalized DANTE RF pulse sequence and a synchronous string of gradient steps. Provided there is no limitation in the number of pulses, CARVE can generate an excitation profile of any shape with any resolution. However, hardware limitations and sample properties restrict the number of RF pulses and gradient steps and, thus, limit attainable resolution of the excitation profile. We theoretically and experimentally showed that spatial resolution can be increased by distributing a long sequence among several CARVE experiments and summing up their signals. This is particularly important for three-dimensional excitation profiles where ann-fold increase in resolution requires ann³-fold increase of the number of events in the sequence. The potential use of three-dimensional CARVE might be in spectroscopic imaging where the excitation profile can be tailored to match the shape of a selected organ or body part.     

The Fourth-Order Non-Linear Sigma Models and Asymptotic Freedom in Four Dimensions

Starting with the most general Lagrangian of the fourth-order non-linear sigma model in four space-time dimensions, we calculate the one-loop, on shell ultra-violet-divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered.     

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einstein's four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.     

Killing Symmetries of Generalized Minkowski Spaces, 3: Spacetime Translations in Four Dimensions

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional case. In particular, the results obtained are specialized to the case of a deformed Minkowski space (i.e. a pseudoeuclidean space with metric coefficients depending on energy).     

Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions

This is the second of two papers on the end-to-end distance of a weakly self-repelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times , which is the same law as has been conjectured for self-avoiding walks on the simple cubic lattice ⁴. Apart from completing the program in the first paper, the main result is that the Green's function is almost equal to the Green's function for the Markov process with no self-repulsion, but at a different value of the killing rate which can be accurately calculated when the interaction is small. Furthermore, the Green's function is analytic in in a sector in the complex plane with opening angle greater than . Research supported by NSF grant DMS-9706166 and NSERC of Canada.     

Enhanced Correlation of Electron-Positron Pair in Two and Three Dimensions

Early time electron-positron correlation in vacuum pair-production in an external field is investigated. The entangled electron and positron wave functions are obtained analytically in the configuration and momentum spaces. It is shown that, relative to that of the one-dimensional theory, two- and three-dimensional calculations yield enhanced spatial correlation and broadened momentum spectra. In fact, at early times the electron and positron almost coincide spatially. The correlation also depends on the direction of the applied field. For the spatial correlation, the transverse correlation is stronger than the longitudinal correlation.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.