Chiral Solitons in 1+2 Dimensions

This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation in 1+2 dimensions. Both constant coefficients and time-dependent coefficients are considered. The topological as well as bright soliton solutions are obtained. The soliton ansatz method is used to carry out the derivation of the soliton.     

Midpoint Distribution of Directed Polymers in the Stationary Regime: Exact Result Through Linear Response

We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic Burgers field to some perturbation. From the symmetries of the stochastic Burgers equation we derive a fluctuation–dissipation relation so that the pdf gets given by the stationary two space-time points correlation function of the Burgers field. An analytical expression for the latter was obtained by Imamura and Sasamoto (J Stat Phys 150:908–939, 2013), thereby rendering our result explicit. In the large length limit that implies that the pdf is nothing but the scaling function \(f_{\mathrm{KPZ}}(y)\) introduced by Prähofer and Spohn (J Stat Phys 115(1):255–279, 2004). Using the KPZ-universality paradigm, we find that this function can therefore also be interpreted as the pdf of the position y of the maximum of the Airy process minus a parabola and a two-sided Brownian motion. We provide a direct numerical test of the result through simulations of the Log-Gamma polymer.     

Properties of Solutions in 2 + 1 Dimensions

We solve the Einstein equations for the 2 + 1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.     

New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with Cylindrical Symmetry in 3+1 Dimensions

We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing SL(2;R) transformations.     

Rotating Kink Spacetime in 2+1 Dimensions

A new family of solutions is presented for the (2+1)-dimensional Einstein equations with a rotating perfect fluid source. The mass density and pressure are everywhere positive. Features of the spacetime include closed timelike curves and Finkelstein-Misner metrical kinks.     

Rotating Dilaton Solutions in 2+1 Dimensions

We report a three parameter family of solutions for dilaton gravity in 2+1 dimensions with finite mass and finite angular momentum. These solutions are obtained by a compactification of vacuum solutions in 3+1 dimensions with cylindrical symmetry. One class of solutions corresponds to conical singularities and the other leads to curvature singularities.     

Transition for Optimal Paths in Bimodal Directed Polymers

The problem for optimal paths in bimodal directed polymers is studied. It is shown that the distribution of the thermal average position of the endpoints of the optimal paths is discontinuous below the threshold p〈pc. The origin is that there is a finite possibility that only one endpoint takes the global minimum energy for p 〈 pc. Our results suggest that the percolation threshold for directed percolation is also the critical point of the transition for the possibility that the optimal paths converge to one endpoint.     

New Bounds for the Free Energy of Directed Polymers in Dimension 1 + 1 and 1 + 2

We study the free energy of the directed polymer in a random environment model in dimension 1 + 1 and 1 + 2. For dimension one, we improve the statement of Comets and Vargas in [8] concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension two, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.     

Plasma Crystal in (3 + 1) Dimensions

JETP Letters - A quasi-two-dimensional plasma crystal in (3 + 1) dimensions has been experimentally observed for the first time; i.e., three spatial coordinates of each microparticles of the...     

Relativity Principles in 1+1 Dimensions and Differential Aging Reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light, and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient β, special relativity being recovered for β = 0. The effect of differential aging is studied for the different value of β. Below the critical values |β| = 1/c the differential aging has the usual direction—after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical value the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.     

Singularity Free Stars in (2+1) Dimensions

We present some new types of non-singular model for anisotropic stars with constant Λ and variable Λ based on the Krori and Barua (KB) metric in (2+1) dimensions. The solutions obtained here satisfy all the regularity conditions and its simple analytical form helps us to study the various physical properties of the configuration.     

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.     

Quasinormal Modes of Charged Dilaton Black Holes in 2 + 1 Dimensions

We have studied the scalar perturbation of static charged dilaton black holes in 2 + 1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2 + 1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.     

Stability of Charged Thin-Shell Wormholes in (2+1) Dimensions

In this paper we construct charged thin-shell wormholes in (2+1)-dimensions applying the cut-and-paste technique implemented by Visser, from a BTZ black hole which was discovered by Bañados, Teitelboim and Zanelli (Phys. Rev. Lett. 69:1849, 1992), and the surface stress are determined using the Darmois-Israel formalism at the wormhole throat. We analyzed the stability of the shell considering phantom-energy or generalised Chaplygin gas equation of state for the exotic matter at the throat. We also discussed the linearized stability of charged thin-shell wormholes around the static solution.     

Collapsed and Adsorbed States of a Directed Polymer Chain in Two Dimensions

A phase diagram for a surface-interacting long flexible partially-directed polymer chain in a two-dimensional poor solvent, where the possibility of collapse in the bulk exists, is determined using exact enumeration methods. We used a model of self-attracting self-avoiding walks and evaluated 30 steps in series. An intermediate phase between the desorbed collapsed and adsorbed expanded phases, having the conformation of a surface-attached globule, is found. The four phases, viz ., (i) desorbed expanded (DE), (ii) desorbed collapsed (DC), (iii) adsorbed expanded (AE), (iv) surface-attached globule (SAG), are found to meet at a multicritical point. These features are in agreement with those of an isotropic (or non-directed) polymer chain.     

On the Extension of Stringlike Localised Sectors in 2+1 Dimensions

In the framework of algebraic quantum field theory, we study the category \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) of stringlike localised representations of a net of observables \({\mathcal{O} \mapsto \mathfrak{A}(\mathcal{O})}\) in three dimensions. It is shown that compactly localised (DHR) representations give rise to a non-trivial centre of \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) with respect to the braiding. This implies that \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) cannot be modular when non-trivial DHR sectors exist. Modular tensor categories, however, are important for topological quantum computing. For this reason, we discuss a method to remove this obstruction to modularity.Indeed, the obstruction can be removed by passing from the observable net \({\mathfrak{A}(\mathcal{O})}\) to the Doplicher-Roberts field net \({\mathfrak{F}(\mathcal{O})}\). It is then shown that sectors of \({\mathfrak{A}}\) can be extended to sectors of the field net that commute with the action of the corresponding symmetry group. Moreover, all such sectors are extensions of sectors of \({\mathfrak{A}}\). Finally, the category \({\Delta_{{\rm BF}}^{\mathfrak{F}}}\) of sectors of \({\mathfrak{F}}\) is studied by investigating the relation with the categorical crossed product of \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) by the subcategory of DHR representations. Under appropriate conditions, this completely determines the category \({\Delta_{{\rm BF}}^{\mathfrak{F}}}\).