Hui, Ping; Fang, Xi-Yan; Shi, Ting-Yun
2004-01-01
Using the coupled cluster expansion with the random phase approximation, we calculate the long wavelength vacuum wave function and the vacuum energy of 2+1 dimensional Hamiltonian SU(2) lattice gauge theory (LGT) up to the seventh order. The coefficients $\\mu_0$, $\\mu_2$ of the vacuum wave function show good scaling behavior and convergence in high order calculations.
Dark soliton solutions of (N+1)-dimensional nonlinear evolution equations
Demiray, Seyma Tuluce; Bulut, Hasan
2016-06-01
In this study, we investigate exact solutions of (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation by using generalized Kudryashov method. (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation can be returned to nonlinear ordinary differential equation by suitable transformation. Then, generalized Kudryashov method has been used to seek exact solutions of the (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation. Also, we obtain dark soliton solutions for these (N+1)-dimensional nonlinear evolution equations. Finally, we denote that this method can be applied to solve other nonlinear evolution equations.
Entropy spectrum of (1+1) dimensional stringy black holes
We explore the entropy spectrum of (1+1) dimensional dilatonic stringy black holes via the adiabatic invariant integral method known as Jiang and Han's method (Phys Lett B 718:584, 2012) and the Bohr-Sommerfeld quantization rule. It is found that the corresponding spectrum depends on black hole parameters like charge, ADM mass, and, more interestingly, on the dilatonic field. We calculate the entropy of the present black hole system via the Euclidean treatment of quantum gravity and study the thermodynamics of the black hole and find that the system does not undergo any phase transition. (orig.)
(2+1)-dimensional quantum gravity
The (2+1)-dimensional pure Einstein gravity is studied in the canonical ADM formalism, assuming that the space-time topology is Σ2 (a closed and compact 2-surface) x R1. The dynamical variables are reduced to the moduli parameters of the 2-surface. Upon quantization, the system becomes a quantum mechanics of moduli parameters in a curved space endowed with the Weil-Petersson metric. In the case of torus in particular, the superspace, on which the wave function of universe is defined, turns out to be the fundamental region in the moduli space. The solution of the Wheeler-DeWitt equation is explicitly given as the Maass form which is perfectly regular in the superspace. (author)
(2+1)-dimensional quantum gravity
The (2+1)-dimensional pure Einstein gravity is studied in the canonical ADM formalism, assuming that the spatial surface is closed and compact. Owing to the constraints, the dynamical variables are reduced to the moduli parameters of the 2-surface. Upon quantization, the system becomes a quantum mechanics of moduli parameters in a curved space endowed with the Weil-Petersson metric. In the case of torus in particular, the superspace, on which the wave function of universe is defined, turns out to be the fundamental region is the moduli space. The solution of the Wheeler-DeWitt equation is explicitly given as the Maass form which is perfectly regular in the superspace. (author)
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Exploration of similarity renormalization group generators in 1-dimensional potentials
Heinz, Matthias
2015-10-01
The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. It includes a matrix called the generator that defines how the transformation will change the Hamiltonian. The commonly used SRG generators evolve the Hamiltonian into a band-diagonal shape. Evolving potentials using SRG induces many-body forces. If these forces are truncated at the N-body level, this systematically introduces errors from omitted (N+1)-body forces when modeling many-body systems. While established generators are fairly successful, alternative generators may converge faster, be faster to calculate, or lead to smaller many-body forces. In particular, recent findings suggest that a block diagonal generator may induce smaller many-body forces. We use 1-dimensional systems of two, three, and four bosons as a theoretical laboratory for studying how these alternative generators perform, and to observe how they induce many-body forces.
Nonpropagating Solitary Waves in (2+1)-Dimensional Nonlinear Systems
MENG Jian-Ping; ZHANG Jie-Fang
2005-01-01
By means of extended homogeneous balance method and variable separation approach, quite a general variable separation solution of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation is derived. From the variable separation solution and by selecting appropriate functions, a new class of (2+1)-dimensional nonpropagating solitary waves are found. The novel features exhibited by these new structures are first revealed.
Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations
The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space—time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space—time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system. (general)
DAI Chao-Qing; YAN Cai-Jie; ZHANG Jie-Fang
2006-01-01
In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+ 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.
Lessons from (2+1)-dimensional quantum gravity
Schroers, B. J.
2007-01-01
Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincare symmetry are examined in the context of (2+1)-dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck's constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)-dimensional quantum gravity. It is emphasised that the much studied bicrossproduct kappa-Poincare ...
Critical behavior of 2+1 dimensional CPN-1 model with a Chern-Simons term
I investigate the critical behaviour of 2+1 dimensional CPN-1 model with a Chern-Simons term. I derive the 1/N expansion in this model and show that the theory is renormalizable in this framework. The critical exponents η and υ are calculated to the O(1/N). They exhibit θ (coefficient of the Chern-Simons term) dependence. (author). 14 refs, 6 figs
Hypocycloidal throat for 2 + 1-dimensional thin-shell wormholes
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2015-11-15
Recently we have shown that for 2 + 1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2 + 1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2 + 1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one. (orig.)
Thermodynamics of event horizons in (2+1)-dimensional gravity
Although gravity in 2+1 dimensions is very different in nature from gravity in 3+1 dimensions, it is shown that the laws of thermodynamics for event horizons can be manifested also for (2+1)-dimensional gravity. The validity of the classical laws of horizon mechanics is verified in general and exemplified for the (2+1)-dimensional analogues of Reissner-Nordstroem and Schwarzschild--de Sitter spacetimes. We find that the entropy is given by 1/4L, where L is the length of the horizon. A consequence of having consistent thermodynamics is that the second law fixes the sign of Newton's constant to be positive
ZHANG Huan; TIAN Bo; ZHANG Hai-Qiang; GENG Tao; MENG Xiang-Hua; LIU Wen-Jun; CAI Ke-Jie
2008-01-01
For describing various complex nonlinear phenomena in the realistic world, the higher-dimensional nonlinear evolution equations appear more attractive in many fields of physical and engineering sciences. In this paper, by virtue of the Hirota bilinear method and Riemann theta functions, the periodic wave solutions for the (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation are obtained. Furthermore, it is shown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.
Geodesic bi-scalars in (n+1)-dimensional spacetimes
This is a sequel to the previous papers RRK 85 - 12 and 85 - 18 (1985), which dealt with the geodesic bi-scalars in a Robertson-Walker universe with flat 3-space and in an anisotropic homogeneous universe, respectively. In the present article, the results obtained before are extended to the case of a (n+1)-dimensional spacetime. (author)
Upon Generating (2+1)-dimensional Dynamical Systems
Zhang, Yufeng; Bai, Yang; Wu, Lixin
2016-06-01
Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.
Md Nur Alam; M Ali Akbar; M Fazlul Hoque
2014-09-01
In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown that the new approach of generalized (′/)-expansion method is a straightforward and effective mathematical tool for solving nonlinear evolution equations in applied mathematics, mathematical physics and engineering. Moreover, this procedure reduces the large volume of calculations.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R.; Nicolini, Piero
2011-01-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\\sqrt{\\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scal...
(N+1)-dimensional Lorentzian evolving wormholes supported by polytropic matter
Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Facultad de Ciencias, Concepcion (Chile); Arostica, Fernanda; Bahamonde, Sebastian [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile)
2013-08-15
In this paper we study (N+1)-dimensional evolving wormholes supported by energy satisfying a polytropic equation of state. The considered evolving wormhole models are described by a constant redshift function and generalizes the standard flat Friedmann-Robertson-Walker spacetime. The polytropic equation of state allows us to consider in (3+1)-dimensions generalizations of the phantom energy and the generalized Chaplygin gas sources. (orig.)
Causality in 1+1-dimensional Yukawa model-II
Asrarul Haque; Satish D Joglekar
2013-10-01
The limits → large, $M →$ large with ($g^{3}/M$) = const. of the 1+1-dimensional Yukawa model are discussed. The conclusion of the results on bound states of the Yukawa model in this limit (obtained in arXiv:0908.4510v3 [hep-th]) is taken into account. It is found that model reduces to an effective non-local 3 theory in this limit. Causality violation also is observed in this limit.
Horizons in (1 + 1)-dimensional dilaton gravity coupled to matter
We study static solutions of a general (1 + 1)-dimensional dilaton gravity coupled to scalar fields and Abelian gauge fields near horizons. This includes, in particular, reductions of higher-dimensional theories invariant under a sufficiently large isometry group. The solution near the horizon can be obtained by solving a system of integral equations or alternatively in the form of a convergent series in the dilaton field
Non-trivial 2+1-Dimensional Gravity
Grigore, D. R.; Scharf, G.
2010-01-01
We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study massive gravity which is not trivial. In the limit of vanishing graviton mass we obtain a non-trivial massless theory different from Einstein gravity. We derive the interaction from descent equations and obtain the cosmological topologically massive gravity. Howe...
A pseudoCoulombian potential in D=1 dimensional space
In the D=1 dimensional space, we study the bound state solutions of the potential V(x)=-c/x+b/x2 (e, b>0). They occur on the right half-plane xin[0, ∞[. In the limit b→0, we recover the spectrum of the D=1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant.
Exact solutions of (3 + 1)-dimensional stochastic Burgers equation
A generalized tan h function method is used for constructing exact travelling wave solutions of nonlinear stochastic partial differential equations. The main idea of this method is to take full advantage of the Riccati equation, which has more exact solutions. More Wick-type stochastic multiple soliton-like solutions and triangular periodic solutions are obtained for the (3 + 1)-dimensional Wick-type stochastic Burgers equation via Hermite transformation
Exact interior solutions in 2 + 1-dimensional spacetime
We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)
X-ray spontaneous emission control by 1-dimensional photonic bandgap structure
André, Jean-Michel; Jonnard, Philippe
2010-01-01
Paper available at http://epjd.edpsciences.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/epjd/abs/2010/06/d09549/d09549.html International audience The possibility of controlling the X-ray spontaneous emission of atoms embedded in a 1-dimensional photonic bandgap structure by the so-called Purcell effect, is studied. Calculations of the spontaneously emitted power are presented from Fermi's golden rule in the framework of the Wigner-time approach extended to ...
GUP Corrected Fermion Tunnelling from 2 + 1 Dimensional Black String
Tang, Jian; Feng, Zhongwen; Ren, Wei; Chen, Bingbing
2016-01-01
In this paper, using the generalized Dirac equation which is modified by GUP, we study the fermion tunneling from 2 + 1 dimensional black string. Our results show that the Hawking temperature is not only depended on the event horizon of black string but also related to the quantum number of emitted fermion (energy and mass). Meanwhile, we find the GUP can slow down the Hawking temperature increase and lead to the remnants. It implies that the GUP can avoid the evaporation of black holes.
Nucleosynthetic Signatures of Asymmetric Supernovae - Lessons from 1-dimensional Explosions
We review the evidence for asymmetries in explosions, and in particular, the nucleosynthetic signatures from these asymmetries. To guide our intuition for these yields, we have modeled a series of spherically symmetric explosions with a range of explosion energies. Here we present the results from these 1-dimensional simulations, focusing on the yields of the radioactive elements 44Ti and 56Ni. We find that, although the abundance yields of 44Ti do depend sensitively on the explosion energy, the trend (whether it increases or decreases with explosion energy) depends very sensitively on the model
Nucleosynthetic Signatures of Asymmetric Supernovae - Lessons from 1-dimensional Explosions
Hungerford, A. L.; Fryer, C. L.; Timmes, F. X.; McGhee, K.
2005-07-01
We review the evidence for asymmetries in explosions, and in particular, the nucleosynthetic signatures from these asymmetries. To guide our intuition for these yields, we have modeled a series of spherically symmetric explosions with a range of explosion energies. Here we present the results from these 1-dimensional simulations, focusing on the yields of the radioactive elements 44Ti and 56Ni. We find that, although the abundance yields of 44Ti do depend sensitively on the explosion energy, the trend (whether it increases or decreases with explosion energy) depends very sensitively on the model.
Quantum Interest in (3+1) dimensional Minkowski space
Abreu, Gabriel
2008-01-01
The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.
A pseudoCoulombian potential in D=1 dimensional space
Lombard, R J [Groupe de Physique theorique, Institut de Physique Nucleaire, 91406 Orsay Cedex (France); Mezhoud, R [Faculty of Sciences, Boumerdes University, 35000 Boumerdes (Algeria); Yekken, R [Institut de Physique, USTHB Bab Ezzouar, Alger (Algeria)], E-mail: lombard@ipno.in2p3.fr, E-mail: mezhoudreda@yahoo.fr, E-mail: rabia_yek@yahoo.fr
2009-12-15
In the D=1 dimensional space, we study the bound state solutions of the potential V(x)=-c/x+b/x{sup 2} (e, b>0). They occur on the right half-plane xin[0, {infinity}[. In the limit b{yields}0, we recover the spectrum of the D=1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant.
Perturbational blowup solutions to the compressible 1-dimensional Euler equations
Yuen, Manwai, E-mail: nevetsyuen@hotmail.com [Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong)
2011-10-24
We construct non-radially symmetry solutions for the compressible 1-dimensional adiabatic Euler equations in this Letter. In detail, we perturb the linear velocity with a drifting term: (1)u=c(t)x+b(t), to seek new solutions. Then, we transform the problem into the analysis of ordinary differential equations. By investigating the corresponding ordinary differential equations, a new class of blowup or global solutions can be given. Here, our constructed solutions can provide the mathematical explanations for the drifting phenomena of some propagation wave like Tsunamis. And when we adopt the Galilean-like transformation to a drifting frame, the constructed solutions are self-similar. -- Highlights: → We construct non-radially symmetry solutions for the 1-dimensional Euler equations. → We perturb the linear velocity with a drifting term to seek new solutions. → We transform the Euler system into the ordinary differential equations analysis. → The solutions model the drifting phenomena of some propagation wave like Tsunamis. → Under the Galilean-like transformation, the constructed solutions are self-similar.
Generalized (2+1) dimensional black hole by Noether symmetry
Darabi, F. [Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM), Maragha (Iran, Islamic Republic of); Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)
2013-12-15
We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D{sub 1} R(n/n+1)(R/K){sup 1/n} + D{sub 2}R + D{sub 3}, where the constant term D{sub 3} plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D{sub 1} = 0, D{sub 2} = 1, namely f(R) = R + D{sub 3}, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D{sub 3} and represents symmetry of the action under the transformation R {yields}R' = R + D{sub 3} along the killing vector {partial_derivative}{sub R}. The ordinary BTZ black hole is obtained as the special case where D{sub 3} is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy-Verlinde formula. (orig.)
Quantum Holonomies in (2+1)-Dimensional Gravity
Nelson, J E
2004-01-01
We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and upper--triangular form are constructed, which in the latter case exhibit additional, non--trivial internal relations for each holonomy matrix. This leads to the notion of quantum matrix pairs. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of powers of the matrices obey the same pattern of internal relations as the original pair. This has implications for the classical moduli space, described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices.
Quench dynamics in confined 1 + 1-dimensional systems
We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT. (letter)
Quench dynamics in confined 1 + 1-dimensional systems
Engelhardt, Dalit
2016-03-01
We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT.
Aspects of noncommutative (1+1)-dimensional black holes
We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length √(θ) cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R.; Nicolini, Piero
2011-08-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length θ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R
2011-01-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\\sqrt{\\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass $M$, cosmological constant $\\Lambda$, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Entanglement and majorization in (1+1)-dimensional quantum systems
Orus, R
2005-01-01
Motivated by the idea of entanglement loss along Renormalization Group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven to hold in the spectrum of the reduced density matrices in a bipartite system when changing the size L of one of the subsystems. Continuous majorization along uniparametric flows is also proven as long as part of the conformal structure is preserved under the deformation and some monotonicity conditions hold as well. As particular examples of our derivations, we study the cases of the XX, Heisenberg and XY quantum spin chains. Our results provide in a rigorous way explicit proves for all the majorization conjectures raised by Latorre, Lutken, Rico, Vidal and Kitaev in previous papers on quantum spin chains.
3+1-dimensional multi-Hamiltonian integrable systems
In this work we will present multi-Hamiltonian systems in 3+1 dimensions. In literature there are many examples for non-linear second order differential equations in 1+1 dimensions which are completely integrable by Magri's theorem. But not too much in 2+1 and almost no examples in 3+1 dimensions. Therefore it becomes very important to get multi-Hamiltonian integrable systems in four dimensions. Very recently Nutku Y, Sheftel M B and collaborates discovered multi-Hamiltonian structure for Plebanski's second heavenly equation and for complex Monge-Ampere (CMA) equation. Both of these equations possess partner symmetries which plays very imported role in constructing the recursion operator for the systems. We will give the method how to obtain multi-Hamiltonian structure for 3+1 dimensional evolutionary systems and the latest development in this subject
Minimal Wormholes in an (n + 1)-Dimensional Cosmological Background
Zangeneh, M Kord
2011-01-01
In this article, we discuss a class of expanding traversable wormholes in an (n+1)-dimensional Robertson-Walker (RW) background with Ricci scalar independent of the r-coordinate. With this condition, we obtain a wormhole metric which in general depends on the curvature constant k. For the flat (k = 0) case, we obtain the scale factor R(t) by using the Friedmann equations in the large r limit and use this to obtain the diagonal energy-momentum tensor. Applying the weak energy condition (WEC) we obtain a critical radius and a critical time that are limits of the violation of WEC. Although it is proved that the throat is a null hypersurface but it is shown that wormhole has no horizon and is traversable from both sides of this hypersurface.
On (2+1)-Dimensional Non-isospectral Toda Lattice Hierarchy and Integrable Coupling System
By considering (2+1)-dimensional non-isospectral discrete zero curvature equation, the (2+1)-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the (2+1)-dimensional Toda lattice hierarchy are given. Finally, the (2+1)-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.
Li-Li, Huang; Yong, Chen
2016-06-01
In this paper, the truncated Painlevé analysis, nonlocal symmetry, Bäcklund transformation of the (2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented. Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system. In addition, the (2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton–cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to find by other traditional methods. Moreover figures are given out to show the properties of the explicit analytic interaction solutions. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213).
Boundary dynamics and the statistical mechanics of the 2 + 1-dimensional black hole
We calculate the density of states of the 2 + 1-dimensional BTZ black hole in the micro-and grand-canonical ensembles. Our starting point is the relation between 2 + 1-dimensional quantum gravity and quantised Chern-Simons theory. In the micro-canonical ensemble, we find the Bekenstein-Hawking entropy by relating a Kac-Moody algebra of global gauge charges to a Virasoro algebra with a classical central charge via a twisted Sugawara construction. This construction is valid at all values of the black hole radius. At infinity it gives the asymptotic isometries of the black hole, and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same Virasoro algebra. In the grand-canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole. We then compute the partition function directly in a boundary Wess-Zumino-Witten theory, and find that we obtain the correct result only after we include a source term at the horizon that induces a non-trivial spin-structure on the WZW partition function
Quantum cosmology in (1 +1 )-dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2016-05-01
In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical (1 +1 )-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of (1 +1 )-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) p =w ρ . The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for w =1 (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for w ≠1 , a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit.
Boundary dynamics and the statistical mechanics of the 2 + 1-dimensional black hole
Baniados, M; Ortiz, M E
1999-01-01
We calculate the density of states of the 2 + 1-dimensional BTZ black hole in the micro-and grand-canonical ensembles. Our starting point is the relation between 2 + 1-dimensional quantum gravity and quantised Chern-Simons theory. In the micro-canonical ensemble, we find the Bekenstein-Hawking entropy by relating a Kac-Moody algebra of global gauge charges to a Virasoro algebra with a classical central charge via a twisted Sugawara construction. This construction is valid at all values of the black hole radius. At infinity it gives the asymptotic isometries of the black hole, and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same Virasoro algebra. In the grand-canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole. We then compute the partition function directly in a boundary Wess-Zumino-Witten theory, and find that we obtain the correc...
We apply Pauli--Villars regularization and discrete light-cone quantization to the nonperturbative solution of a (3+1)-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex symmetric Lanczos algorithm. This permits the calculation of each Fock-sector wave function, and from these we obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form factor slope
(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves
2015-01-01
By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV eq...
2 + 1-dimensional traversable wormholes supported by positive energy
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2015-02-01
We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in 2 + 1 dimensions. In particular, in the case of TSWs this is done in a flat 2 + 1-dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., r = a(t) for the throat, we employ a θ-dependent closed loop of the form r = R(t, θ), and in terms of R(t, θ) we find the surface energy density σ on the throat. For the specific convex shapes we find that the total energy which supports the wormhole is positive and finite. In addition, we analyze the general wormhole's throat. By considering the specific equation of r = R(θ) instead of r = r{sub 0} = const., and upon certain choices of functions for R(θ), we find the total energy of the wormhole to be positive. (orig.)
2 + 1-dimensional traversable wormholes supported by positive energy
We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in 2 + 1 dimensions. In particular, in the case of TSWs this is done in a flat 2 + 1-dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., r = a(t) for the throat, we employ a θ-dependent closed loop of the form r = R(t, θ), and in terms of R(t, θ) we find the surface energy density σ on the throat. For the specific convex shapes we find that the total energy which supports the wormhole is positive and finite. In addition, we analyze the general wormhole's throat. By considering the specific equation of r = R(θ) instead of r = r0 = const., and upon certain choices of functions for R(θ), we find the total energy of the wormhole to be positive. (orig.)
3+1 dimensional viscous hydrodynamics at high baryon densities
Karpenko, Iu; Bleicher, M.; Huovinen, P.; Petersen, H.
2015-05-01
A 3+1 dimensional event-by-event viscous hydrodynamic + cascade model is applied for the simulation of heavy ion collision reactions at \\sqrt{sNN} = 6.3... 200 GeV. UrQMD cascade is used for the pre-thermal (pre-hydro) and final (post-hydro) stages of the reaction. The baryon, as well as electric charge densities are consistently taken into account in the model. For this aim the equation of state based on a Chiral model coupled to the Polyakov loop is used in hydrodynamic phase of evolution. As a result of the model adjustment to the experimental data, the effective values of the shear viscosity over entropy density η/s are obtained for different collision energies in the BES region. A decrease of the effective values of η/s from 0.2 to 0.08 is observed as collision energy increases from \\sqrt{s} ≈ 7 to 39 GeV.
The Casimir energy of skyrmions in the 2+1-dimensional O(3)-model
Walliser, H
1999-01-01
One-loop quantum corrections to the classical vortices in 2+1 dimensional O(3)-models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound-states and scattering phase-shifts are calculated for vortices with winding index n=1 and n=2. For both cases the S-matrix shows a pronounced series of resonances for magnon-vortex scattering in analogy to the well-established baryon resonances in hadron physics, while vortices with n>2 are already classically unstable against decay. The quantum corrections destabilize the classically bound n=2 configuration. Approximate independence of the results with respect to changes in the renormalization scale is demonstrated.
张解放; 吴锋民
2002-01-01
We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.
3+1 -dimensional Schwinger terms and non-commutative geometry
Langmann, E; Edwin Langmann; Jouko Mickelsson
1994-01-01
Abstract: We discuss 2-cocycles of the Lie algebra \\Map(M^3;\\g) of smooth, compactly supported maps on 3-dimensional manifolds M^3 with values in a compact, semi-simple Lie algebra \\g. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili cocycle \\f{\\ii}{24\\pi^2}\\int\\trac{A\\ccr{\\dd X}{\\dd Y}} is cohomologous to the one obtained from the cocycle given by Mickelsson and Rajeev for an abstract Lie algebra \\gz of Hilbert space operators modeled on a Schatten class in which \\Map(M^3;\\g) can be naturally embedded. This completes a rigorous field theory derivation of the former cocycle as Schwinger term in the anomalous Gauss' law commutators in chiral QCD(3+1) in an operator framework. The calculation also makes explicit a direct relation of Connes' non-commutative geometry to (3+1)-dimensional gauge theory and motivates a novel calculus generalizing integration of \\g-valued forms on 3-dimensional manifolds to the non-commutative case.
(3+1)-dimensional light-front model with spontaneous breaking of chiral symmetry
We investigate a (3+1)-dimensional toy model that exhibits spontaneous breakdown of chiral symmetry, both in a light-front (LF) Hamiltonian and in a Euclidean Schwinger-Dyson (SD) formulation. We show that both formulations are completely equivalent, provided the renormalization is properly done. The counterterm can be constructed explicitly by eliminating zero-mode degrees of freedom, giving rise to to an effective interaction: i.e., zero-mode dynamics, in the sense of an effective action, leads to a very simple set of modifications for the nonzero modes. We find that it is sufficient to renormalize terms that exist already in the canonical LF Hamiltonian independently. Chiral symmetry breaking is manifested via a open-quotes kinetic massclose quotes counterterm, which is eventually responsible for the mass generation of the physical fermion of the model. The vertex mass in the LF calculation must be taken to be the same as the current quark mass in the SD calculation. copyright 1997 The American Physical Society
Variable separation solutions and new solitary wave structures to the (1+1)-dimensional Ito system
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2006-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physics system.The variable separation solution of (1+1)-dimensional Ito system is obtained.Some special types of solutions such as non-propagating solitary wave solution,propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.
Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations
Guo, Xiu-Rong
2016-06-01
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
Electrostatic self-force in (2+1)-dimensional cosmological gravity
Furtado, C; Furtado, Claudio; Moraes, Fernando
1996-01-01
Point sources in (2+1)-dimensional gravity are conical singularities that modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge in the presence of point masses in (2+1)-dimensional gravity with a cosmological constant.
Horizons in 2+1-dimensional collapse of particles
Dieter Brill; Puneet Khetarpal; Vijay Kaul
2007-07-01
A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry will be that of a particle, or of a black hole. In the black hole case the horizon is calculated. It is found that the horizon typically starts at a point and spreads into a closed curve with corners, which propagate along spacelike caustics and disappear as the horizon passes the particles.
3+1 dimensional viscous hydrodynamics at high baryon densities
Karpenko, Iu; Huovinen, P; Petersen, H
2013-01-01
We apply a 3+1D viscous hydrodynamic + cascade model to the heavy ion collision reactions with $\\sqrt{s_{NN}}=6.3\\dots39$ GeV. To accommodate the model for a given collision energy range, the initial conditions for hydrodynamic phase are taken from UrQMD, and the equation of state at finite baryon density is based on Chiral model coupled to the Polyakov loop. We study the collision energy dependence of pion and kaon rapidity distributions and $m_T$-spectra, as well as charged hadron elliptic flow and how shear viscosity affects them. The model calculations are compared to the data for Pb-Pb collisions at CERN SPS, as well as for Au-Au collisions in the Beam Energy Scan (BES) program energies at BNL RHIC. The data favours the value of shear viscosity $\\eta/s\\gtrsim0.2$ for this collision energy range.
Zhou, Tianci; Faulkner, Thomas; Fradkin, Eduardo
2016-01-01
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2+1-dimensional quantum Lifshitz model, whose ground state wave function is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose weight is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term as well as the mutual information are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy's relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information al...
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; González-Arroyo, Antonio; Okawa, Masanori
2013-09-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λ N L and an angle defined in terms of the magnetic flux (λ is `t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence ( N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; Okawa, Masanori
2013-01-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=\\lambda NL and an angle defined in terms of the magnetic flux (\\lambda\\ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable sc...
Logarithmic corrections in (4+1) -dimensional directed percolation.
Grassberger, Peter
2009-05-01
We simulate directed site percolation on two lattices with four spatial and one timelike dimensions (simple and body-centered hypercubic in space) with the standard single cluster spreading scheme. For efficiency, the code uses the same ingredients (hashing, histogram reweighing, and improved estimators) as described by Grassberger [Phys. Rev. E 67, 036101 (2003)]. Apart from providing the most precise estimates for p_{c} on these lattices, we provide a detailed comparison with the logarithmic corrections calculated by [Janssen and Stenull [Phys. Rev. E 69, 016125 (2004)]. Fits with the leading logarithmic terms alone would give estimates of the powers of these logarithms which are too big by typically 50%. When the next-to-leading terms are included, each of the measured quantities (the average number of sites wetted at time t , their average distance from the seed, and the probability of cluster survival) can be fitted nearly perfectly. But these fits would not be mutually consistent. With a consistent set of fit parameters, one obtains still much improvement over the leading log approximation. In particular we show that there is one combination of these three observables which seems completely free of logarithmic terms. PMID:19518501
Ruiyu Hao; Guosheng Zhou
2008-01-01
The(2+1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations
Two Darboux transformations of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka (CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
New Soliton-like Solutions for (2+1)-Dimensional Breaking Soliton Equation
XIE Zheng; ZHANG Hong-Qing
2005-01-01
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method.
Bosonic and Fermionic Entropy of (2+1)-Dimensional Charged Black Hole
CHEN Ju-Hua; WANG Yong-Jiu; JING Ji-Liang
2001-01-01
From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.
Lei Ya; Yang Duo
2013-01-01
In this paper,the finite symmetry transformation group of the (2+ 1)-dimensional coupled Burgers equation is studied by the modified direct method,and with the help of the truncated Painlevé expansion approach,some special localized structures for the (2+ 1)-dimensional coupled Burgers equation are obtained,in particular,the dromion-like and solitoff-like structures.
New Explicit Exact Solutions to (2+1)-Dimensional Generalized Broer-Kaup System
HUANG Ding-Jiang; ZHANG Hong-Qing
2005-01-01
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
Lie symmetry group of (2+1-dimensional Jaulent-Miodek equation
Ma Hong-Cai
2014-01-01
Full Text Available In this paper, we consider a system of (2+1-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.
In this paper, the multiple Riccati equations rational expansion method is further extended to construct non-travelling wave solutions of the (2 + 1)-dimensional Painleve integrable Burgers equation and the (2 + 1)-dimensional Breaking soliton equation, as a result, some double solitary-like wave solutions and complexiton solutions of the two equations are obtained. The extended method can also be applied to solve some other nonlinear evolution equations
Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
Ariwahjoedi, Seramika; Rovelli, Carlo; Zen, Freddy P
2015-01-01
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.
Anomaly-Induced Magnetic Screening in 2+1 dimensional QED at Finite Density
Stefano ForteINFN Torino, Italy
1993-01-01
We show that in 2+1 dimensional Quantum Electrodynamics an external magnetic field applied to a finite density of massless fermions is screened, due to a $2+1$-dimensional realization of the underlying $2$-dimensional axial anomaly of the space components of the electric current. This is shown to imply screening of the magnetic field, i.e., the Meissner effect. We discuss the physical implications of this result.
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field
Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in [Saha Institute of Nuclear Physics, Kolkata (India)
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Topological aspects of classical and quantum (2+1)-dimensional gravity
In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g=0 and g=1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g=1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace model of (2+1)-dimensional gravity with the matter fields in the case of g=0 and g=1. For g=0, a wormhole solution is found but for g=1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g=1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity. (author)
In this Letter, We present a further generalized algebraic method to the (2 + 1)-dimensional dispersive long-wave equations (DLWS), As a result, we can obtain abundant new formal exact solutions of the equation. The method can also be applied to solve more (2 + 1)-dimensional (or (3 + 1)-dimensional) nonlinear partial differential equations (NPDEs)
Bulk-boundary correspondence in (3+1)-dimensional topological phases
Chen, Xiao; Tiwari, Apoorv; Ryu, Shinsei
2016-07-01
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level K , and its generalization. In particular, we put these theories on a flat (2+1)-dimensional torus T3 parameterized by its modular parameters, and compute the partition functions obeying various twisted boundary conditions. We show the partition functions are transformed into each other under S L (3 ,Z ) modular transformations, and furthermore establish the bulk-boundary correspondence in (3+1) dimensions by matching the modular S and T matrices computed from the boundary field theories with those computed in the bulk. We also propose the three-loop braiding statistics can be studied by constructing the modular S and T matrices from an appropriate boundary field theory.
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
We have studied the Hawking radiation from generalized rotating and static (2+1)-dimensional BTZ black holes. In this regard, we have benefited from the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized (2+1)-dimensional BTZ black holes are different from ordinary (2+1)-dimensional BTZ black holes due to the Noether symmetry. In other words, the Noether symmetry can change the tunneling rate and Hawking temperature of the BTZ black holes. This symmetry may cause the BTZ black holes to avoid evaporation and its breakdown may start the evaporation. (orig.)
Casana, R.; Ferreira, M.M., E-mail: manojr.ufma@gmail.com; Mouchrek-Santos, V.E.; Silva, Edilberto O.
2015-06-30
We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov–Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov–Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters.
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
Lu, W F
1999-01-01
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum in the field system is asymmetrical, which verifies an earlier conjecture. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for some portion of the aforementioned region. Besides, the masses of one particle and tow-particle bound state upon the symmetric vacuum are also calculated, and the resultant masses agree with the recent second-order results of fermion-mass perturbation for the massive Schwinger model.
One plotted the Green function of the Dirac equation within external constant and uniform field in terms of (2 + 1)-dimensional quantum electrodynamics (QRD2+1) with nonzero density of fermions. In terms of QRD2+1 single-loop approximation one derived expression for polarization operator within external constant and uniform magnetic field at nonzero chemical potential. One calculated contribution of the Chern-Simon induced term into polarization operator and efficient Lagrangian at fermion density corresponding to occupation of the Landau n relativistic levels by them in the external magnetic field. One derived expression for the Chern-Simon induced term in the magnetic field at end temperature and nonzero chemical potential
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
Zhengde Dai; Chuanjian Wang; Jun Liu
2014-10-01
A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.
Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
Mazharimousavi, S Habib
2015-01-01
Recently we have shown that for $2+1-$dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider angular dependent throat geometry embedded in a $2+1-$dimensional flat spacetime in polar coordinates. It is shown that a generic, natural example of throat geometry is provided remarkably by a hypocycloid. That is, two flat $2+1-$dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.
Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
Mazharimousavi, S. Habib; Halilsoy, M.
2015-11-01
Recently we have shown that for 2+1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2+1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2+1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.
New Multi-soliton Solutions for the (2+1)-Dimensional Kadomtsev-Petviashvili Equation
LIU Yang-Kui; Zhaqilao; FANG Jian-Hui; LI Zhi-Bin; PANG Ting; LIN Peng
2008-01-01
In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a (1+1)-dimensional Broer Kaup (BK) equation and a (1+1)-dimensional high-order Broer Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new ba-sic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili (KP) equation are obtained.
Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation
A new (2+1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1+1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2+1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.
A new hierarchy of (1 + 1)-dimensional soliton equations and its quasi-periodic solutions
A new spectral problem is proposed, from which a hierarchy of (1 + 1)-dimensional soliton equations is derived. With the help of nonlinearization approach, the soliton systems in the hierarchy are decomposed into two new compatible Hamiltonian systems of ordinary differential equations. The generating function flow method is used to prove the involutivity and the functional independence of the conserved integrals. The Abel-Jacobi coordinates are introduced to straighten out the associated flows. Using the Riemann-Jacobi inversion technique, the explicit quasi-periodic solutions for the (1 + 1)-dimensional soliton equations are obtained
Symmetry Reductions of (2 + 1-Dimensional CDGKS Equation and Its Reduced Lax Pairs
Na Lv
2014-01-01
Full Text Available With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.
The quantum interest conjecture in (3+1)-dimensional Minkowski space
Abreu, Gabriel
2010-01-01
The quantum inequalities, and the closely related quantum interest conjecture, impose restrictions on the distribution of the energy density measured by any time-like observer, potentially preventing the existence of exotic phenomena such as Alcubierre warp-drives or traversable wormholes. It has already been proved that both assertions can be reduced to statements concerning the existence or non-existence of bound states of a certain 1-dimensional quantum mechanical Hamiltonian. Using this approach, we will informally review a simple variational proof of one version of the Quantum Interest conjecture in (3+1)-dimensional Minkowski space.
Conservation laws for two (2 + 1)-dimensional differential-difference systems
Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080 (China) and Graduate School of the Chinese Academy of Sciences, Beijing (China)]. E-mail: gfyu@lsec.cc.ac.cn; Tam, H.-W. [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China)]. E-mail: tam@comp.hkbu.edu.hk
2006-10-15
Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced.
Chaotic solutions of(2+1)-dimensional Broek-Kaup equation with variable coefficients
Yang Zheng; Ma Song-Hua; Fang Jian-Ping
2011-01-01
In this paper, an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the(2+1)-dimensional Broek-Kaup equation with variable coefficients(VCBK). Based on the derived solitary wave solution and using a known chaotic system, some novel chaotic solutions are investigated.
Soliton Fission and Fusion in (2+1)-Dimensional Boiti-Leon-Pempinelli System
ZHENG Chun-Long; FANG Jian-Ping; CHEN Li-Qun
2005-01-01
By means of a special Painlevé-Backlund transformation and a multilinear variable separation approach,an exact solution with arbitrary functions of the (2+1)-dimensional Boiti-Leon-Pempinelli system (BLP) is derived.Based on the derived variable separation solution, we obtain some special soliton fission and fusion solutions for the higher dimensional BLP system.
Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System
无
2007-01-01
By means of an improved mapping method and a variable separation method, a scries of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
Variable Separation Solutions for the (2+1)-Dimensional Burgers Equation
唐晓艳; 楼森岳
2003-01-01
Considering that the multi-linear variable separation approach has been proved to be very useful to solve many (2+1)-dimensional integrable systems, we obtain the variable separation solutions of the Burgers equation with arbitrary number of variable separated functions. The Y-shaped soliton fusion phenomenon is revealed.
Nonpropagating Solitons in (2+1)-Dimensional Dispersive Long-Water Wave System
FANG Jian-Ping; ZHENG Chun-Long; LIU Qing
2005-01-01
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations
In this paper, two (3+1)-dimensional equations are investigated. Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types of exact solutions including some arbitrary functions. When these arbitrary functions are taken as some special functions, these solutions possess abundant structures. These solutions contain soliton-like solutions and rational solutions.
2+1-dimensional wormhole from a doublet of scalar fields
Mazharimousavi, S. Habib; Halilsoy, Mustafa
2015-01-01
We present a class of exact solutions in the framework of (2+1)-dimensional Einstein gravity coupled minimally to a doublet of scalar fields. Our solution can be interpreted upon the tuning of parameters as an asymptotically flat wormhole as well as a particle model in 2+1 dimensions.
Path Integral Evaluation of the Free Propagator on the (D-1)-dimensional Pseudosphere
Wospakrik, Hans J.
1999-01-01
We present an explicit path integral evaluation of the free Hamiltonian propagator on the (D-1)-dimensional pseudosphere, in the horicyclic coordinates, using the integral equation method. This method consists in deriving an integral equation for the propagator that turns out to be of Abel's type.
A Phase Space Path Integral for (2+1)-Dimensional Gravity
Carlip, Steven
1995-01-01
I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two approaches, and discuss some subtleties in the definition of the path integral necessary to prove this equivalence.
In this paper, by using symbolic and algebra computation, Chen and Wang's multiple Riccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the (2+1)-dimensional Breaking soliton equation are derived by using the extended multiple Riccati equations expansion method.
Linear superposition method for (2+1)-dimensional nonlinear wave equations
Lin Ji; Wang Rui-Min; Ye Li-Jun
2006-01-01
New forms of different-periodic travelling wave solutions for the(2+1)-dimensional Zakharov-Kuznetsov(ZK) equation and the Davey-Stewartson(DS)equation are obtained by the linear superposition approach of Jacobi elliptic function.A sequence of cyclic identities plays an important role in these procedures.
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Jean-Michel CORON; Jesús Ildefonso D（I）AZ; Abdelmalek DRICI; Tommaso MINGAZZINI
2013-01-01
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control.They assume that the internal control is only time dependent.The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
New soliton solutions of dissipative (2+1)-dimensional AKNS equation
Mohammad Najafi; Somayeh Najafi; Malihe Najafi
2013-01-01
We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of dissipative (2+1)-dimensional AKNS equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Periodic Wave Solution to the (3+1)-Dimensional Boussinesq Equation
WU Yong-Qi
2008-01-01
@@ One- and two-periodic wave solutions for (3+1)-dimensional Boussinesq equation are presented by means of Hirota's bilinear method and the Riemann theta function. The soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.
New nonlocal symmetries and conservation laws of the (1+1)-dimensional Sine-Gordon equation
A system of linearized equations of the (1+1)-dimensional Sine-Gordon (SG) equation and its Bäcklund transformation are given to determine not only nonlocal symmetries but also nonlocal conservation laws of the SG equation. Through the parameter expansion procedure, a sequence of infinitely many nonlocal symmetries and a sequence of infinitely many nonlocal conservation laws are obtained
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
Ma, Xuekai; Yang, Zhenjun; Lu, Daquan; Guo, Qi; Hu, Wei
2011-03-01
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System
无
2007-01-01
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
On (2+1) Dimensional Topologically Massive Non-linear Electrodynamics
Slusarczyk, M.; Wereszczynski, A.
2002-01-01
The (2+1) dimensional non-linear electrodynamics, the so called Pagels--Tomboulis electrodynamics, with the Chern--Simons term is considered. We obtain "generalized self--dual equation" and find the corresponding generalized massive Chern--Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained.
Lattice versions with restricted suppersymmetry of simple (1+1)-dimensional supersymmetric models are numerically studied using a local hamiltonian Monte Carlo method. The pattern of supersymmetry breaking closely follows the expectations of Bartels and Bronzan obtain in an alternative lattice formulation. (orig.)
Evaluation of the performance of the WRF 1-Dimensional Lake model over the East Africa Great Lakes
Gudoshava, M.; Semazzi, F. H. M.
2015-12-01
This study seeks to investigate the performance of the 1-Dimensional lake model coupled to WRF over East Africa. The Africa Great lakes exert a great influence on the climate of the region and a number of studies have shown how the lake influences the circulation and the total precipitation over the region. The lakes have highly variable depths, with Lake Victoria having an average depth of 40m and Lake Tanganyika a depth of 450m. The Lake model for WRF was tested and calibrated for the Great lakes, however it was not tested for tropical lakes. We hypothesize that the inclusion of a 1-dimensional lake will reduce the precipitation bias as compared to the WRF model without the lake model. In addition initializing the lake temperature using a vertical temperature profile that closes resembles the one over these lakes will greatly reduce the spin up time. The simulations utilized three nested domains at 36, 12 and 4km. The 4km domain is centered over Lake Victoria Basin, while the 12 km domain includes all the lakes in East Africa. The Tropical Rainfall Measuring Mission (TRMM) datasets are used in evaluating the precipitation, and the following statistics were calculated: root mean square error, standard deviation of the model and observations and mean bias. The results show that the use of the 1-dimensional lake model improves the precipitation over the region considerably compared to an uncoupled model. The asymmetrical rainfall pattern is evident in the simulations. However using the default vertical temperature profile with a three-month spin up is not adequate to transfer heat to the bottom of the lake. Hence the temperatures are still very cold at the bottom. A nine-month spin up improves the lake surface temperatures and lake temperatures at the bottom. A two year spin up greatly improves the lake surface temperatures and hence the total precipitation over the lake. Thus longer spin up time allows for adequate heat transfer in the lake. Initializing the
Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations
Liu, Han-Ze; Xin, Xiang-Peng
2016-08-01
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009, and the doctorial foundation of Liaocheng University under Grant No. 31805
Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation
WANG Jun-Min
2012-01-01
Two classes of periodic wave solutions to the (3+1)-dimensional soliton equation are derived by employing the Hirota bilinear method and theta function identities.These solutions are expressed in terms of Riemann theta functions of genus one and can be converted into an elliptic function format,both their long wave limit and extremum value are discussed in detail.%Two classes of periodic wave solutions to the (3+1)-dimensional soliton equation are derived by employing the Hirota bilinear method and theta function identities. These solutions are expressed in terms of Riemann theta functions of genus one and can be converted into an elliptic function format, both their long wave limit and extremum value are discussed in detail.
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
Darabi, F.; Atazadeh, K.; Rezaei-Aghdam, A.
2014-01-01
We have studied the Hawking radiation from {\\it generalized} rotating and static $(2+1)$-dimensional BTZ black holes. In this regard, we have benefited the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized $(2+1)$-dim...
The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations
M Matinfar; M Eslami; S Roshandel
2015-10-01
In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.
Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation
YING Jin-Ping
2001-01-01
By means of the heat conduction equation and the standard truncated Painlevé expansion, the (1+1) dimensional Kupershmidt equation is solved. Some significant exact multi-soliton solutions are given. Especially; for the interaction of the multi-solitons of the Kupershmidt equation, we find that a single (resonant) kink or bell soliton may be fissioned to several kink or bell solitons. Inversely, several kink or bell solitons may also be fused to one kink or bell soliton.
Exact solution of Dirac equation in 2+1 dimensional gravity
We find exact solutions of the Dirac equation in the 2+1 dimensional curved background by separation of variables. These solutions are given in terms of hypergeometric functions. We also perform the Gordon decomposition for the Dirac current to discuss the time dependence of the polarization densities and the magnetization density, and to show that the polarization densities are more effective than the magnetization density in the pair production in finite time intervals
Counter-rotational effects on stability of 2 + 1-dimensional thin-shell wormholes
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2014-09-15
The role of angular momentum in a 2 + 1-dimensional rotating thin-shell wormhole (TSW) is considered. Particular emphasis is given to stability when the shells (rings) are counter-rotating. We find that counter-rotating halves make the TSW supported by the equation of state of a linear gas more stable. Under a small velocity dependent perturbation, however, it becomes unstable. (orig.)
Expanding $(n+1)$-Dimensional Wormhole Solutions in Brans-Dicke Cosmology
Ebrahimi, E.; Riazi, N.
2009-01-01
We have obtained two classes of $(n+1)$-dimensional wormhole solutions using a traceless energy-momentum tensor in Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric spacetime also appear among the solutions as special cases. We have also considered the travesibility of the wormhole solutions...
Perturbation of higher-genus spatial surfaces in (2+1)-dimensional gravity
We study dynamical evolutions of spatial surfaces with genus g≥2 in (2+1)-dimensional pure Einstein gravity by the perturbation analysis around static moduli solutions. We find that an action of the perturbed Teichmueller parameters has a harmonic-oscillator form with a time-dependent mass and frequency. It is also shown that a set of the static moduli solutions is an attractor of nearby solutions
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Symbolic Computation Study of (2+1)-Dimensional Dispersive Long Wave Equations
Seeking exact analytical solutions of nonlinear evolution equations is of fundamental importance in mathematical physics. In this paper, based on a constructive algorithm and symbolic computation, abundant new exact solutions of the (2+1)-dimensional dispersive long wave equations are obtained, among which there are soliton-like solutions, mult-soliton-like solutions and formal periodic solutions, etc. Certain special solutions are considered and some interesting localized structures are revealed.
In this paper, the F-expansion method is extended and applied to construct the exact solutions of the (2 + 1)-dimensional generalized Wick-type stochastic Kadomtsev-Petviashvili equation by the aid of the symbolic computation system Maple. Some new stochastic exact solutions which include kink-shaped soliton solution, singular soliton solution and triangular periodic solutions are obtained via this method and Hermite transformation
The Multisoliton Solutions for the (2+1-Dimensional Sawada-Kotera Equation
Zhenhui Xu
2013-01-01
Full Text Available Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. These results show that the high-dimensional nonlinear evolution equation has rich dynamical behavior.
Painlevé Analysis and Some Solutions of(2+1)-Dimensional Generalized Burgers Equations
HONG Ke-Zhu; WU B-in; CHEN Xian-Feng
2003-01-01
Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach.
Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory
On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)
A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
Hongli An
2012-08-01
Full Text Available A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ=2 to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical cross-section, remarkably, satisfy a Ermakov-Ray-Reid system.
A Bilinear B(a)cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation
WU Jian-Ping
2008-01-01
@@ Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation.As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
Topological entanglement entropy of (2+1) dimensional Chern-Simons gauge theories on a general manifold is usually calculated with Witten's method of surgeries and replica trick, in which the spacetime manifold under consideration is very complicated. In this work, we develop an edge theory approach, which greatly simplifies the calculation of topological entanglement entropy of a Chern-Simons theory. Our approach applies to a general manifold with arbitrary genus. The effect of braiding and fusion of Wilson lines can be straightforwardly calculated within our framework. In addition, our method can be generalized to the study of other entanglement measures such as mutual information and entanglement negativity of a topological quantum field theory on a general manifold.
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
Ammon, A.; T. Hartung; Jansen, K.; Leövey, H.; Volmer, J.
2016-01-01
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the c...
Strings and string breaking in 2+1 dimensional nonabelian theories
Kovner, Alex; Rosenstein, Baruch
1998-01-01
We consider properties of confining strings in 2+1 dimensional SU(2) nonabelian gauge theory with the Higgs field in adjoint representation. The analysis is carried out in the context of effective dual Lagrangian which describes the dynamics of t'Hooft's $Z_{N}$ vorices. We point out that the same Lagrangian should be interpreted as an effective Lagrangian for the lightest glueballs. It is shown how the string tension for a fundamental string arises in this description. We discuss the propert...
The Nernst theorem and statistical entropy in a (1+1)-dimensional charged black hole
It was derived that the bosonic and fermionic entropies in (1+1)-dimensional charged black hole directly by using the quantum statistical method. The result is the same as the integral expression obtained by solving the wave equation approximately. Then it is obtained the statistical entropy of the black hole by integration via the improved brick-wall method, membrane model. The derived entropy satisfies the thermodynamic relation. When the radiation temperature of the black hole tends to zero, so does the entropy. It obeys Nernst theorem. So it can be taken as Planck absolute entropy
Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation
Huang Wen-Hua
2009-01-01
A general solution,including three arbitrary functions,is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method.Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution,special types of periodic folded waves are derived.In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions of the periodic folded waves and the degenerated single folded solitary waves axe investigated graphically and found to be completely elastic.
Bolokhov, A A; Bolokhov, T A; Sherman, S G
1996-01-01
We present the analysis of the phase space geometry of 2 \\rightarrow 3 reaction for the general case of nonzero and unequal particle masses. Its purpose is to elaborate an alternative approach to the problem of integration over phase space which does not exploit the Monte Carlo principle. The fast and effective algorithm of integration based on Gauss method is developed for treating 1--dimensional distributions in two--particle invariant variables. The algorithm is characterized by significantly improved accuracy and it can meet requirements of interactive processing.
Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
Gecim, Ganim
2016-01-01
In this paper, we study early-time inflation and late-time acceleration of the universe in the presence of non-minimal coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background by using the Noether symmetry approach. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with the results obtained in the context of the 3+1 dimensional teleparallel gravity under Noether symmetry approach, and we see that the two models have similar physically results about the inflation of the universe.
Distributions of self-interactions and voids in (1+1)-dimensional directed percolation
We investigate the scaling of self-interactions and voids in (1+1)-dimensional directed percolation clusters and backbones. We verify that the meandering of the backbone scales like the directed cluster. A geometric relation between the size distribution and the fractal dimensions of a set of objects is applied to find the scaling properties of self-interactions in directed percolation. Lastly we connect the geometric properties of the backbone with the avalanche distribution generated by interface dynamics at the depinning transition
Distributions of self-interactions and voids in (1+1)-dimensional directed percolation
Huber, G.; Jensen, M.H.; Sneppen, K. [Center for Chaos and Turbulence Studies, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
1995-09-01
We investigate the scaling of self-interactions and voids in (1+1)-dimensional directed percolation clusters and backbones. We verify that the meandering of the backbone scales like the directed cluster. A geometric relation between the size distribution and the fractal dimensions of a set of objects is applied to find the scaling properties of self-interactions in directed percolation. Lastly we connect the geometric properties of the backbone with the avalanche distribution generated by interface dynamics at the depinning transition.
LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS
张解放; 刘宇陆
2002-01-01
By using the extended homogeneous balance method, the localized coherentstructures are studied. A nonlinear transformation was first established, and then thelinearization form was obtained based on the extended homogeneous balance method for thehigher order ( 2 + 1 ) -dimensional Broer-Kaup equations. Starting from this linearizationform equation, a variable separation solution with the entrance of some arbitrary functionsand some arbitrary parameters was constructed. The quite rich localized coherent structureswere revealed. This method, which can be generalized to other (2 + 1 )-dimensionalnonlinear evolution equation, is simple and powerful.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
APPLICATION OF EXP-FUNCTION METHOD TO THE (2+1-DIMENSIONAL CALOGERO BOGOYAVLANSKII SCHIFF EQUATION
Z. AYATI
2009-07-01
Full Text Available In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1 -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving Calogero Bogoyavlanskii Schiff equation.
Exact periodic waves and their interactions for the (2+1)-dimensional KdV equation
Yan-Ze Peng
2005-08-01
By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic. The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones reported previously in the literature.
Soliton solutions for (2+1-dimensional Breaking Soliton Equation: Three Wave Method
Somayeh Arbabi Mohammad-Abadi
2012-04-01
Full Text Available By means of the three-wave method one can solve some nonlinear partial differential equations (NLPDEs in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of three-wave method to obtain some analytic solutions for the (2+1-dimensional Breaking soliton equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and EHTA, we can see that the new idea is very easy and straightforward.
Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation
ZHANG JieFang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying thc abundantlocalized solution structures in the (2-k1)-dimensional dispersive long-wave equations uty + xx + (u2)xy/2 = 0, ηt +(u + u + uxy)x = 0. Starting from the homogeneous balance method, we find that the richness of the localized coherentstructures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selectionsof the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers,instantons and ring solitons.
Dai Chao-Qing; Zhou Guo-Quan
2007-01-01
Starting from the extended tanh-function method (ETM) based on the mapping method, the variable separation solutions of the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.
Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
Gecim, Ganim; Sucu, Yusuf(Department of Physics, Akdeniz University, 07058 Antalya, Turkey)
2016-01-01
In this paper, we study early-time inflation and late-time acceleration of the universe in the presence of non-minimal coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background by using the Noether symmetry approach. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with the results obtained in the context of the 3+1 dimensional teleparallel gr...
Effective actions of 2+1 dimensional gravity and BF theory
We develop the perturbation theory of the BF theory, which is equivalent to 2+1 dimensional gravity without a cosmological constant if we take SO(1,2) as the gauge group. We show that the BF theory, which may have a Chern-Simons term, has only tree- or one loop connected Feynman diagrams and that the theory is completely finite (at all orders). We evaluate the effective actions of the BF theory and the generalized BF theory which has a 'cosmological constant' and show that quantum corrections lead to 'Chern-Simons terms', using a BRST invariant regularization based on Pauli-Villars. (author). 19 refs, 4 figs, 2 tabs
Baskonus, Haci Mehmet; Bulut, Hasan
2016-04-01
In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion.
无
2005-01-01
The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less system.Namely, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically.
Zhao, Zhonglong; Han, Bo
2016-05-01
In this paper, we focus on a (2+1)-dimensional generalized breaking soliton equation, which describes the (2+1)-dimensional interaction of a Riemann wave propagating along the y -direction with a long wave along the x-direction. Based on a multidimensional Riemann theta function, the quasiperiodic wave solutions of a (2+1)-dimensional generalized breaking soliton equation are investigated by means of the bilinear Bäcklund transformation. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. The dynamical behaviors of the quasiperiodic wave solutions are discussed by presenting the numerical figures.
Quantum Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2016-01-01
In a recent paper [Phys. Rev. D 92:084012, 2015], the author studied the classical $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in Ho\\v{r}ava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will give one step further in the understanding of (1+1)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with equation of state (EoS) $p=w\\rho$. The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schr\\"odinger equation for the wave function of the universe has the following properties: for $w=1$ (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for $w\
XU Chang-Zhi; ZHANG Jie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+ 1)-dimensional nonlinear models related to Schrodinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A (2+1)-dimensional multi-component DLW integrable hierarchy is obtained by using a (2+1)-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.
Bilinear Form and Two Bäcklund Transformations for the (3+1-Dimensional Jimbo-Miwa Equation
He Li
2015-01-01
Full Text Available With Bell polynomials and symbolic computation, this paper investigates the (3+1-dimensional Jimbo-Miwa equation, which is one of the equations in the Kadomtsev-Petviashvili hierarchy of integrable systems. We derive a bilinear form and construct a bilinear Bäcklund transformation (BT for the (3+1-dimensional Jimbo-Miwa equation, by virtue of which the soliton solutions are obtained. Bell-polynomial-typed BT is also constructed and cast into the bilinear BT.
2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the 3D-Ising Model
Bonacina, G; Rasetti, M; Bonacina, Giuseppe; Martellini, Maurizio; Rasetti, Mario
1992-01-01
We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $\\Sigma_g\\times\\RrR$ with $\\Sigma_g$ a closed and oriented Riemann surface of genus $g$, the corresponding 2+1-dimensional Euclidean quantum gravity may be related to the 3D-lattice Ising model before its thermodynamic limit.
Jin-Yuan, Li; Nian-Qiao, Fang; Ji, Zhang; Yu-Long, Xue; Xue-Mu, Wang; Xiao-Bo, Yuan
2016-04-01
In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. Project supported by the National Natural Science Foundation of China (Grant No. 41406018).
RUAN Hang-Yu
2005-01-01
A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.
Consistent interactions of the 2+1 dimensional noncommutative Chern-Simons field
We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this happens only in a particular gauge
Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity
In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
Ammon, A; Jansen, K; Leövey, H; Volmer, J
2016-01-01
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that our new method leads to orders of magnitude reduced errors also in other regions of parameter space.
Extremal curves in 2+1-dimensional Yang-Mills theory
Orland, P; Orland, Peter; Semenoff, Gordon W.
2000-01-01
We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. The curves of extremal potential energy in orbit space satisfy a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the dimensions of the torus. The intersections with the Gribov horizon are determined explicitly. The results are discussed in the context of Feynman's ideas about the origin of the mass gap.
Neutron beam applications; development of texture measuring technique using 1-dimensional PSD
Park, No Jin; Lee, Moon Kyu; Joung, Tae Won; Lee, In Sung [Kumoh National University of Technology, Kumi (Korea)
2002-03-01
The new developed materials have often a low crystal symmetry or/and multi-phase state. Because the diffraction patterns of those materials are very complex and some peaks are overlapped, the measured pole figures with a conventional detector (0-dimensional detector) are not sufficient to use for the texture analysis. And also the widely broaden diffraction patterns caused by sever deformation, can only measured with lots of measuring errors using 0-dimensional detector. In this study the 1-dimensional and 2-dimensional position sensitive detector(PSD) is used such pattern to analyse. With PSD the more accurate pole figures can be measured, and the texture analysis, the estimation of the properties are determined more precisely. The measurement using PSD needs special technique for the analysis of the measured pattern. In this study the measuring and analysing technique is developed and compared with the conventional detector. 11 refs., 92 figs., 21 tabs. (Author)
Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation
Gui Mu; Zhengde Dai; Zhanhui Zhao
2013-09-01
It is shown that Painlevé integrability of (2+1)-dimensional Boiti–Leon–Pempinelli equation is easy to be verified using the standard Weiss–Tabor–Carnevale (WTC) approach after introducing the Kruskal’s simplification. Furthermore, by employing a singular manifold method based on Painlevé truncation, variable separation solutions are obtained explicitly in terms of two arbitrary functions. The two arbitrary functions provide us a way to study some interesting localized structures. The choice of rational functions leads to the rogue wave structure of Boiti–Leon–Pempinelli equation. In addition, for the other choices, it is observed that two solitons may evolve into breather after interaction. Also, the interaction between two kink compactons is investigated.
Quantum Probes of Timelike Naked Singularities in 2+1-Dimensional Power-Law Spacetimes
The formation of naked singularities in 2+1-dimensional power-law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field, respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed at r=0. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remain singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity cannot be associated with the energy conditions
Symmetry Reduction of the (2+1)-Dimensional Modified Dispersive Water-Wave System
Ma, Zheng-Yi; Fei, Jin-Xi; Du, Xiao-Yang
2015-08-01
Using the standard truncated Painlevé expansion, the residual symmetry of the (2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived by utilizing the obtained symmetries. The symmetries of the system are also derived through the Clarkson-Kruskal direct method, and several types of explicit reduction solutions relate to the trigonometric or the hyperbolic functions are obtained. Finally, some special solitons are depicted from one of the solutions. Supported by the National Natural Science Foundation of China under Grant No. 11447017 and the Natural Science Foundation of Zhejiang Province under Grant Nos. LY14A010005 and LQ13A010013
New Exact Solutions of (1 + 1)-Dimensional Coupled Integrable Dispersionless System
DAI Chao-Qing; YANG Qin; WANG Yue-Yue
2011-01-01
This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) in our solutions, the annihilation phenomena of the flat-basin soliton,arch-basin soliton, and flat-top soliton are discussed.
Large phase shift of (1+1)-dimensional nonlocal spatial solitons in lead glass
Shou, Qian; Guo, Qi
2014-01-01
The large phase shift of strongly nonlocal spatial optical soliton(SNSOS) in the (1+1)-dimensional [(1+1)D] lead glass is investigated using the perturbation method. The fundamental soliton solution of the nonlocal nonlinear Schodinger equation(NNLSE) under the second approximation in strongly nonlocal case is obtained. It is found that the phase shift rate along the propagation direction of such soliton is proportional to the degree of nonlocality, which indicates that one can realize Pi-phase-shift within one Rayleigh distance in (1+1)D lead glass. A full comprehension of the nonlocality-enhancement to the phase shift rate of SNSOS is reached via quantitative comparisons of phase shift rates in different nonlocal systems.
Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation
ZHANG SHENG; TIAN CHI; QIAN WEI-YI
2016-06-01
The (4+1)-dimensional Fokas equation is derived in the process of extending the integrable Kadomtsev–Petviashvili and Davey–Stewartson equations to higher-dimensional nonlinear wave equations. This equation is under investigation in this paper. Hirota’s bilinear method is, for the first time, used to solve such a higher-dimensional equation. In order to bilinearize the Fokas equation, some appropriate transformations are adopted. As a result, single-soliton solution,double-soliton solution and three-soliton solution are obtained. A new uniform formula of n-soliton solution is derived from this. It is shown that the transformations adopted in this work play a key role in converting the Fokas equation into Hirota’s bilinear form.
Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2015-01-01
The $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid with equation of state $p=\\omega \\rho$ is analyzed through the view of Ho\\v rava-Lifshitz (HL) theory of gravity. In this theory, the anisotropic scaling of space and time breaks Lorentz invariance of General Relativity (GR) in such a way that the gravitational action is no longer a topological invariant and the theory becomes dynamical. With the introduction of a perfect fluid through Schutz formalism, it is shown that the resulting dynamical theory is very similar to the two-dimensional Jackiw-Teitelboim (JT) model, where a dilatonic degree of freedom is introduced to force a dynamical theory. However, in HL theory, the introduction of a dilaton field is not necessary.
Cosmology in (1 +1 ) -dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2015-10-01
The (1 +1 )-dimensional Friedmann-Robertson-Walker universe filled with a perfect fluid with equation of state p =ω ρ is analyzed through the view of Hořava-Lifshitz (HL) theory of gravity. In this theory, the anisotropic scaling of space and time breaks Lorentz invariance of general relativity in such a way that the gravitational action is no longer a topological invariant and the theory becomes dynamical. With the introduction of a perfect fluid through Schutz formalism, it is shown that the resulting dynamical theory is very similar to the two-dimensional Jackiw-Teitelboim model, where a dilatonic degree of freedom is introduced to force a dynamical theory. However, in HL theory, the introduction of a dilaton field is not necessary.
Regularization strategy for an inverse problem for a 1 + 1 dimensional wave equation
Korpela, Jussi; Lassas, Matti; Oksanen, Lauri
2016-06-01
An inverse boundary value problem for a 1 + 1 dimensional wave equation with a wave speed c(x) is considered. We give a regularization strategy for inverting the map { A } :c\\mapsto {{Λ }}, where Λ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed c. That is, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map \\tilde{{{Λ }}}={{Λ }}+{ E }, where { E } corresponds to the measurement errors, and reconstruct an approximative wave speed \\tilde{c}. We emphasize that \\tilde{{{Λ }}} may not be in the range of the map { A }. We show that the reconstructed wave speed \\tilde{c} satisfies \\parallel \\tilde{c}-c\\parallel ≤slant C\\parallel { E }{\\parallel }1/54. Our regularization strategy is based on a new formula to compute c from Λ.
Bellucci, S; Bragança, E; Saharian, A A
2016-01-01
We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even funct...
Dynamical formation and evolution of (2+1)-dimensional charged black holes
In this paper, we investigate the dynamical formation and evolution of (2 + 1)-dimensional charged black holes. We numerically study dynamical collapses of charged matter fields in an anti-de Sitter background and note the formation of black holes using the double-null formalism. Moreover, we include renormalized energy-momentum tensors assuming the S-wave approximation to determine thermodynamical back-reactions to the internal structures. If there are no semi-classical effects, the amount of charge determines the causal structures. If the charge is sufficiently small, the causal structure has a space-like singularity. However, as the charge increases, an inner Cauchy horizon appears. If we have sufficient charge, we see a space-like outer horizon and a time-like inner horizon, and if we give excessive charge, black hole horizons disappear. We have some circumstantial evidence that weak cosmic censorship is still satisfied, even for such excessive charge cases. Also, we confirm that there is mass inflation along the inner horizon, although the properties are quite different from those of four-dimensional cases. Semi-classical back-reactions will not affect the outer horizon, but they will affect the inner horizon. Near the center, there is a place where negative energy is concentrated. Thus, charged black holes in three dimensions have two types of curvature singularities in general: via mass inflation and via a concentration of negative energy. Finally, we classify possible causal structures. (paper)
A model of random center vortex lines in continuous 2+1-dimensional space-time
Altarawneh, Derar; Höllwieser, Roman
2016-01-01
A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining ph...
Expanding (n+1)-dimensional wormhole solutions in Brans-Dicke cosmology
We have obtained two classes of (n+1)-dimensional wormhole solutions using a traceless energy-momentum tensor in the Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry, while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric space-time also appear among the solutions as special cases. We have also considered the traversability of the wormhole solutions and have shown that they are indeed traversable. Finally, we have discussed the energy-momentum tensor which supports this geometry and have checked for the energy conditions. We have found that wormhole solutions in the first class of solutions violate the weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate the WEC, but in an open universe with a suitable choice of constants the supporting matter energy-momentum tensor can satisfy the WEC. However, even in this case the full effective energy-momentum tensor including the scalar field and the matter energy-momentum tensor still violates the WEC.
Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain
A characterization of net infiltration rates is needed for site-scale evaluation of groundwater flow at Yucca Mountain, Nevada. Shallow infiltration caused by precipitation may be a potential source of net infiltration. A 1-dimensional finite difference model of shallow infiltration with a moisture-dependent evapotranspiration function and a hypothetical root-zone was calibrated and verified using measured water content profiles, measured precipitation, and estimated potential evapotranspiration. Monthly water content profiles obtained from January 1990 through October 1993 were measured by geophysical logging of 3 boreholes located in the alluvium channel of Pagany Wash on Yucca Mountain. The profiles indicated seasonal wetting and drying of the alluvium in response to winter season precipitation and summer season evapotranspiration above a depth of 2.5 meters. A gradual drying trend below a depth of 2.5 meters was interpreted as long-term redistribution and/or evapotranspiration following a deep infiltration event caused by runoff in Pagany Wash during 1984. An initial model, calibrated using the 1990 to 1992 record, did not provide a satisfactory prediction of water content profiles measured in 1993 following a relatively wet winter season. A re-calibrated model using a modified, seasonally-dependent evapotranspiration function provided an improved fit to the total record. The new model provided a satisfactory verification using water content changes measured at a distance of 6 meters from the calibration site, but was less satisfactory in predicting changes at a distance of 18 meters
Vacuum energy is non-positive for (2 + 1)-dimensional holographic CFTs
Hickling, Andrew; Wiseman, Toby
2016-02-01
We consider a (2 + 1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are ‘good’ so are hidden by horizons at finite temperature.
Vacuum energy is non-positive for (2+1)-dimensional holographic CFTs
Hickling, Andrew
2015-01-01
We consider a (2+1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are `good' so are hidden by horizons at finite temperature.
A first look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations
We study a lattice regularization of the gravitational path integral—causal dynamical triangulations—for (2 + 1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein–Hilbert action supplemented by the Gibbons–Hawking–York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the Euclidean de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs in detail from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach. We also uncover tantalizing evidence suggesting that Lorentzian not Euclidean de Sitter spacetime dominates the ground state on sufficiently large scales. (paper)
Polar magneto-optical Kerr effect instrument for 1-dimensional magnetic nanostructures
Pathak, Sachin; Sharma, Manish
2014-01-01
The magneto-optical Kerr effect (MOKE) is a powerful technique to investigate the magnetization behaviour in magnetic nanostructures. We describe the design of a polar MOKE instrument for investigating the magnetization variation in MOKE signal observed in the exciting regime where the size of the magnetic nanostructures is around 20-350 nm. In particular, when the magnetization of the sample is perpendicular to its plane (i.e., along the axis of a cylindrical nanowire) we use polar MOKE configuration. The sign and magnitude of the small rotation measured in the signal is found proportional to the magnetization and its direction. The MOKE measurements indicate that the hysteresis depends on the shape as well as the density of nanostructures formed. The instrument is sensitive enough to clearly indicate the effect of magneto-static interaction on shape of M-H loop. We have observed the coercive field of ˜269 G for cylindrical nanowire grown in anodic aluminium oxide template and ˜135 G for "pin" shaped nanowire grown in polycarbonate track etched template. The magnetization reversal measurements are intricate in the case of "pin" or "X" shaped nanostructures as seen from the loop. These typical MOKE measurements on the 1-dimensional (1-D) nanostructures explore the effect of magneto-static interaction between the nanostructures.
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability.
Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain
A characterization of net infiltration rates is needed for site-scale evaluation of groundwater flow at Yucca Mountain, Nevada. Shallow infiltration caused by precipitation may be a potential source of net infiltration. A 1-dimensional finite difference model of shallow infiltration with a moisture-dependant evapotranspiration function and a hypothetical root-zone was calibrated and verified using measured water content profiles, measured precipitation, and estimated potential evapotranspiration. Monthly water content profiles obtained from January 1990 through October 1993 were measured by geophysical logging of 3 boreholes located in the alluvium channel of Pagany Wash on Yucca Mountain. The profiles indicated seasonal wetting and drying of the alluvium in response to winter season precipitation and summer season evapotranspiration above a depth of 2.5 meters. A gradual drying trend below a depth of 2.5 meters was interpreted as long-term redistribution and/or evapotranspiration following a deep infiltration event caused by runoff in Pagany Wash during 1984. An initial model, calibrated using the 1990 to 1 992 record, did not provide a satisfactory prediction of water content profiles measured in 1993 following a relatively wet winter season. A re-calibrated model using a modified, seasonally-dependent evapotranspiration function provided an improved fit to the total record. The new model provided a satisfactory verification using water content changes measured at a distance of 6 meters from the calibration site, but was less satisfactory in predicting changes at a distance of 18 meters
Theta-function Solutions to the(2+1)-Dimensional Breaking Soliton Equation
WANG Jun-Min; YANG Xiao
2011-01-01
@@ A new periodic wave solution in terms of theta functions is presented for a kind of elliptic equation.Based on the results,with the help of Mathematica and the improved generalized F-expansion method,some periodic wave solutions in terms of theta functions are obtained for the(2+1)-dimensional breaking soliton equation.In addition,x-direction periodic wave solutions are derived,their properties and profiles are displayed in 3D figures.To our knowledge,these solutions are reported for the first time.%A new periodic wave solution in terms of theta functions is presented for a kind of elliptic equation. Based on the results, with the help of Mathematica and the improved generalized F-expansion method, some periodic wave solutions in terms of theta functions are obtained for the (2+l)-dimensional breaking soliton equation. In addition, x-direction periodic wave solutions are derived, their properties and proBles are displayed in 3D figures. To our knowledge, these solutions are reported for the first time.
Khalilov, V R
2015-01-01
The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.
Khalilov, V.R.; Mamsurov, I.V. [M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow (Russian Federation)
2015-04-01
The polarization operator (tensor) for planar charged fermions in a constant uniform magnetic field is calculated in the one-loop approximation of 2 + 1-dimensional quantum electrodynamics (QED{sub 2+1}) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in QED{sub 2+1} at a finite chemical potential, find the imaginary part of this Green function, and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem likely to be revealed in a monolayer graphene sample in the presence of an external constant uniform magnetic field B perpendicular to it. (orig.)
Dromion and Multi-soliton Structures of the (2+1)-Dimensional Higher-Order Broer-Kaup System
林机
2002-01-01
Using the standard truncated Painlevé analysis and the Backlund transformation, we can obtain many significant exact soliton solutions of the (2+1)-dimensional higher-order Broer-Kaup (HBK) system. A special type of soliton solution is described by the variable coefficient heat-conduction-like equation. The inclusion of three arbitrary functions in the general expressions of the solitons makes the solitons of the (2+1)-dimensional HBK system possess abundant structures such as solitofT solutions, multi-dromion solutions, ring solitons and so on.
An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions
Hu Xingbiao [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Li Chunxia [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Nimmo, Jonathan J C [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China)
2005-01-07
A symmetric (2+1)-dimensional Lotka-Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Baecklund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka-Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions.
YANG Qiu-Ying; MA Song-Hua; ZHANG Ying-Yue; FANG Jian-Ping; CHEN Tian-Lun; HONG Bi-Hai; ZHENG Chun-Long
2008-01-01
By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system.
In this paper, the Exp-function method is used to obtain generalized solitonary solutions and periodic solutions of the Generalized Zakharov system and (2 + 1)-dimensional Nizhnik-Novikov-Veselov system. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
WEN Xiao-Yong
2009-01-01
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
XU Chang-Zhi
2006-01-01
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.
The double Wronskian solutions whose entries satisfy matrix equation for a (2+1)-dimensional breaking soliton equation ((2+1) DBSE) associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for (2+1) DBSE are obtained by taking special cases in general double Wronskian solutions. (general)
With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation are constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m → 0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions
The improved tanh function method [Chaos, Solitons and Fractals 2005;24:257] is further improved by constructing new ansatz solution of the considered equation. As its application, the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are considered and abundant new exact non-travelling wave solutions are obtained
Jianping Shi; Jibin Li; Shumin Li
2013-11-01
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations.
Space-time-resolved quantum electrodynamics: A (1+1)-dimensional model
Glasgow, Scott; Smith, Dallas; Pritchett, Luke; Gardner, John; Ware, Michael J.
2016-06-01
We develop a model that reduces quantum electrodynamics (QED) in time plus three spatial dimensions to time plus a single spatial dimension, making it is possible to numerically calculate the dynamic behavior of simple QED systems. The dimensionality is restricted in such a way as to preserve the influence of spin and angular momentum. In contrast to the S -matrix scattering approach, these calculations are not perturbative within the zero- and one-photon sector of the relevant Hilbert space. The model restricts the electron occupation number to one and the photon occupation number to zero or one. We use this model to calculate the dynamics of a so-called bare electron that dresses itself by a photon field.
Entropy of 2+1 dimensional de Sitter space without cutoff
Kim, W; Park, Y J; Kim, Wontae; Kim, Yong-Wan; Park, Young-Jai
2006-01-01
By introducing the generalized uncertainty principle on the quantum state density, we calculate the statistical entropy of a scalar field on the background of three-dimensional de Sitter space without artificial cutoff. The desired entropy proportional to the horizon perimeter is obtained.
In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma–Tamborenea growth model, the (1+1)-dimensional Das Sarma–Tamborenea model is simulated on a large length scale by using the kinetic Monte–Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma–Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma–Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour. (general)
Lü, Xing; Tian, Bo; Zhang, Hai-Qiang; Xu, Tao; Li, He
2010-12-01
Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painlevé integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to γ(t), the coefficient of the cubic nonlinear term u(2)u(x). Then, an independent transformation of the variable t transforms the reduced γ(t)-dependent equation into a constant-coefficient integrable one. Painlevé test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable. PMID:21198095
In this paper, the (2+1)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the (2+1)-dimensional generalization of shallow water wave equation possesses the Painlevé property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation (DT) is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water. (general)
Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painleve integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to γ(t), the coefficient of the cubic nonlinear term u2ux. Then, an independent transformation of the variable t transforms the reduced γ(t)-dependent equation into a constant-coefficient integrable one. Painleve test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable.
The fermion in the gauge invariant formulation of the chiral Schwinger model and its relation to the fermion in the anomalous formulation is studied. A gauge invariant fermion operator is constructed that does not give rise to an asymptotic fermion field. It fits in the scheme prepared by generalized Schwinger models. Singularities in the short-distance limit of the chiral Schwinger model in the anomalous formulation lead to the conclusion that it is not a promising starting point for investigations towards realistic (3+1)-dimensional gauge theories with chiral fermion content. A new anomalous (1+1)-dimensional model is studied, the chiral quantum gravity. It is proven to be consistent if only a limited number of chiral fermions couple. The fermion propagator behaves analogously to the one in the massless Thirring model. A general rule is derived for the change of the fermion operator, which is induced by the breakdown of a gauge symmetry. (orig.)
Zitian Li
2014-09-01
A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer–Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instantonlike and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution.
LI De-Sheng; LUO Cheng-Xin; ZHANG Hong-Qing
2004-01-01
Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.
2015-01-01
Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting ap...
ZHANG Jie-Fang; MENG Jian-Ping; HUANG Wen-Hua
2004-01-01
From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.
A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)
Sachin Kumar
2012-10-01
Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG expansion method whereG G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.
Layden, A.; S. MacCallum; Merchant, C.
2015-01-01
FLake, a 1-dimensional freshwater lake model, is tuned for 244 globally distributed large lakes using lake surface water temperatures (LSWTs) derived from Along-Track Scanning Radiometers (ATSRs). The model, tuned using only 3 lake properties; lake depth, albedo (snow and ice) and light extinction co-efficient, substantially improves the measured biases in various features of the LSWT annual cycle, including the LSWTs of saline and high altitude lakes. The daily ...
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
Teo, L. P.
2013-01-01
We consider the finite temperature Casimir free energy acting on a spherical shell in (D+1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar and electromagnetic fields. Dirichlet, Neumann, perfectly conducting and infinitely permeable boundary conditions are considered. The Casimir free energy is regularized using zeta functional regularization technique. To renormalize the Casimir free energy, we compute the heat kernel coefficients $c_n$, $0\\leq n\\leq D+1$, from the ...
Cong Sun; Bo Jiang
2015-01-01
We study the existence and orbital stability of smooth periodic traveling waves solutions of the (n +1)-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava’s results (2007), and by applying the stability theory established by Grillakis et al. (1987), we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.
Cong Sun
2015-01-01
Full Text Available We study the existence and orbital stability of smooth periodic traveling waves solutions of the (n +1-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava’s results (2007, and by applying the stability theory established by Grillakis et al. (1987, we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.
Ahmet Bekir; Özkan Güner
2013-08-01
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech$^{p}$ and tanh$^{p}$ functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Yan Wang; Zhenhui Wang
2013-01-01
By employing Hirota bilinear method, we mainly discuss the ( $3+1$ )-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its $N$ exponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly...
Sperstad, Einar B. Stiansen. Iver B.; Sudbø, Asle
2012-01-01
We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase $\\theta$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\\Delta \\theta$, not in $\\theta$. Significantly, the most ordered state therefore does not have 3D XY ordering. Rather, it featur...
In this paper, a detailed Lie symmetry analysis of the (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method, which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. (general)
Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in (1+1)-Dimensional Spacetime
HE Xiao-Kai; LIU Wen-Biao; QIU Wei-Gang
2009-01-01
The Casimir energy of maesive scalar field with hybrid (Dirichlet-Neumann) boundary condition is calcu-lated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures.
In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman—Nuseir method generated by the Jaulent—Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation. (general)
SRD 166 MEMS Calculator (Web, free access) This MEMS Calculator determines the following thin film properties from data taken with an optical interferometer or comparable instrument: a) residual strain from fixed-fixed beams, b) strain gradient from cantilevers, c) step heights or thicknesses from step-height test structures, and d) in-plane lengths or deflections. Then, residual stress and stress gradient calculations can be made after an optical vibrometer or comparable instrument is used to obtain Young's modulus from resonating cantilevers or fixed-fixed beams. In addition, wafer bond strength is determined from micro-chevron test structures using a material test machine.
Groups Analysis and Localized Solutions of the (2+1)-Dimensional Ito Equation
Hu, Xiao-Rui; Chen, Jun-Chao; Chen, Yong
2015-07-01
Not Available Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014, the National Natural Science Foundation of China under Grant Nos 11326164, 11401528, 11435005 and 11375090, the Global Change Research Program of China (No 2015CB953904), the Research Fund for the Doctoral Program of Higher Education of China (No 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (No ZF1213), and Shanghai Minhang District Talents of High Level Scientific Research Project.
Thermodynamics of hot quantum scalar field in a (D+1) dimensional curved spacetime
C., W A Rojas
2016-01-01
We use the brick wall model to calculate the free energy of quantum scalar field in a curved spacetime (D +1) dimensions. We find the thermodynamics properties of quantum scalar field in several scenaries: Minkowski spacetime, Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the thermodynamical properties of quantum scalar field is exactly with the reported. It was found that the entropy of the gas is proportional to the horizon area in a gravity field strong, which is consistent with the holographic principle.
(2+1)-dimensional QED with dynamically massive fermions in vacuum polarization
We study chiral symmetry breaking in three-dimensional QED with Nf flavors of four-component fermions. A closed system of Schwinger-Dyson equations for fermion and photon propagators and the full fermion-photon vertex is proposed, which is consistent with the Ward-Takahashi identity. A simplified version of that set of equations is reduced (in the nonlocal gauge) to the equation for a dynamical fermion mass function, where the one-loop vacuum polarization with dynamically massive fermions has been taken into account. The linearized equation for the fermion mass function is analyzed in real space. The analytical solution is compared with the results of numerical calculations of the nonlinear integral equation in momentum space. copyright 1996 The American Physical Society
Lakshminarayana, S.
Letters to the Editor Dynamic Ranking with n H11001 1 Dimensional Vector Space Models: An Alternative Search Mechanism for World Wide Web Sir: The World Wide Web (WWW) has grown both in depth and width of technology typically giving scope for new databases.../links based on the algo- rithm characteristics. To optimize the results we need to apply dynamically extendable vector based ranking techniques because of the properties that depend for ranking a page are growing and not finite. Kleinberg (1998) classified...
Harun-Or- Roshid
2014-01-01
Full Text Available Periodic and soliton solutions are presented for the (1+1-dimensional classical Boussinesq equation which governs the evolution of nonlinear dispersive long gravity wave traveling in two horizontal directions on shallow water of uniform depth. The equation is handled via the exp(−Φ(η-expansion method. It is worth declaring that the method is more effective and useful for solving the nonlinear evolution equations. In particular, mathematical analysis and numerical graph are provided for those solitons, periodic, singular kink and bell type solitary wave solutions to visualize the dynamics of the equation.
CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx +4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions.
$Q-\\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
Ma, Yu-Bo; Cao, Shuo
2016-01-01
In order to achieve a deeper understanding of gravity theories, it is important to further investigate the thermodynamic properties of black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose $T,Q,\\Phi$ as the state parameters and study the phase equilibrium problem of general $(n+1)$-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide theoretical foundation for studying the phase transition and phase structure of black hole systems.
ZHENHUI XU; HANLIN CHEN; ZHENGDE DAI
2016-08-01
In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3+1)-dimensional B-type Kadomtsev--Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich thevariety of the dynamics of higher-dimensional nonlinear wave field.
Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlevé property of the (3+1)-dimensional Burgers equation, and then Bäcklund transformation is derived according to the truncated expansion of the obtained Painlevé analysis. Using the Bäcklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures. (general)
Nikita AgasianITEP, Moscow; Dmitri Antonov
2015-01-01
Confining strings and RG flow at finite temperature are investigated in the (2+1)-dimensional Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of ...
Storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in a coherent atomic gas
Chen, Zhiming; Li, Hui-jun; Hang, Chao; Huang, Guoxiang
2016-01-01
A robust light storage and retrieval (LSR) in high dimensions is highly desirable for light and quantum information processing. However, most schemes on LSR realized up to now encounter problems due to not only dissipation, but also dispersion and diffraction, which make LSR with a very low fidelity. Here we propose a scheme to achieve a robust storage and retrieval of weak nonlinear high-dimensional light pulses in a coherent atomic gas via electromagnetically induced transparency. We show that it is available to produce stable (3+1)-dimensional light bullets and vortices, which have very attractive physical property and are suitable to obtain a robust LSR in high dimensions.
Full Symmetry Groups and Similar Reductions of a (2+1)-Dimensional Resonant Davey-Stewartson System
Applying the classical Lie symmetry method to the (2+1)-dimensional resonant Davey-Stewartson system introduced by Tang [X.Y. Tang et al., Chaos, Solitons and Fractals 42 (2007) 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived. (general)
Öziş, Turgut; Aslan, İsmail
2008-11-01
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the ( 3+1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences.
Ozis, Turgut [Department of Mathematics, Ege University, 35100 Bornova, Izmir (Turkey)], E-mail: turgut.ozis@ege.edu.tr; Aslan, Ismail [Department of Mathematics, Izmir Institute of Technology, 35430 Urla, Izmir (Turkey)
2008-11-24
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3+1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences.
Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge
Kotikov, A V; Teber, S
2016-01-01
The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N
In nonlinear optical fibres, the evolution of two polarization envelopes is governed by a system of coupled nonlinear Schroedinger (CNLS) equations. In this paper, with the aid of symbolic computation, the analytical bright one- and two-soliton solutions of the (2+1)-dimensional CNLS equations under certain constraints are presented by employing the Hirota method. We have discussed the head-on and overtaking interactions which include elastic and inelastic collisions between two parallel bright solitons. In the interaction process, the intensities of solitons can exhibit various redistributions. We also point out that these properties have important physical applications in constructing various logic gates and nonlinear optical fibers
In a cosmic dusty plasma, both azimuthal and height perturbations of a nonplanar cylindrical geometry are considered. For dust-ion-acoustic waves and with symbolic computation (3+1)-dimensional generalized Johnson [(3+1)DGJ] model is derived and analytic solutions are constructed. Supernova-shell-typed expanding bright (3+1)DGJ nebulons and Saturn-F-ring-type expanding dark (3+1)DGJ nebulons are both pictured and discussed. Essential difference of this letter from the existing literature is pointed out, with the relevant, possibly observable (3+1)DGJ-nebulonic structures for the future cosmic experiments proposed
Cloud of strings as source in 2 + 1-dimensional f(R) = R{sup n} gravity
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-02-15
We present three parameters exact solutions with possible black holes in 2 + 1-dimensional f(R) = R{sup n} modified gravity coupled minimally to a cloud of strings. These three parameters are n, the coupling constant of the cloud of strings ξ, and an integration constant C. Although in general one has to consider each set of parameters separately, for n an even integer greater than one we give a unified picture providing black holes. For n ≥ 1 we analyze a null/timelike geodesic within the context of particle confinement. (orig.)
Conformal invariance at a second-order phase transition yields an exact finite-size scaling theory on a two-dimensional cylinderical geometry. We combine this two-dimensional conformal field theory with a numerical investigation of the deconfinement phase transition of (2 + 1)-dimensional SU(2) lattice gauge theory. Results of this study and a more general finite-size scaling analysis on square lattices yield excellent agreement with d = 2 Ising critical behavior, as has been conjectured on the basis of universality. (orig.)
Conformal invariance at a 2nd order phase transition yields an exact finite size scaling theory on a 2-dimensional cylindrical geometry. We combine this two-dimensional conformal field theory with a numerical investigation of the deconfinement phase transition of (2+1)-dimensional SU(2) lattice gauge theory. Results of this study and a more general finite size scaling analysis on square lattices yield excellent agreement with d=2 Ising critical behavior, as has been conjectured on the basis of universality. (orig.)
Hitender Kumar
2013-03-01
Full Text Available The (2+1-dimensional Maccari and nonlinear Schrödinger equations are reduced to a nonlinear ordinary differential equation (ODE by using a simple transformation, various solutions of the nonlinear ODE are obtained by using extended F-expansion and projective Ricatti equation methods. With the aid of solutions of the nonlinear ODE more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Wen-guang Cheng
2014-01-01
Full Text Available The bilinear form, bilinear Bäcklund transformation, and Lax pair of a (2 + 1-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived through Bell polynomials. The integrable constraint conditions on variable coefficients can be naturally obtained in the procedure of applying the Bell polynomials approach. Moreover, the N-soliton solutions of the equation are constructed with the help of the Hirota bilinear method. Finally, the infinite conservation laws of this equation are obtained by decoupling binary Bell polynomials. All conserved densities and fluxes are illustrated with explicit recursion formulae.
Shaolin Li
2014-01-01
Full Text Available The bilinear operator and F-expansion method are applied jointly to study (2+1-dimensional Kadomtsev-Petviashvili (KP equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.