Vol 193, No 3 (2017)
- Year: 2017
- Articles: 14
- URL: https://journals.rcsi.science/0040-5779/issue/view/10449
Article
Hamiltonian operators in differential algebras
Abstract
We develop a previously proposed algebraic technique for a Hamiltonian approach to evolution systems of partial differential equations including constrained systems and propose a defining system of equations (suitable for computer calculations) characterizing the Hamiltonian operators of a given form. We demonstrate the technique with a simple example.
Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics
Abstract
We propose a method for determining asymptotic solutions of stationary problems for pencils of differential (and pseudodifferential) operators whose symbol is a self-adjoint matrix. We show that in the case of constant multiplicity, the problem of constructing asymptotic solutions corresponding to a distinguished eigenvalue (called an effective Hamiltonian, term, or mode) reduces to studying objects related only to the determinant of the principal matrix symbol and the eigenvector corresponding to a given (numerical) value of this effective Hamiltonian. As an example, we show that stationary solutions can be effectively calculated in the problem of plasma motion in a tokamak.
Rogue-wave solutions of the Zakharov equation
Abstract
Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane (x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey–Stewartson equation analytically and graphically.
Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column
Abstract
We consider a planar evolution problem for perturbations of the ice cover by a dipole starting its uniform rectilinear horizontal motion in a column of an initially stationary fluid. Using asymptotic Fourier analysis, we show that at supercritical velocities, waves of two types form on the water–ice interface. We describe the process of establishing these waves during the dipole motion. We assume that the fluid is ideal and incompressible and its motion is potential. The ice cover is modeled by the Kirchhoff–Love plate.
The critical boundary RSOS M(3,5) model
Abstract
We consider the critical nonunitary minimal model M(3, 5) with integrable boundaries and analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory using the thermodynamic Bethe ansatz (TBA) equations. Solving the TBA functional equation satisfied by the transfer matrices of the associated A4restricted solid-on-solid Forrester–Baxter lattice model in regime III in the continuum scaling limit, we derive the integral TBA equations for all excitations in the (r, s) = (1, 1) sector and then determine their corresponding energies. We classify the excitations in terms of (m, n) systems.
Holographic control of information and dynamical topology change for composite open quantum systems
Abstract
We analyze how the compositeness of a system affects the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by nonequilibrium heating. We use a holographic description of the evolution of entanglement entropy. The nonsmooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jumplike velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We find five qualitatively different types of behavior of the mutual information dynamics and indicate the corresponding regions of the system parameters.
q-Deformed Barut–Girardello su(1, 1) coherent states and Schrödinger cat states
Abstract
We define Schrödinger cat states as superpositions of q-deformed Barut–Girardello su(1, 1) coherent states with an adjustable angle φ in a q-deformed Fock space. We study the statistical properties of the q-deformed Barut–Girardello su(1, 1) coherent states and Schrödinger cat states. The statistical properties of photons are always sub-Poissonian for q-deformed Barut–Girardello su(1, 1) coherent states. For Schrödinger cat states in the cases φ = 0, π/2, π, the statistical properties of photons are always sub-Poissonian if φ = π/2, and the other cases are hard to determine because they depend on the parameters q and k. Moreover, we find some interesting properties of Schrödinger cat states in the limit |z| → 0, where z is the parameter of those states. We also derive that the statistical properties of photons are sub-Poissonian in the undeformed case where π/2 ≤ φ ≤ 3π/2.
Dynamical magnetic susceptibility in the spin-fermion model for cuprate superconductors
Abstract
Using the method of diagram techniques for the spin and Fermi operators in the framework of the SU(2)-invariant spin-fermion model of the electron structure of the CuO2plane of copper oxides, we obtain an exact representation of the Matsubara Green’s function D⊥(k, iωm) of the subsystem of localized spins. This representation includes the Larkin mass operator ΣL(k, iωm) and the strength and polarization operators P(k, iωm) and Π(k, iωm). The calculation in the one-loop approximation of the mass and strength operators for the Heisenberg spin system in the quantum spin-liquid state allows writing the Green’s function D⊥(k, iωm) explicitly and establishing a relation to the result of Shimahara and Takada. An essential point in the developed approach is taking the spin-polaron nature of the Fermi quasiparticles in the spin-fermion model into account in finding the contribution of oxygen holes to the spin response in terms of the polarization operator Π(k, iωm).
A Bianchi type-II dark-energy cosmology with a decaying Λ-term in the Brans–Dicke theory of gravity
Abstract
We present a sequence of anisotropic Bianchi type-II dark-energy models in the framework of the Brans–Dicke theory of gravity with a variable equation of state (EoS) parameter and a constant deceleration parameter. We use power-law relations between the scalar field φ and the scale factor A and between the average Hubble parameter H and the average scale factor A to obtain most of the analytic solutions. The dark-energy EoS parameter ω and its range admitted by the models agrees well with the most recent observational data. It has been observed that the cosmological constant Λ is decreasing with time, which is consistent with recent cosmological observations. We study the dynamical stability and physical features of the models.
p-Adic solid-on-solid model on a Cayley tree
Abstract
We consider a p-adic solid-on-solid (SOS) model with a nearest-neighbor coupling, m+1 spins, and a coupling constant J ∈ Qpon a Cayley tree. We find conditions under which a phase transition does not occur in the model. We show that if p | m + 1 for some J, then a phase transition occurs. Moreover, we formulate a criterion for the boundedness of p-adic Gibbs measures for the (m+1)-state SOS model.
Algebro-geometric solutions of the Dirac hierarchy
Abstract
We introduce a Lenard equation and present two special solutions of it. We use one solution to derive an extended Dirac hierarchy and the other to construct the generating function. The generating function yields conserved integrals of the Dirac Hamiltonian system and defines an algebraic curve. Based on the theory of algebraic curves, we prove that the Dirac Hamiltonian system is integrable and obtain algebro-geometric solutions of the Dirac hierarchy.