Broken symmetries and directed collective energy transport in spatially extended systems

We study the appearance of directed energy current in homogeneous spatially extended systems coupled to a heat bath in the presence of an external ac field E(t). The systems are described by nonlinear field equations. By making use of a symmetry analysis, we predict the right choice of E(t) and obtain directed energy transport for systems with a nonzero topological charge Q. We demonstrate that the symmetry properties of motion of topological solitons (kinks and antikinks) are equivalent to the ones for the energy current. Numerical simulations confirm the predictions of the symmetry analysis and, moreover, show that the directed energy current drastically increases as the dissipation parameter alpha reduces.     

The explicit symmetry breaking solutions of the Kadomtsev-Petviashvili equation

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.     

Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation

By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation.     

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explain earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.     

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.     

Confinement from spontaneous breaking of scale symmetry

We show that one can obtain naturally the confinement of static charges from the spontaneous symmetry breaking of scale invariance in a gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge invariant but path-dependent variables formalism, the Cornell confining potential is explicitly obtained. Our procedure answers completely to the requirements by 't Hooft for “perturbative confinement”.     

Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations

In this Letter, the formation of complex oscillations of the type 2n M oscillations per period at the Mth superharmonic excitation is reported for electrostatic microelectromechanical systems. A dc bias (beyond "dc symmetry breaking") and an ac signal (at the Mth superharmonic frequency) with an amplitude around "ac symmetry breaking" gives rise to M oscillations per period or period M response. On increasing the ac voltage, a cascade of period doubling bifurcations take place giving rise to 2n M oscillations per period. An interesting chaotic transition (1-band and 2-band chaos) is observed during the first period doubling bifurcation. The nonlinear nature of the electrostatic force is shown to be responsible for the reported observations.     

Theory of retardation of magnetic domain walls in rhombic magnetic materials

We calculate the retardation of a magnetic soliton describing a magnetic domain wall by using the generalized phenomenological theory of relaxation. We show that in this theory, based on the real dynamical symmetry of magnetic materials, the dissipation function has a different structure for high and low wall velocities. Finally, we calculate the viscous force of the wall in the Walker model and show that certain features, not discussed in the literature, emerge even when the generalized theory is applied to this simple model. In particular, the dependence of the viscous friction force on the wall velocity may be highly nonlinear and regions of unstable motion may appear. Zh. éksp. Teor. Fiz. 111, 158–173 (January 1997)     

Internal mode dynamics in driven nonlinear Klein-Gordon systems

We study analytically and numerically the action of a constant force on the propagation of kinks in the φ⁴ and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution. Finally, we show that for the φ⁴ system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical simulations. Received 6 June 2000     

Lie Symmetry and Nonlinear Instability in Computation of KdV Solitons

The soliton calculation method put forward by Zabusky and Kruskal has played an important role in the development of soliton theory, however numerous numerical results show that even though the parameters satisfy the linear stability condition, nonlinear instability will also occur. We notice an exception in the numerical calculation of soliton, gain the linear stability condition of the second order Leap-frog scheme constructed by Zabusky and Kruskal, and then draw the perturbed equation with the finite difference method. Also, we solve the symmetry group of the KdV equation with the knowledge of the invariance of Lie symmetry group and then discuss whether the perturbed equation and the conservation law keep the corresponding symmetry. The conservation law of KdV equation satisfies the scaling transformation, while the perturbed equation does not satisfy the Galilean invariance condition and the scaling invariance condition. It is demonstrated that the numerical simulation destroy some physical characteristics of the original KdV equation. The nonlinear instability in the calculation of solitons is related to the breaking of symmetry.     

On Fermion Grading Symmetry for Quasi-Local Systems

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every complementary outside system of a local region specified by the given quasi-local structure. Under a completely model independent setting, we show the absence of SSB for fermion grading symmetry in the above sense. We obtain some structural results for equilibrium states of lattice systems. If there would exist an even KMS state for some even dynamics that is decomposed into noneven KMS states, then those noneven states inevitably violate our local thermal stability condition.     

Quantum and statistical fluctuations in dynamical symmetry breaking

Dynamical symmetry breaking in an expanding nuclear system is investigated in a semi-classical and quantum framework by employing a collective transport model which is constructed to mimic the collective behavior of expanding systems. It is shown that the fluctuations in collective coordinates during the expansion are developed mainly by the enhancement of the initial fluctuations by the driving force, and that statistical and quantum fluctuations have similar consequences. It is pointed out that the quantal fluctuations may play an important role in the development of instabilities by reducing the time needed to break the symmetry, and the possible role of quantal fluctuations in spinodal decomposition of nuclei is discussed.     

Symmetry breaking in honeycomb photonic lattices

We study the phenomena associated with symmetry breaking in honeycomb photonic lattices. As the honeycomb structure is gradually deformed, conical diffraction around its diabolic points becomes elliptic and eventually no longer occurs. As the deformation is further increased, a gap opens between the first two bands, and the lattice can support a gap soliton. The existence of the gap soliton serves as a means to detect the symmetry breaking and provide an estimate of the size of the gap.     

Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation

The (2 1)-dimensional nonlinear barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a beta-plane channel is investigated by using the classical Lie symmetry approach. Some types of group-invariant wave solutions are expressed by means of the lower-dimensional similarity reduction equations. In addition to the known periodic Rossby wave solutions, some new types of exact solutions such as the ring solitary waves and the breaking soliton type of vorticity solutions with nonlinear and nonconstant shears are also obtained.     

Lie Symmetries,Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations

Abstract

The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik – Novikov – Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation, the (2+1)-dimensional generalization of the nonlinear Schrödinger equation by Fokas as well as the (2+1)-dimensional generalized sine-Gordon equation of Konopelchenko and Rogers. We show that in all these cases the Lie symmetry algebra is infinite-dimensional; however, in the case of the breaking soliton equation they do not possess a centerless Virasorotype subalgebra as in the case of other typical integrable (2+1)-dimensional evolution equations. We work out the similarity variables and special similarity reductions and investigate them.     

Dissipative squeezed vacuum in non-equilibrium thermo field dynamics

Degenerate parametric amplification accompanied by dissipation is analyzed within the canonical operator formalism for quantum dissipative systems named non-equilibrium thermo field dynamics. The vacuum of the system is subject to both dissipation and breaking of phase symmetry due to squeezing. The annihilation-creation operators for the vacuum are derived and the structure of the vacuum is examined. The effects of dissipation on squeezing and uncertainty relation are estimated.     

An intrinsic limit to quantum coherence due to spontaneous symmetry breaking

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is t(spon) approximately = 2piNH/(kBT), given in terms of the number of microscopic degrees of freedom N, temperature T, and the constants of Planck (h) and Boltzmann (kB).     

ac Magnetization transport and power absorption in nonitinerant spin chains

We investigate the ac transport of magnetization in nonitinerant quantum systems such as spin chains described by the XXZ Hamiltonian. Using linear response theory, we calculate the ac magnetization current and the power absorption of such magnetic systems. Remarkably, the difference in the exchange interaction of the spin chain itself and the bulk magnets (i.e., the magnetization reservoirs), to which the spin chain is coupled, strongly influences the absorbed power of the system. This feature can be used in future spintronic devices to control power dissipation. Our analysis allows us to make quantitative predictions about the power absorption, and we show that magnetic systems are superior to their electronic counterparts.     

Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation

The (2 1)-dimensional nonlinear barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a beta-plane channel is investigated by using the classical Lie symmetry approach. Some types of group-invariant wave solutions are expressed by means of the lower-dimensional similarity reduction equations. In addition to the known periodic Rossby wave solutions, some new types of exact solutions such as the ring solitary waves and the breaking soliton type of vorticity solutions with nonlinear and nonconstant shears are also obtained.