No abstract

We show that classical-quantum correspondence of center of mass motion in two coupled deltakicked rotors can be obtained from intrinsic decoherence of the system itself which occurs due to the entanglement of the center of mass motion to the internal degree of freedom without coupling to external environment.Classical-quantum correspondence in a classically chaotic system has been one of the most interesting problem in physics for a long time [1,2]. In quantum mechanics, the time evolution of a wave function follows a linear Schrödinger equation, and so there is no possibility of a sensitivity on the initial condition, a trademark of classical chaos. Also, chaotic diffusion is suppressed by quantum localization [3]. It has been revealed that some crossover time t r = log(I/h)/λ (I is a characteristic action and λ is a Lyapunov exponent) exists so that classical-quantum correspondence breaks down for t > t r [4]. Ash → 0 the crossover time increases indefinitely and classicality is recovered. However, the problem is thath is a nonzero constant and t r is not sufficiently large considering its logarithmic dependence ofh [5].Recently, the relation between decoherence and the classical-quantum correspondence has been investigated extensively [2,[5][6][7][8][9][10][11][12]. Decoherence breaks the purity of initial superposition, which should be conserved in the absence of coupling to the environment, and thus only the partial fraction of whole Hilbert space, namely pointer states, are selected by the environment [6]. The dynamics of the system coupled to the environment shows the unique characteristics of the system independent of the coupling strength as long as it is not too large or small [10]. In other words, with appropriate coupling to environment, the Lyapunov exponent or entropy production rates, which are important physical quantities characterizing a chaotic system, can be reproduced quantum mechanically. However, there has been some debate on whether decoherence from environment is indispensable to obtain the classical-quantum correspondence for classically chaotic systems [5].In this letter, we show that decoherence can occur naturally in composed system even when we ignore the coupling to the outer environment. The initially pure center of mass states become dynamically entangled to the internal degrees of freedom, which effectively acts like the environment. Let us consider a classical object governed by a Hamiltonian H 0 = P 2 /2M + V (X), where M is the mass of the classical object. Since classical objects are composed of many particles, a complete Hamiltonian will be given by, where p i and x i are momenta and coordinates of the constituents, respectively. We assume that the mass of each constituent m i is equal to m. If the force f i = −dV 1 (x i )/dx i is linear, we can ignore the motion of the individual constituent particles to describe the center of mass dynamics of the macroscopic classical object since MẌ= f i = k x i = N kX, where X, N , and k are a position of center of mass, the number of c...

This study identifies the existence of a novel route to chaos from a fixed point, to a limit cycle, to a torus, and then a cascade of period doubling of the torus, which has been predicted theoretically. This route to chaos has been found in the destabilization of a solitonlike structure present in a continuous dissipative medium. ͓S1063-651X͑97͒11803-7͔ PACS number͑s͒: 05.45.ϩb, 02.40.Ϫk, 03.40.Kf, 47.52.ϩj Much effort has been devoted to the understanding of chaotic behavior in dissipative dynamical systems in recent years. One of the questions of great interest lately concerns a transition to chaos through a torus, i.e., a dynamical motion characterized by two incommensurate frequencies. As one way a torus can be destabilized, many researchers have noticed that a torus is destabilized by successive period doubling ͑often referred to as torus doubling͒. Such an investigation has been based on the study of the abstract lowdimensional iterative mappings. The mappings model a discrete flow obtained by the method of Poincaré surface of section, from a continuous flow governed by differential equations.Kaneko ͓1͔ found a torus doubling in the study of threeand four-dimensional dissipative mappings. In the sevenmode study of the Navier-Stokes equations, Franceschini ͓2͔ observed two successive torus doublings, followed by a strange attractor. Arnéodo et al. ͓3͔ also found that a torus may undergo a few doublings before being replaced by a strange attractor in their investigation of three-dimensional dissipative mappings. Significantly, their three-dimensional model could show a cascade of an infinite number of torus doublings in the transition into a strange attractor. This discovery implies that the same dynamic behavior may also exist in real physical systems. Experimentally, the phenomenon of the torus doubling was observed in the RayleighBénard convection ͓4,5͔, in the convection in molten gallium ͓6͔, and in the electrochemical reactions ͓7͔.Up to now, theoretical investigations of torus doubling have been focused on abstract low-dimensional model equations mainly because it is very difficult to find a lowdimensional subspace confining a chaotic attractor for an infinite-dimensional dynamical system. In our investigations of destabilization mechanisms of localized structures in continuous media, we could actually identify the existence of the cascade of torus doubling in a localized structure present in the quintic complex Ginzburg-Landau equation ͓8,9͔:

A variant of the complex Ginzburg-Landau equation is used to investigate the frequency-locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, pi fronts, labyrinths, and 2pi/3 fronts emerge. We show that in spatially extended systems, frequency locking can be enhanced or suppressed by diffusive coupling. Novel patterns such as chaotically bursting domains and target patterns are also observed during the transition to locking.