相关论文: The Quantum Emergence of Chaos
Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two…
Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic…
Quantum systems interacting with their environments can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. Yet, despite many attempts, the toolbox for quantifying dissipative…
The vast majority of dynamical systems in classical physics are chaotic and exhibit the butterfly effect: a minute change in initial conditions can soon have exponentially large effects elsewhere. But this phenomenon is difficult to…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincar\'{e} sections and compute Lyapunov…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics,…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…
Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…