Decoherence, Quantum To Classical Transition Casused By Few Degrees Of Freedom

We investigate the quantum to classical transition in chaotic systems. The typical character of classical chaos is the exponential deviation of nearby trajectories. Such exponential dependence on initial conditions is not exhibited by quantum dynamics. Due to unitary time evolution, the inner product of two quantum states remains the same as the initial value. This demonstrates that the distance between two initial states is unchanged during quantum evolutions. Such stability of quantum behaviors is very different from classically chaotic dynamics. Decoherence theory gives an reasonable explanation of quantum to classical transition. The unavoidable interaction between system and environment makes entanglement between them. Such entanglement suppresses the quantum coherence of the system, and consequently leads to the quantum to classical transition.We investigate the decoherence caused by an environment consisting of only one degree of freedom. We are interested in the case that the mass of the environment is much smaller than that of the system. Our results show that the influence from a small weightless particle makes the decoherence of the system, even when the classical motion is almost unaffected.We firstly investigate the quantum to classical transition in a system of two coupled kicked rotors. In this system, the mass of the second kicked rotor is smaller than that of the first one by several orders. For large coupling strength, the entanglement between the two rotors rapidly becomes strong with time evolution. This process is accompanied by the disappearance of quantum coherence of the first rotor. The decoherence results in the emergence of classical diffusion from quantum dynamics.We further investigate the case that both the mass m2 of the second rotor and the coupling strengthεchange proportionally with the effective Planck's constant h. With the decrease of h, both the second rotor and the coupling become small, so that the classical diffusion of the first rotor is almost unaffected. In the limit h→0, this small weightless part is strongly entangled with the first rotor. This makes decoherence and the quantum to classical transition of the first rotor.The last system which we investigated consists of two kicked particles in an infinite square wall. They are coupled by repulsive potential. In classical dynamics, as the mass of particle 2 m2 decreases its effect on particle 1 decreases. When the mass of particle 2 is smaller than that of particle 1 by several orders m2<