Recent Directions in Quantum Chaos
The traditional topics in quantum chaos concerns spectral statistics (universal and non-universal features), and the study of eigenfunctions (Quantum ergodicity, scars) of various chaotic Hamiltonian .
Further studies concern the parametric dependence of the Hamiltonian, as reflected in e.g. the statistics of avoided crossings, and the associated mixing as reflected in the (parametric) local density of states (LDOS). There is vast literature on wavepacket dynamics, including the study of fluctuations, recurrences, quantum irreversibility issues etc. Special place is reserved to the study of the dynamics of quantized maps: The Standard map and The Kicked Rotator are considered to be prototype problems.
Recent works are also focused in the study of driven chaotic systems, where the Hamiltonian is time dependent, in particular in the adiabatic and in the linear response regimes.
Read more about this topic: Quantum Chaos
Famous quotes containing the words directions, quantum and/or chaos:
““Have we any control over being born?,” my friend asked in despair. “No, the job is done for us while we’re sleeping, so to speak, and when we wake up everything is all set. We merely appear, like an ornate celebrity wheeled out in a wheelchair.” “I don’t remember,” my friend claimed. “No need to,” I said: “what need have us free-loaders for any special alertness? We’re done for.””
—Marvin Cohen, U.S. author and humorist. The Self-Devoted Friend, New Directions (1967)
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“I say to you: we must still have chaos within us to be able to give birth to a dancing star. I say to you: you still have chaos within you.”
—Friedrich Nietzsche (1844–1900)