chaotic wfun Nonlinear Dynamics, Chaos and Quantum Chaos

Quantum kicked rotor :

Periodically kicked particle is the "standard" model of quantum chaos. Since the late 1990s, it has been experimentally realised using cold atoms in optical lattices. In this system, as we tune the nonlinearity parameter, chaos sets in gradually. Quantum mechanically, kicked rotor displays localisation arising from destructive quantum interferences. We study variants of kicked rotor, in particular, kicked rotor in the presence of barriers that lead to non-KAM type classical dynamics. Many interesting phenomena can be realised in this system and in addition it is possible to experimentally realise this in a laboratory.

Chaotic Ratchets :

Ratchets are devices that will allow motion only in one direction even in the absence of any net bias in the potential. Common place examples of macroscopic ratchets are the turnstiles in malls, railway stations etc., pedals in bicycles and self-winding wrist watches. In the human body, many molecules are known to climb up the inclines through ionic pathways and they are examples of ratchet mechanisms at work.

For the last 20 years or so, quite an amount of work has gone in to studying classical, noisy ratchets. They have served as models to understand many features of biological molecules, enzymes that use ratchet mechanism to climb up ionic channels, molecular pathways. How does this happen ? In simple terms, the ratcheting particle extracts work from noise and is able to make its way up the incline, often defying gravity.

If noise can be exploited to do useful work, why not use chaos for the same purpose ? The main idea is to dispense with noise and associated dissipation and use deterministic chaos without dissipation. As the recent results have shown, it is possible to do this, especially in the quantum regime. So, we can produce 'clean' quantum ratchets. This has also been experimentally realised using cold atoms in flashing optical lattices.

We are interested in quantum ratchets of systems that are classically chaotic. Typically, they are the so-called periodically kicked rotors. We are studying various aspects of ratchet phenomena in chaotic, kicked systems.

Quantum chaos in coupled oscillators :

Coupled oscillators in two or larger dimensions are excellent models of chaos with smooth potentials. Think of them as 'simplest harmonic oscillators' that can show chaos. (Ofcourse, harmonic oscillator in any number of dimensions does not display chaos). Many problems like the atoms in strong magnetic fields can be put in the form of coupled oscillators. They display richer classical dynamics; bifurcations, invariant tori, and chaos. Their quantum versions are even more interesting. They display phenomena that range from localisation of eigenstates to quantum tunneling. We study these systems to primarily understand quantum chaos. One of the integral tools for this is the random matrix theory which we apply in good measure.

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