Biomedical subjects

Dima L Shepelyansky

Publications and source records attributed to Dima L Shepelyansky.

3 recordsLinked to original sources

PubMed2005

Dissipative quantum chaos: transition from wave packet collapse to explosion.

Using the quantum trajectories approach, we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which follows classical chaotic dynamics and whose area is proportional to the Planck constant. At weak dissipation the exponential instability of quantum dynamics on the Ehrenfest time scale dominates and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically disappears leaving place to collapse.

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PubMed2005

Quantum chaos algorithms and dissipative decoherence with quantum trajectories.

Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, the quantum ergodic regime, and quasi-integrable motion. As an example we use the quantum sawtooth algorithm which can be implemented in a polynomial number of quantum gates. It is shown that the fidelity of quantum computation decays exponentially with time and that the decay rate is proportional to the number of qubits, number of quantum gates, and per gate dissipation rate induced by external decoherence. In the limit of strong dissipation the quantum algorithm generates a quantum attractor which may have a complex or simple structure. We also compare the effects of dissipative decoherence with the effects of static imperfections.

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PubMed2005

Quantum ratchets in dissipative chaotic systems.

Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.

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