Dynamics of observables in a q-deformed harmonic oscillator

@article{Pradeep2020DynamicsOO,
  title={Dynamics of observables in a q-deformed harmonic oscillator},
  author={Aditi Pradeep and S. Anupama and C. Sudheesh},
  journal={The European Physical Journal D},
  year={2020},
  volume={74},
  pages={1-8}
}
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic quantum systems based on expectation values of dynamical variables has not been reported in the literature. In this paper, we extend the study of dynamical behaviour using expectation values of variables to a q-deformed harmonic oscillator. The system is found to… 
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References

SHOWING 1-10 OF 54 REFERENCES

Random matrix theory in semiclassical quantum mechanics of chaotic systems

The statistical properties of the spectrum of systems which have a chaotic classical limit have been found to be similar to those of random matrix ensembles. The author explains this correspondence,

Recurrence statistics of observables in quantum-mechanical wave packet dynamics

We investigate the recurrence properties of the time series of quantum-mechanical expectation values, in terms of representative models for a single-mode radiation field interacting with a nonlinear

Characteristics of power spectra for regular and chaotic systems

Power spectra for chaotic and quasiperiodic systems are analyzed in detail. Differences in convergence with increasing T are carefully examined and a number of important results are emphasized.

Stochastic behavior in classical and quantum hamiltonian systems : Volta Memorial Conference, Como, 1977

Integrable and stochastic behaviour in dynamical astronomy.- Adiabatic and stochastic motion of charged particles in the field of a single wave.- Numerical study of particle motion in two waves.-

Semiclassical theory of short periodic orbits in quantum chaos

We have developed a semiclassical theory of short periodic orbits to obtain all the quantum information of a bounded chaotic Hamiltonian system. If T1 is the period of the shortest periodic orbit, T2

Dynamics of an open quantum system interacting with a quantum environment

We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a

The q-deformed harmonic oscillator, coherent states, and the uncertainty relation

For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as

Dynamics of a Q-analogue of the Quantum Harmonic Oscillator

Abstract We analyse the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the q-analogue of the coherent state. Non-trivial behaviour of the mean values of the q-position
...