Vaibhav Madhok - Academia.edu (original) (raw)
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CSIC (Consejo Superior de Investigaciones Científicas-Spanish National Research Council)
Centre National de la Recherche Scientifique / French National Centre for Scientific Research
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Papers by Vaibhav Madhok
Physical Review E, 2015
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively mo... more We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions, the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behaviour of two-qubit discord versus two-qubit entanglement. Our calculations provide the first evidence of signatures of chaos in dynamically generated discord.
ABSTRACT We explain how the long-time average dynamically generated entanglement in a Hamiltonian... more ABSTRACT We explain how the long-time average dynamically generated entanglement in a Hamiltonian bipartite system is related to the corresponding classical dynamics in the semiclassical limit. Where classical dynamics is chaotic, ergodic mixing leads to the generation of ``random quantum states.'' These states possess the typical entanglement of a state randomly sampled from the appropriate Hilbert space under the unitarily invariant Haar measure. We exemplify these results using a system of coupled kicked-tops in which entanglement and chaos arise from the same physical effect in contrast to previous studies. We present quantitive predictions of the dynamically generated entanglement, which is influenced by the time symmetries of the system and the structure of the Hilbert space, under a variety of different conditions, and show a close fit to numerical simulations.
For dissipative dynamical systems described by a system of ordinary differential equations, we ad... more For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE's with quadratic and cubic nonlinearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10 −5 − 10 −4 for d = 3 to essentially one for d ~ 50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos.
Physical Review E, 2015
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively mo... more We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions, the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behaviour of two-qubit discord versus two-qubit entanglement. Our calculations provide the first evidence of signatures of chaos in dynamically generated discord.
ABSTRACT We explain how the long-time average dynamically generated entanglement in a Hamiltonian... more ABSTRACT We explain how the long-time average dynamically generated entanglement in a Hamiltonian bipartite system is related to the corresponding classical dynamics in the semiclassical limit. Where classical dynamics is chaotic, ergodic mixing leads to the generation of ``random quantum states.'' These states possess the typical entanglement of a state randomly sampled from the appropriate Hilbert space under the unitarily invariant Haar measure. We exemplify these results using a system of coupled kicked-tops in which entanglement and chaos arise from the same physical effect in contrast to previous studies. We present quantitive predictions of the dynamically generated entanglement, which is influenced by the time symmetries of the system and the structure of the Hilbert space, under a variety of different conditions, and show a close fit to numerical simulations.
For dissipative dynamical systems described by a system of ordinary differential equations, we ad... more For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE's with quadratic and cubic nonlinearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10 −5 − 10 −4 for d = 3 to essentially one for d ~ 50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos.