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Vaibhav Madhok
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Vaibhav Madhok
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Vaibhav Madhok
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Madhok, Vaibhav
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4 results
Now showing 1 - 4 of 4
- PublicationTypicality in quasispecies evolution in high dimensions(10-10-2019)
;Alfred Ajay Aureate, R.We study quasispecies and closely related evolutionary dynamics like the replicator-mutator equation in high dimensions. In particular, we show that under certain conditions, the average fitness of almost all quasispecies of a given dimension becomes independent of mutational probabilities in high dimensional sequence spaces. This result is a consequence of concentration of measure on a high dimensional hypersphere and its extension to Lipschitz functions known as the Levy's Lemma. Our results naturally extend to other functional capabilities that can be described as Lipschitz functions and whose input parameters are the frequencies of individual constituents of the quasispecies. In order to show this, we give a generalization of Levy's Lemma and discuss possible biological consequences of our work. - PublicationQuantum signatures of chaos, thermalization, and tunneling in the exactly solvable few-body kicked top(19-06-2019)
;Dogra, Shruti; Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to nonintegrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the three- and four-qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons-based experiment realizing the three-qubit case, we find agreement for short times, including a peculiar steplike behavior in correlations of some states. In the case of four qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation. - PublicationQuantum correlations as probes of chaos and ergodicity(01-08-2018)
; ;Dogra, ShrutiLong-time average behavior of quantum correlations in a multi-qubit system, collectively modeled as a kicked top, is addressed here. The behavior of dynamical generation of quantum correlations such as entanglement, discord, concurrence, as previously studied, and Bell correlation function and tangle, as identified in this study, is a function of initially localized coherent states. Their long-time average reproduces coarse-grained classical phase space structures of the kicked top which contrast, often starkly, chaotic and regular regions. Apart from providing numerical evidence of such correspondence in the semiclassical regime of a large number of qubits, we use data from a recent transmons based experiment to explore this in the deep quantum regime of a 3-qubit kicked top. The degree to which quantum correlations can be regarded as a quantum signature of chaos, and in what ways the various correlation measures are similar or distinct are discussed. - PublicationTripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos(06-11-2018)
;Seshadri, Akshay; Many-body states that are invariant under particle relabeling, the permutation symmetric states, occur naturally when the system dynamics is described by symmetric processes or collective spin operators. We derive expressions for the reduced density matrix for arbitrary subsystem decomposition for these states and study properties of permutation symmetric states and their subsystems when the joint system is picked randomly and uniformly. Thus defining an appropriate random matrix ensemble, we find the average linear entropy and von Neumann entropy, which implies that random permutation symmetric states are marginally entangled and as a consequence the tripartite mutual information (TMI) is typically positive, preventing information from being shared globally. Applying these results to the quantum kicked top viewed as a multiqubit system, we find that entanglement, mutual information, and TMI all increase for large subsystems across the Ehrenfest or logarithmic time and saturate at the random state values if there is global chaos. During this time the out-of-time-order correlators evolve exponentially, implying scrambling in phase space. We discuss how positive TMI may coexist with such scrambling.