Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems, investigated recently, entails an universal distribution of the eigenvalues of the reduced density matrices. We demonstrate that these distributions are realized in quantized chaotic systems by using a model of two coupled and kicked tops. We derive an explicit statistical universal bound on entanglement, that is also valid for the case of unequal dimensionality of the Hilbert spaces involved, and show that this describes well the bounds observed using composite quantized chaotic systems such as coupled tops.PACS numbers : 03.65. Ud, 05.45.Mt Recently, entanglement has been discussed extensively due to its crucial role in quantum computation and quantum information theory [1]. Since a quantum computer is a many particle system, entanglement is inevitable and even desirable. Entanglement is important both at the hardware and software levels of a quantum computer, as the efficiency of all proposed quantum algorithms are based on it, hence its characterization as a quantum resource. The many particle nature of a quantum computer brings another phenomenon to the fore, that is chaos. Some studies have enquired whether chaos will help or hinder in the operation of a quantum computer [2]. At a more basic level several studies have explored the connections between quantum entanglement and classical chaos [3][4][5], two phenomena that are prima facie uniquely quantum and classical respectively. Such a connection between entanglement and chaos has been previously studied with the example of an N -atom Jaynes-Cummings model [3]. It was found that the entanglement rate is considerably enhanced if the initial wave packet was placed in a chaotic region. In another work of similar kind, the authors have related such rates to classical Lyapunov exponents with the help of a coupled kicked top model [4]. Recently, one of us studied entanglement in coupled standard maps [5] and found that entanglement increased with coupling strength, but after a certain magnitude of coupling strength corresponding to the emergence of complete classical chaos, the entanglement saturated. The saturation value depended on the Hilbert space dimensions and was less than its maximum possible value. This result implies that though there exists a maximum kinematical limit for entanglement, dynamically it is not possible to create it by using generic Hamiltonian evolutions on unentangled states. It should be emphasized that such bounds are statistical and are more unlikely to be violated the larger the Hilbert space dimension.Recent related work [6] calculates the mean entanglement of pure states for the case M = N by using a RMT model that allows specification of the joint probability distribution of the eigenvalues of the reduced density matrices (RDM). Below we calculate the entanglement from a eigenvalue distribution t...

Entanglement production in coupled chaotic systems is studied with the help of kicked tops. Deriving the correct classical map, we have used the reduced Husimi function, the Husimi function of the reduced density matrix, to visualize the possible behaviors of a wave packet. We have studied a phase-space based measure of the complexity of a state and used random matrix theory (RMT) to model the strongly chaotic cases. Extensive numerical studies have been done for the entanglement production in coupled kicked tops corresponding to different underlying classical dynamics and different coupling strengths. An approximate formula, based on RMT, is derived for the entanglement production in coupled strongly chaotic systems. This formula, applicable for arbitrary coupling strengths and also valid for long time, complements and extends significantly recent perturbation theories for strongly chaotic weakly coupled systems.

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks, namely, random, scale-free, and small-world networks. These distributions follow the Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenvalues we study spectral rigidity via the Delta_{3} statistic of RMT as well. It follows RMT prediction of linear behavior in semilogarithmic scale with the slope being approximately 1pi;{2} . Random and scale-free networks follow RMT prediction for very large scale. A small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.

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Migratory birds and other species have the ability to navigate by sensing the geomagnetic field. Recent experiments indicate that the essential process in the navigation takes place in bird's eye and uses chemical reaction involving molecular ions with unpaired electron spins (radical pair). Sensing is achieved via geomagnetic-dependent dynamics of the spins of the unpaired electrons. Here we utilize the results of two behavioral experiments conducted on European Robins to argue that the average life-time of the radical pair is of the order of a microsecond and therefore agrees with experimental estimations of this parameter for cryptochrome -a pigment believed to form the radical pairs. We also found a reasonable parameter regime where sensitivity of the avian compass is enhanced by environmental noise, showing that long coherence time is not required for navigation and may even spoil it.PACS numbers: 03.65.Yz, Recently there has been a growing interest in the application of quantum mechanics to understand many biological phenomena such as photosynthesis [1][2][3][4][5][6][7], process of olfaction [8,9], enzymatic reactions [10,11] or avian magnetoreception [12][13][14][15]. These interests have brought physicists, chemists, and biologists at the same platform and led to the beginning of a new interdisciplinary subject called quantum biology [16,17]. A major motivation of these studies is to understand how nature utilizes purely quantum phenomena to optimize various biological processes.Here we are specifically interested in the avian magnetoreception. It is very plausible that the navigation ability of some migratory birds is governed by the mechanism based on geomagnetic-dependent dynamics of spins of unpaired electrons in a radical pair. A recent theoretical study has estimated both the life-time of the pair and the coherence time of this dynamics to be of the order of tens of microsecond [15]. The basic criterion used there postulates that bird's navigation is disturbed if the signal produced by the dynamics is independent of the orientation of the geomagnetic field. This criterion together with the results of behavioral experiments in which European Robins could not navigate in a weak oscillating magnetic field [18,19] led to the estimated life time and coherence time. Here we additionally take into account the results of other behavioral experiments in which the same species were observed to be temporarily disoriented in a constant magnetic field sufficiently stronger or weaker than the geomagnetic field [20,21]. We estimate the life time and coherence time of the order of several microseconds. Our estimate is consistent with that obtained in a recent behavioral experiment [13] and also with the in vitro experiment using cryptochrome [22], a pigment believed to form the radical pairs. Furthermore, we demonstrate theoretically that environmental noise can enhance * jnbandyo@gmail.com the sensitivity of the avian compass, i.e. sensitivity in the presence of noise is better than without noise. This increase ...

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scalefree, small-world and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Secondly we show an analogy between the onset of small-world behavior, quantified by the structural properties of networks, and the transition from Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody parameter characterizing a spectral property. We also present our analysis for a protein-protein interaction network in budding yeast.

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f −γ noise and γ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.PACS numbers: 05.45. Mt, 05.45.Pq, 05.40.Ca Quantum chaos, the study of quantum analogues of classically chaotic systems, is characterized by the fluctuation properties of the spectrum of its Hamiltonian operator. For quantum systems with regular classical dynamics the spectral fluctuations are Poisson distributed [1], i.e, the eigenvalues tend to cluster together. On the other hand, one of the remarkable results established by Bohigas et al is that the level fluctuation properties of quantum systems, whose classical limit is chaotic, are identical to those of an appropriate ensemble from random matrix theory (RMT) [2]. This is the level repulsion regime where the eigenvalues tend to repel one another. In this sense, characterizing quantum chaos in terms of presence or absence of level repulsion requires invoking the spectral properties of random matrix ensembles. Recently, in analogy with time series, a method has been proposed to characterize spectral fluctuations using inherent properties of the spectrum [3]. If the eigenvalues of Hamiltonian operators could be thought of as a time series and its index the time in some units, then the methods of traditional time series analysis can be applied to it. It was shown that the ensemble averaged power spectrum S(f ) of the fluctuations in the cumulative level density, goes as 1/f or 1/f 2 depending on whether the system is classically chaotic or regular [4]. This work also showed examples of atomic level sequences displaying 1/f noise. Thus, atomic levels join the host of other systems and phenomena that display 1/f noise lending strength to the well known cliché that 1/f noise is ubiquitous in nature [5].In this paper, we study the transition from regularity to chaos in the mixed systems. In such systems the regular and chaotic motion coexist and this is a generic feature. For instance, the entire class of atoms in strong fields and the range of problems involving atoms in timevarying fields belong to this class. We study a smooth Hamiltonian system, the quartic oscillator and a time dependent system, the kicked top. In both these systems, a single parameter that controls the classical chaos can be varied to get a smooth transition from regular to predominantly chaotic dynamics. It is well known that the level fluctuations in these systems can be modelled by RMT [2]. From an RMT point of view, these models possess symmetries (...

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