Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field $\Gamma$. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.Comment: 7 pages, 4 figure

Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation

We study the real-time dynamics of a quantum Ising chain driven periodically by instantaneous quenches of the transverse field (the transverse field varying as rectangular wave symmetric about zero). Two interesting phenomena are reported and analyzed: (1) We observe dynamical many-body freezing or DMF (Phys. Rev. B, vol. 82, 172402, 2010), i.e. strongly non-monotonic freezing of the response (transverse magnetization) with respect to the driving parameters (pulse width and height) resulting from equivocal freezing behavior of all the many-body modes. The freezing occurs due to coherent suppression of dynamics of the many-body modes. For certain combination of the pulse height and period, maximal freezing (freezing peaks) are observed. For those parameter values, a massive collapse of the entire Floquet spectrum occurs. (2) Secondly, we observe emergence of a distinct solitary oscillation with a single frequency, which can be much lower than the driving frequency. This slow oscillation, involving many high-energy modes, dominates the response remarkably in the limit of long observation time. We identify this slow oscillation as the unique survivor of destructive quantum interference between the many-body modes. The oscillation is found to decay algebraically with time to a constant value. All the key features are demonstrated analytically with numerical evaluations for specific results.Comment: Published version (with minor changes and typo corrections

Optimizing the location of the colony of foragers with Collective Learning

Animal groups collaborate with one another throughout their lives to better comprehend their surroundings. Here, we try to model, using continuous random walks, how the entire process of birth, reproduction, and death might impact the searching process. We attempt to simulate an ecosystem where the post-reproductive foragers leave their colonies to discover where the targets are while others stay and breed at the base. Actually, a group of foragers searches for a location from where they access the targets for food supply. Particularly, we have explored a hypothetical situation in which the relocation to the new position depends on the agreement level of the species as well as an additional waiting time due to this agreement level. In this backdrop, detailed numerical results reveal that searching for an optimal position at an optimal mean time can be captured for a suitable range of the agreement level. We have also shown, for a given agreement level, the optimal mean time linearly increases with the Death-to-Birth ratio.Comment: 9 pages, 6 figure

Crossover of cation partitioning in olivines: a combination of ab initio and Monte Carlo study

We report studies based on a combination of ab initio electronic structure and Monte Carlo (MC) technique on the problem of cation partitioning among inequivalent octahedral sites, M1 and M2 in mixed olivines containing Mg<SUP>2+</SUP> and Fe<SUP>2+</SUP> ions. Our MC scheme uses interactions derived out of ab initio, density functional calculations carried out on measured crystal structure data. Our results show that there is no reversal of the preference of Fe for M1 over M2 as a function of temperature. Our findings do not agree with the experimental findings of Redfern et al. (Phys Chem Miner 27:630-637, 2000), but are in agreement with those of Heinemann et al. (Eur J Mineral 18:673-689, 2006) and Morozov et al. (Eur J Mineral 17:495-500, 2005)

Response of a three-species cyclic ecosystem to a short-lived elevation of death rate

Abstract A balanced ecosystem with coexisting constituent species is often perturbed by different natural events that persist only for a finite duration of time. What becomes important is whether, in the aftermath, the ecosystem recovers its balance or not. Here we study the fate of an ecosystem by monitoring the dynamics of a particular species that encounters a sudden increase in death rate. For exploration of the fate of the species, we use Monte-Carlo simulation on a three-species cyclic rock-paper-scissor model. The density of the affected (by perturbation) species is found to drop exponentially immediately after the pulse is applied. In spite of showing this exponential decay as a short-time behavior, there exists a region in parameter space where this species surprisingly remains as a single survivor, wiping out the other two which had not been directly affected by the perturbation. Numerical simulations using stochastic differential equations of the species give consistency to our results