In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence is defined as the time during which a given site remains unvisited by the walker. We also investigated the behavior of related quantities, e.g., the first-passage time and the succession probability (newly defined), etc. The study reveals power-law scaling behavior of these quantities with new exponents. Comparable features of the classical and the quantum walks are discussed.

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. An earlier work suggested that a walk in an abstract gain-loss space can be conceived for the agents. For models in which agents do not save, or save with uniform saving propensity, the walk has diffusive behavior. For the case in which the saving propensity λ is distributed randomly (0≤λ<1), the resultant walk showed a ballistic nature (except at a particular value of λ*≈0.47). Here we consider several other features of the walk with random λ. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency toward making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

h i g h l i g h t s• We propose a set of conservative wealth exchange models.• Three parameters α, β and γ are introduced to mimic real trading. • Wealth distribution, network properties and activity, etc., have been studied.• Phase transition and other interesting features are presented. • Correspondence to real data is shown for different combinations of α, β and γ . a b s t r a c tWe propose a set of conservative models in which agents exchange wealth with a preference in the choice of interacting agents in different ways. The common feature in all the models is that the temporary values of financial status of agents is a deciding factor for interaction. Other factors which may play important role are past interactions and wealth possessed by individuals. Wealth distribution, network properties and activity are the main quantities which have been studied. Evidence of phase transitions and other interesting features are presented. The results show that certain observations of the real economic system can be reproduced by the models.

We report the calculation of heat capacity of an attractive Bose-Einstein condensate, with the number N of bosons increasing and eventually approaching the critical number N cr for collapse, using the correlated potential harmonics (CPH) method. Boson pairs interact via the realistic van der Waals potential. It is found that the transition temperature T c initially increases slowly, then rapidly as N becomes closer to N cr . The peak value of heat capacity for a fixed N increases slowly with N , for N far away from N cr . But after reaching a maximum, it starts decreasing when N approaches N cr . The effective potential calculated by the CPH method provides insight into this strange behavior.