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In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…
Flory-Huggins theory is a mean field theory for modelling the free energy of dense polymer solutions and polymer melts. In this paper we use Flory-Huggins theory as a model of a dense two dimensional self-avoiding walk confined to a square…
We analyze the dynamics of multiparticle discrete-time quantum walk on the two-dimensional lattice, with an interaction inspired on a classical model for gas collision, called HPP model. In this classical model, the direction of motion…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
Long linear polymers in dilute solutions are known to undergo a collapse transition from a random coil (expand itself) to a compact ball (fold itself up) when the temperature is lowered, or the solvent quality deteriorates. A natural model…
We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on the square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases…
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…
We find, and analyse, the exact solution of two friendly directed walks, modelling polymers, which interact with a wall via contact interactions. We specifically consider two walks that begin and end together so as to imitate a polygon. We…
We study by computer simulation a recently introduced generalised model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely crossings where the…
Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…
We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for…
In this work, we present a nonlinear dynamics perspective on generating and connecting gaits for energetically conservative models of legged systems. In particular, we show that the set of conservative gaits constitutes a connected space of…
It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of…
The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for…
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle…
In this paper we study cosmological application of interacting holographic dark energy density in the scalar-Gauss-Bonnet framework. We employ the interacting holographic model of dark energy to obtain the equation of state for the…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…