In this paper, we present results of our calculations on the effects of next to nearest neighbor boson hopping ($t^{\prime}$) energy on Bose-Einstein condensation in cubic lattices. We consider both non-interacting and repulsively interacting bosons moving in the lowest Bloch band. The interacting bosons are studied making use of the Bogoliubov method. We find that the bose condensation temperature is enhanced with increasing $t^{\prime}$ for bosons in a simple cubic (sc) lattice and decreases for bosons in body-centered cubic (bcc) and face-centered cubic (fcc) lattices. We also find that interaction induced depletion of the condensate is reduced for bosons in a sc lattice while is enhanced for bosons in bcc and fcc lattices.
We study the Bose--Einstein condensation in a tight-binding model with a hopping rate enhanced only on a surface. We show that this model exhibits two different critical phenomena depending on whether the hopping rate on the surface $t_s$ exceeds the critical value $5t/4$, where $t$ is the hopping rate in the bulk. For $t_s/t<5/4$, normal Bose--Einstein condensation occurs, while the Bose--Einstein condensation for $t_s/t\geq5/4$ is characterized by the spatial localization of the macroscopic number of particles at the surface. By exactly calculating the surface free energy, we show that for $…
We study the one-dimensional nearest neighbor tight binding model of electrons with independently distributed random hopping and no on-site potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to sub-lattice symmetry, for each realization). For non-singular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) \sim 1/|E \ln^3|E||$ and of the localization length $ξ(E) \sim |\ln|E||$, near the band center $E = 0$. (This singular behavior is also applicable to random XY and Heisenberg spin chains; it w…
We study the continuous time quantum walk of a single particle (initially localized at a single site) on a one-dimensional spatial lattice with complex nearest neighbour and next-nearest neighbour hopping amplitudes. Complex couplings lead to chiral propagation and a causal cone structure asymmetric about the origin. We provide a hydrodynamic description for quantum walk dynamics in large space time limit. We find a global "quasi-stationary state" which can be described in terms of the local quasi-particle densities satisfying Euler type of hydrodynamic equation and is characterized by an infi…
We introduce and numerically study the branching annihilating random walks with long-range attraction (BAWL). The long-range attraction makes hopping biased in such a manner that particle's hopping along the direction to the nearest particle has larger transition rate than hopping against the direction. Still, unlike the Lévy flight, a particle only hops to one of its nearest-neighbor sites. The strength of bias takes the form $x^{-σ}$ with non-negative $σ$, where $x$ is the distance to the nearest particle from a particle to hop. By extensive Monte Carlo simulations, we show that the critical…
We study the annihilating random walk with long-range interaction in one dimension. Each particle performs random walks on a one-dimensional ring in such a way that the probability of hopping toward the nearest particle is $W= [1 - ε(x+μ)^{-σ}]/2$ (the probability of moving away from its nearest particle is $1-W$), where $x$ is the distance from the hopping particle to its nearest particle and $ε$, $μ$, and $σ$ are parameters. For positive (negative) $ε$, a particle is effectively repulsed (attracted) by its nearest particle and each hopping is generally biased. On encounter, two particles are…
We consider a sublattice-symmetric free-fermion model on a one-dimensional lattice with random hopping amplitudes decaying with the distance as $|t_l|\sim l^{-α}$, and address the question how far an analogue of the random-singlet state (RSS) conceived originally for describing the ground state of certain random spin chains is valid for this model. For this purpose, we study the effective central charge characterizing the logarithmic divergence of the entanglement entropy (EE) and the prefactor of the distribution of distances between localization centers on the two sublattices, which must ful…
