Exact parastatistics are developed which describe the occupation of a one-dimensional lattice space by any arbitrary distribution of particles {gλ}, (λ=1,2,3,…,), where λ is the particle correlation distance, i.e., the number of contiguous lattice sites occupied by a particle.
Continuous measurements simultaneously reveal and modify the dynamics of a quantum system. In this work we consider the tunneling motion of particles between the sites of a one-dimensional lattice. We investigate how weak continuous probing of the occupation of a single lattice site induces entanglement and selects definite values for system properties such as wave function parity and permutation symmetry. Our simulations show how continuous measurement can steer systems of two and three particles, with no prior permutation symmetry, into stable bosonic, fermionic and parastatistical symmetry sectors.
We consider an extended one-dimensional Hubbard model in which the magnitude of the hopping between two sites for particles with given spin depends on the occupation of the states with opposite spin at both sites. Diagonalizing exactly finite-size chains, and using known results of conformal field theory we delimit the regions of parameters for which two particles bind and the pair superconducting correlation functions are the dominant ones at large distances. For Coulomb repulsion U smaller than a critical density-dependent value Uc and any density, there are ranges of the ratios of the hopping parameters for which the superconducting fluctuations dominate. At half filling, for parameters within this range, a transition from a regime with dominant superconducting correlations to an insulating state takes place as a function of U. We also study the model for parameters near a recently found exactly solvable limit in which the number of doubly occupied sites is conserved.
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.