Coupled pair approach for strongly-interacting trapped fermionic atoms

We present a coupled pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of $N$ particles. A stochastically variational gaussian expansion method is applied, focusing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The groundstate energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations.Comment: 7 pages, 4 figure

Universality in rotating strongly interacting gases

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal, however the entropy changes as a function of the rotation or synthetic magnetic field strength.Comment: 4 pages, 2 figure

Universality and itinerant ferromagnetism in rotating strongly interacting Fermi gases

We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Thermodynamic quantities such as the entropy and energy are calculated from the third order quantum virial expansion. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems.Comment: 5 pages with 3 figure

Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks

In order to study the competition of pulling a long chain polymer with its other system properties models of lattice polymers accomodate an applied pulling force to some part of a lattice polymer in addition to features such as energetic interaction between the lattice polymer and a surface. However, the critical behaviour of the pulling force alone is less well studied, such as characterizing the nature of the phase transition and particularly the values of the associated exponents. We investigate a simple model of lattice polymers subject to forced extension, namely self-avoiding walks (SAWs) on the square and simple cubic lattices with one endpoint attached to an impermeable surface and a force applied to the other endpoint acting perpendicular to the surface. In the thermodynamic limit the system undergoes a transition to a ballistic phase as the force is varied and it is known that this transition occurs whenever the magnitude of the force is positive, i.e. $f>f_\text{c}=0$. Using well established scaling arguments we show that the crossover exponent $\phi$ for the finite-size model is identical to the well-known exponent $\nu_d$, which controls the scaling of the size of the polymer in $d$-dimensions. With extensive Monte Carlo simulations we test this conjecture and show that the value of $\phi$ is indeed consistent with the known values of $\nu_2 = 3/4$ and $\nu_3 = 0.587 597(7)$. Scaling arguments, in turn, imply the specific heat exponent $\alpha$ is $2/3$ in two dimensions and $0.29815(2)$ in three dimensions.Comment: 11 pages, 4 figure