33 research outputs found
Effective field theory of interactions on the lattice
We consider renormalization of effective field theory interactions by
discretizing the continuum on a tight-binding lattice. After studying the
one-dimensional problem, we address s-wave collisions in three dimensions and
relate the bare lattice coupling constants to the continuum coupling constants.
Our method constitutes a very simple avenue for the systematic renormalization
in effective field theory, and is especially useful as the number of
interaction parameters increases.Comment: 7 pages, 0 figure
Emergence of junction dynamics in a strongly interacting Bose mixture
We study the dynamics of a one-dimensional system composed of a bosonic
background and one impurity in single- and double-well trapping geometries. In
the limit of strong interactions, this system can be modeled by a spin chain
where the exchange coefficients are determined by the geometry of the trap. We
observe non-trivial dynamics when the repulsion between the impurity and the
background is dominant. In this regime, the system exhibits oscillations that
resemble the dynamics of a Josephson junction. Furthermore, the double-well
geometry allows for an enhancement in the tunneling as compared to the
single-well case.Comment: 20 pages, 9 figure
Dynamical realization of magnetic states in a strongly interacting Bose mixture
We describe the dynamical preparation of magnetic states in a strongly
interacting two-component Bose gas in a harmonic trap. By mapping this system
to an effective spin chain model, we obtain the dynamical spin densities and
the fidelities for a few-body system. We show that the spatial profiles transit
between ferromagnetic and antiferromagnetic states as the intraspecies
interaction parameter is slowly increased.Comment: 6 pages, 7 figure
Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
The paper examines a trapped one-dimensional system of multicomponent
spinless fermions that interact with a zero-range two-body potential. We show
that when the repulsion between particles is very large the system can be
approached analytically. To illustrate this analytical approach we consider a
simple system of three distinguishable particles, which can be addressed
experimentally. For this system we show that for infinite repulsion the energy
spectrum is sixfold degenerate. We also show that this degeneracy is partially
lifted for finitely large repulsion for which we find and describe
corresponding wave functions.Comment: Paper in connection with the 22nd European Conference on Few-Body
Problems in Physics, Krakow, Poland, 9-13 September 201
A Solvable Model for Decoupling of Interacting Clusters
We consider M clusters of interacting particles, whose in-group interactions
are arbitrary, and inter-group interactions are approximated by oscillator
potentials. We show that there are masses and frequencies that decouple the
in-group and inter-group degrees of freedom, which reduces the initial problem
to M independent problems that describe each of the relative in-group systems.
The dynamics of the M center-of-mass coordinates is described by the
analytically solvable problem of M coupled harmonic oscillators. This paper
derives and discusses these decoupling conditions. Furthermore, to illustrate
our findings, we consider a charged impurity interacting with a ring of ions.
We argue that the impurity can be used to probe the center-of-mass dynamics of
the ions.Comment: Version accepted for publication in EP