Inverse Problems in Boson Systems

Victor Gurarie

We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave model solved by the inverse scattering method thirty years ago. Its solution describes one or two branches of dressed chiral right moving molecules depending on the chemical potential (particle density). We also briefly discuss the possibility of experimental realization of such a system.

Masao Hirokawa

In this paper, we treat a quantum harmonic oscillator in thermal equilibrium with any systems in certain classes of bosons with infinitely many degrees of freedom. We describe the following results: (i) when a canonical correlation function is given, we so reconstmct a Hamiltonian by the rotating wave approximation from it that the Hamiltonian restores it. Namely, we solve an inverse problem in the quantum field theory at finite temperature in a finite volume. (ii) Taking an infinite volume limit for the result in (i), we consider long-time behavior of the canonical correlation function in the finite volume limit.

Richard David Etters

Richard David Etters

Yuhai Tu, Peter B. Weichman

We construct large-$n$ (spherical) limits for a series of interesting quantum phase transitions in disordered systems, including quantum ferromagnets and spin glasses, superconducting thin films with and without an external magnetic field, the dirty boson problem, the fractional quantum Hall effect, and Nelson's model of flux lines in high-temperature superconductors. The spherical limit always produces a random matrix inversion problem with self-consistency conditions, which then must be solved numerically. We present preliminary results for the dirty boson problem in two spatial dimensions.