One-Dimensional Many-Fermion System. I: Exact Solution in a Field Theoretical Framework

Exact solution of a one-dimensional fermion model with interchain tunneling.

A fermion model consisting of two chains with interchain tunneling is formulated and solved exactly by the Bethe ansatz method. The interchain tunneling leads to Cooper pair like bound states and a threshold energy is required to overcome the binding energy. The correlation functions manifest superconducting properties.

Theoretical framework for quasi-one dimensional systems.

Exact solution of a one-dimensional deterministic sandpile model.

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary N , where N is the size of a single toppling. The oneand two-point functions are given in term of the eigenvalues of an N × N transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also presen...

Exact Solution of a Three-Dimensional Dimer System

We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional ...

An Exact Cosmological Solution of the Coupled Einstein-Majorana Fermion-Scalar Field Equations

We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.