Related papers: Transfer Matrix Method in Sandpile Models
A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…
We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
The abelian sandpile model is a simple combinatorial model for critical behaviour which has the "abelian property" that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's…
In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of…
Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations…
We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$ and derive its basic properties. We outline a dynamical formulation of the time-independent scattering theory for this…
A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have…
We diagonalize the double-row transfer matrix of the SU(N) vertex model for certain classes of non-diagonal boundary conditions. We derive explicit expressions for the corresponding eigenvectors and eigenvalues by means of the algebraic…
The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the…
Transfer learning can significantly improve the sample efficiency of neural networks, by exploiting the relatedness between a data-scarce target task and a data-abundant source task. Despite years of successful applications, transfer…
The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…
We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
By using the Transfer Matrix Method, explicit formulas for the embedding distribution of doubly hexagonal chain graphs are computed.
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…