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We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretising continuous-spin models, and show that, except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.
We show that the Schrodinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schrodinger operators. Some striking numerical results are included at the end of the article.
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main theorem, whi
In this paper we study a one-dimensional space-discrete transport equation subject to additive Levy forcing. The explicit form of the solutions allows their analytic study. In particular we discuss the invariance of the covariance structure of the st
The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The honeycomb point sets are constructed by subtracting the root lattice from the weight lattice points of the crystallographic root system $A_
The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrodinger equation of the spin system model is so