429 research outputs found

    Derivation of theories: structures of the derived system in terms of those of the original system in classical mechanics

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    We present the technique of derivation of a theory to obtain an (n+1)f(n+1)f-degrees-of-freedom theory from an ff-degrees-of-freedom theory and show that one can calculate all of the quantities of the derived theory from those of the original one. Specifically, we show that one can use this technique to construct, from an integrable system, other integrable systems with more degrees of freedom.Comment: LaTex, 10 page

    Models solvable through the empty-interval method

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    The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is shown that turning on the reactions which generate particles from two adjacent empty sites, results in a gap in the spectrum of the evolution operator (or equivalently a finite relaxation time).Comment: 8 page

    Exactly solvable reaction diffusion models on a Cayley tree

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    The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.Comment: 9 pages, 2 figure

    Autonomous models solvable through the full interval method

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    The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating function method, the general solution for, FnF_n, the probability that nn consecutive sites be full, is obtained. Some other correlation functions of number operators at nonadjacent sites are also explicitly obtained. It is shown that for a special choice of initial conditions some correlation functions of number operators called full intervals remain uncorrelated

    A pseudo-conformal representation of the Virasoro algebra

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    Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary- or logarithmic-conformal field theories. This representation is parametrized by two matrices. We classify these two matrices, and calculate some of the correlators for a simple example.Comment: LaTex, 5 page

    Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions

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    Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ena(t)E^{\mathbf a}_n(t)'s, the expectation value of the product of certain linear combination of the number operators on nn consecutive sites at time tt.Comment: 10 pages, LaTe

    The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)

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    We introduce a universal R matrix for the Jordanian deformation of \U{ \sl(2)}. Using \Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2)), we obtain the universal R matrix for \Uh{\so(4)}. Applying the graded contractions on the universal R matrix of \Uh{\so(4)}, we show that there exist three distinct R matrices for all of the contracted algebras. It is shown that \Uh{\sl(2)}, \Uh{\so(4)}, and all of these contracted algebras are triangular.Comment: LaTeX, 8 page

    Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants

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    An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method, it is shown that there are cases where the system exhibits a dynamical phase transition. There may be two phases, the fast phase and the slow phase. For some region of the parameter space, the relaxation time is independent of the reaction rates at the boundaries. Changing continuously the reaction rates at the boundaries, however, there is a point where the relaxation times begins changing, as a continuous (nonconstant) function of the reaction rates at the boundaries, so that at this point there is a jump in the derivative of the relaxation time with respect to the reaction rates at the boundaries.Comment: 17 page
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