32,798 research outputs found

    New class of practically solvable systems of difference equations of hyperbolic-cotangent-type

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    The systems of difference equations xn+1=unvn2+aun+vn2,yn+1=wnsn2+awn+sn2,nN0,x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0, where a,u0,w0,vj,sja, u_0, w_0, v_j, s_j j=2,1,0,j=-2,-1,0, are complex numbers, and the sequences unu_n, vn,v_n, wnw_n, sns_n are xnx_n or yny_n, are studied. It is shown that each of these sixteen systems is practically solvable, complementing some recent results on solvability of related systems of difference equations

    Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

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    We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.Comment: 15 pages, standard LaTe

    Analytic calculation of nonadiabatic transition probabilities from monodromy of differential equations

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    The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2x2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. The application of this method to multi-level systems is also discussed.Comment: 13 pages, 2 figure

    Quasi-Exact Solvability in Local Field Theory. First Steps

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    The quantum mechanical concept of quasi-exact solvability is based on the idea of partial algebraizability of spectral problem. This concept is not directly extendable to the systems with infinite number of degrees of freedom. For such systems a new concept based on the partial Bethe Ansatz solvability is proposed. In present paper we demonstrate the constructivity of this concept and formulate a simple method for building quasi-exactly solvable field theoretical models on a one-dimensional lattice. The method automatically leads to local models described by hermitian hamiltonians.Comment: LaTeX, 11 page

    Commensurate-Incommensurate Phase Transitions for Multichain Quantum Spin Models: Exact Results

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    The behavior in an external magnetic field is studied for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent. A scenario for the transition from one to two space dimensions for the integrable multichain models is proposed. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The exponents for the gaps caused by relevant perturbations of the models are calculated.Comment: 23 pages, LaTeX, typos correcte
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