32,798 research outputs found
New class of practically solvable systems of difference equations of hyperbolic-cotangent-type
The systems of difference equations
where are complex numbers, and the sequences , , are or , 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
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
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
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
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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