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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: In this article, a Hamiltonian model with two-photon interaction with a two-level atom and a degenerate parametric amplifier is considered, and an exact solution of the wave function in the Schrodinger picture is obtained.
47 citations
TL;DR: In this paper, the authors define a space having a canonical symplectic structure where they appear as conjugate variables and the associated intensive variables γ i, the partial derivatives of the entropy S = Sq1,..., qn ≡q0, in the form γi = - pi/p0 where p0 behaves as a gauge factor.
Abstract: Denoting by qii = 1,..., n the set of extensive variables which characterize the state of a thermodynamic system, we write the associated intensive variables γ i, the partial derivatives of the entropy S = Sq1,..., qn ≡q0, in the form γ i = - pi/p0 where p0 behaves as a gauge factor. When regarded as independent, the variables qi, pii = 0,..., n define a space having a canonical symplectic structure where they appear as conjugate. A thermodynamic system is represented by a n + 1-dimensional gauge-invariant Lagrangian submanifold of. Any thermodynamic process, even dissipative, taking place on is represented by a Hamiltonian trajectory in, governed by a Hamiltonian function which is zero on. A mapping between the equations of state of different systems is likewise represented by a canonical transformation in. Moreover a Riemannian metric arises naturally from statistical mechanics for any thermodynamic system, with the differentials dqi as contravariant components of an infinitesimal shift and the dpi's as covariant ones. Illustrative examples are given.
47 citations
TL;DR: In this paper, a canonical transformation is described for uniformizing the coordinates used in Paper I of this series, which is based on elastic collision trajectories, and the question of invariance of S-matrix elements with respect to semiclassical unitary transformations is also discussed.
Abstract: A canonical transformation is described for uniformizing the coordinates used in Paper I of this series. For comparison with the results of Paper III, which based a uniformization on exact trajectories, the present article describes one based on elastic collision trajectories. The question of invariance of S‐matrix elements with respect to semiclassical unitary transformations is also discussed.
46 citations
TL;DR: In this paper, a modified Jaynes-Cummings model is introduced, which consists of a two-level atom interacting with two modes of the electromagnetic field and it is shown that the existence of the second field coupling parameter reduces the amount of squeezing in all quadratures, while the effect of the detuning parameter would lead to the superstructure phenomenon which becomes more pronounced upon increasing the mean photon numbers, in the states which are taken to be converter states.
46 citations
TL;DR: In this article, a new model of Hamiltonian which represents the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a cavity was introduced, which can be regarded as a generalization of the Jaynes-Cummings model.
46 citations