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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, the integrability conditions of a time-dependent Hartree-Bogolubov (TDHB) equation were studied from a group-theoretical viewpoint.
Abstract: We study the integrability conditions of a time-dependent Hartree-Bogolubov (TDHB) equation to determine collective submanifolds from the group-theoretical viewpoint. The basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe collective co-ordinates. This manner enables us to take a one-form Ω which is linearly composed of a TDHB Hamiltonian and infinitesimal generators induced by collective variable differentials of aSO2N (Bogolubov) canonical transformation. The integrability conditions of our system read dΩ−ΩΛΩ=0, which is a fundamental equation to determine the collective submanifolds in the TDHB method. This equation may work wellin the large scale beyond aSO2N RPA as the small-amplitude limit, with an appropriate boundary condition.
8 citations
TL;DR: In this paper, the authors apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent, and apply them to a time-independent Schrodinger equation.
Abstract: A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.
8 citations
8 citations
TL;DR: In this paper, a geometric interpretation for the variational equations of the canonical transformation methed is given, and a criterion is deduced to distinguish, among the solutions, the one that gives the lowest average energy in the quasi-particle vacuum.
8 citations
TL;DR: In this article, the method of canonical transformation is applied in quantizing phonons around a general static solution in a continuum version of a model for t-(CH) x, and the transformed effective Hamiltonian in the perfectly dimerized case is used to calculate the first and second order Raman scattering amplitudes.
Abstract: The method of canonical transformation is applied in quantizing phonons around a general static solution in a continuum version of a model for t-(CH) x . The transformed effective Hamiltonian in the perfectly dimerized case is used to calculate the first and second order Raman scattering amplitudes. Especially it is shown that, through the measurement of the second order Raman process, the phonon dispersion can be derived. The application of the formulation to the case with a soliton or a polaron is also discussed.
8 citations