Search results for "Canonical transformation"

On time-resolved approach for phonon assisted interband transitions

2015

Photoexcited dynamics of electrons and holes in two-band dielectric, with special emphasis on back reaction of phonons are developed by combining the quantum electrodynamics and Baker-Campbell-Hausdorff (BCH) canonical transformation. These methods create an explicit time-domain representation of photoinduced processes and contribute in unifying phonon-assisted description of distribution functions of electron and hole quasiparticles for the description of observable effects of photoinduced processes in dielectrics.

Canonical transformation for single-atom resonance fluorescence: The strong-driving-field limit

1980

Backlund transformations in 2-D dilaton gravity

1998

We give a B\"acklund transformation connecting a generic 2D dilaton gravity theory to a generally covariant free field theory. This transformation provides an explicit canonical transformation relating both theories.

A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

1997

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenv…

Interaction between strong radiation fields and two-level atoms: A canonical transformation approach

2008

Time-Independent Canonical Perturbation Theory

2001

First we consider the perturbation calculation only to first order, limiting ourselves to only one degree of freedom. Furthermore, the system is to be conservative, ∂ H∕∂ t = 0, and periodic in both the unperturbed and perturbed case. In addition to periodicity, we shall require the Hamilton–Jacobi equation to be separable for the unperturbed situation. The unperturbed problem H0(J0) which is described by the action-angle variables J0 and w0 will be assumed to be solved. Thus we have, for the unperturbed frequency: $$\displaystyle{ \nu _{0} = \frac{\partial H_{0}} {\partial J_{0}} }$$ (10.1) and $$\displaystyle{ w_{0} =\nu _{0}t +\beta _{0}\;. }$$ (10.2) Then the new Hamiltonian reads, up t…

Sine-Gordon Statistical Mechanics

1984

The Classical partition-function $$ Z = \int {D\Pi {\text{ }}D\phi {\text{ }}\exp - } \beta H\left[ \phi \right]$$ (1) in which \( {\beta ^{{ - 1}}} = {k_{B}}T{\text{ and }}H\left[ \phi \right]\) is the sine-Gordon (s-G) Hamiltonian $$ H\left[ \phi \right] = {\Upsilon _{0}}^{{ - 1}}\int {\left[ {\frac{1}{2}{\Upsilon _{0}}^{2}{\Pi ^{2}} + \frac{1}{2}{\phi _{z}}^{2} + {m^{2}}\left( {1 - \cos \phi } \right)} \right]} dz $$ (2) has been evaluated by transfer integral methods [1,2].

Geometric Aspects of Thermodynamics

2016

This chapter deals with mathematical aspects of thermodynamics most of which will be seen to be primarily of geometrical nature. Starting with a short excursion to differentiable manifolds we summarize the properties of functions, of vector fields and of one-forms on thermodynamic manifolds. This summary centers on exterior forms over Euclidean spaces and the corresponding differential calculus. In particular, one-forms provide useful tools for the analysis of thermodynamics. A theorem by Caratheodory is developed which is closely related to the second law of thermodynamics. The chapter closes with a discussion of systems which depend on two variables and for which there is an interesting a…