Search results for "Canon"

Exercises, Hints and Selected Solutions

2016

1.1. Prove the formula (1.8a) in Sect. 1.3, $$\displaystyle{ \int \mathrm{d}^{n}x\; =\int _{ 0}^{+\infty }\!\!\!\mathrm{d}r\;r^{n-1}\int _{ 0}^{2\pi }\!\!\!\mathrm{d}\phi \prod _{ k=1}^{n-2}\int _{ 0}^{\pi }\!\!\!\mathrm{d}\theta _{ k}\sin ^{k}(\theta _{ k}) }$$ (1.1) by means of induction.

Canonical Adiabatic Theory

2001

In the present chapter we are concerned with systems, the change of which—with the exception of a single degree of freedom—should proceed slowly. (Compare the pertinent remarks about \(\varepsilon\) as slow parameter in Chap. 7) Accordingly, the Hamiltonian reads: $$\displaystyle{ H = H_{0}{\bigl (J,\varepsilon p_{i},\varepsilon q_{i};\varepsilon t\bigr )} +\varepsilon H_{1}{\bigl (J,\theta,\varepsilon p_{i},\varepsilon q_{i};\varepsilon t\bigr )}\;. }$$ (12.1) Here, \((J,\theta )\) designates the “fast” action-angle variables for the unperturbed, solved problem \(H_{0}(\varepsilon = 0),\) and the (p i , q i ) represent the remaining “slow” canonical variables, which do not necessarily have…

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.

Pseudobosons, Riesz bases, and coherent states

2010

In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are re-considering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated to the model.

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

1980

New solutions of the hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation

1991

Abstract We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space.

Thermal density fluctuations in amorphous polymers as revealed by small angle X-ray diffraction

1973

In the case of equilibrium the mean square relative fluctuations of the thermodynamic parameters vanish asymptotically as the number of degrees of freedom approach infinity. There are various observable effects, however, which are related to local fluctuations of the thermodynamic quantities within small parts of the macroscopic system. In particular the scattering of electromagnetic waves by a one-component, one-phase system is due to thermal density fluctuations within small volumes V of the sample. Considering a grand canonical ensemble the phenomenological theory of local fluctuations (1) for a one component system shows that the fluctuation of the number of particles N in the volume V …

Electrocatalytic thermodynamics and kinetics at constant electrode potentials: The grand canonical ensemble approach

2020

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.

Quantum cosmological approach to 2d dilaton gravity

1993

We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the space of solutions is properly truncated to provide the physical Hilbert space. We establish the quantum equivalence of both models and relate the results with the covariant phase-space quantization. We also discuss the relation between the quantum wavefunctions and the classical space-time solutions and propose the wave function representing the ground state.