arXiv subjects

Przemyslaw Brzykcy

Publications and source records attributed to Przemyslaw Brzykcy.

4 recordsLinked to original sources

arXiv2017

(1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator

It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillators are indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. In depth analysis of the coadjoint orbits of the $(1+1)$ dimensional Newton-Hooke group are presented. Further, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.

math-ph↗

arXiv2017

On the Derivation and Interpretation of the Poincaré-Maxwell Group

The Lie algebra of the Poincaré-Maxwell group is derived in a manner that provides the interpretation of the equations of motion. It is clarified that the dynamics obtained from the orbit method is exactly equivalent to the classical description of the charged particle moving in the constant electromagnetic field. The multiplicity of the coadjoint orbits of the group under consideration is discussed.

math-ph↗

arXiv2015

On some properties of number-phase Wigner function

It is shown that the number-phase Wigner function defines uniquely the respective density operator. Relations between the Glauber-Sudarshan distribution $\mathcal{P}(α)$ and the number-phase Wigner function is found. This result is then generalised to the case of the Cahil-Glauber distributions $\mathcal{W}^{(s)}(α)$, $-1\leq s \leq 1$.

math-ph↗

arXiv2013

From the Weyl quantization of a particle on the circle to number-phase Wigner functions

A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its properties are analyzed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner function are considered.

math-ph↗