scholarly journals Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions

2012 ◽  
Vol 370 (1979) ◽  
pp. 5437-5451 ◽  
Author(s):  
D. Gwion Evans ◽  
John E. Gough ◽  
Matthew R. James
Keyword(s):  
Heisenberg Group ◽  
Commutation Relation ◽  
Stochastic Models ◽  
General Rule ◽  
Product Formula ◽  
Input Output ◽  
Trotter Product Formula ◽  
Commutation Relations ◽  
Series Product ◽  
Weyl Commutation Relation

We show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie–Trotter product formula.

scholarly journals Deformation of the Wheeler–DeWitt equation

2014 ◽  
Vol 29 (20) ◽  
pp. 1450106 ◽  
Author(s):  
Mir Faizal
Keyword(s):  
Commutation Relation ◽  
Canonical Commutation Relation ◽  
Big Bang ◽  
Minimum Length ◽  
Second Quantization ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Big Bang ◽  
Big Bang Singularity ◽  
Modified Theory

In this paper, we will analyze the consequences of deforming the canonical commutation relations consistent with the existence of a minimum length and a maximum momentum. We first generalize the deformation of first quantized canonical commutation relation to second quantized canonical commutation relation. Thus, we arrive at a modified version of second quantization. A modified Wheeler–DeWitt equation will be constructed by using this deformed second quantized canonical commutation relation. Finally, we demonstrate that in this modified theory the big bang singularity gets naturally avoided.

Accretive perturbations and error estimates for the Trotter product formula

2001 ◽  
Vol 39 (4) ◽  
pp. 396-412 ◽  
Author(s):  
Vincent Cachia ◽  
Hagen Neidhardt ◽  
Valentin A. Zagrebnov
Keyword(s):  
Error Estimates ◽  
Product Formula ◽  
Trotter Product Formula

scholarly journals Observation of ultra-fine structures in energy levels of prolate nuclei

2018 ◽  
Vol 96 (9) ◽  
pp. 1059-1062 ◽  
Author(s):  
Hassan Hassanabadi ◽  
Hadi Sobhani
Keyword(s):  
Energy Spectrum ◽  
Commutation Relation ◽  
Atomic Physics ◽  
Nuclear Physics ◽  
Energy Levels ◽  
Zeeman Effect ◽  
Three Dimensions ◽  
Energy Splitting ◽  
Commutation Relations ◽  
Fine Structures

This work discusses the observation of splitting in the energy levels of prolate nuclei. Similar effects in atomic physics are known as the Zeeman effect, but in nuclear physics the feasibility of such phenomena has not been observed. After introducing a deformation in the commutation relation in three dimensions, we used these commutation relations in X(3) model. After enough derivation, we then evaluate the energy spectrum relation for the considered system, which has resulted in energy splitting. With these observations in the energy splitting we referred to such an effect as the ultra-fine structures in energy levels. At the end some plots have been depicted to illustrate the results.

Sign in / Sign up

Export Citation Format

Share Document