We introduce quantum heat engines that perform Otto cycle and the Stirling by using a coupled pair of harmonic oscillator as its working substance. In regime, different medium is considered for analysis engine models to boost efficiency cycles. this work, we present in realm where phase space non-commutative nature. By notion thermodynamics, develop thermodynamic variables space. encounter cata...

Quantum heat cycles and quantum refrigerators are analyzed using various systems as their working mediums. For example, to evaluate the efficiency work done of Carnot cycle in regime, one can consider harmonic oscillator a medium. all these well-defined substances (which commutative space structure), engine is not up mark efficiency. So, inevitable question arise, observe catalytic effect on en...

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a Non-Commutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of ...

A rational function belongs to the Hardy space, H 2 H^2 , of square-summable power serie...

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.