In this paper we propose a new form of generalized uncertainty principle which involves both a linear as well as a quadratic term in the momentum. From this we have obtained the corresponding modified dispersion relation which is compared with the corresponding relation in rainbow gravity.The new form of the generalized uncertainty principle reduces to the known forms in appropriate limits. We then calculate the modified velocity of photons and we find that it is energy dependent, allowing therefore for a superluminal propagation. We then derive the 1+1 -dimensional Klein-Gordon equation taking into account the effects of the modified dispersion relation. The positive frequency mode solution of this equation is then used to calculate the power spectrum arising due to the Unruh effect. The result shows that the power spectrum depends on the energy of the particle owing its origin to the presence of the generalized uncertainty principle. Our results capture the effects of both the simplest form as well as the linear form of the generalized uncertainty principle and also points out an error in the result of the power spectrum up to first order in the generalized uncertainty principle parameter existing in the literature. * a.m.official.

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We introduce a new model of relativistic quantum analogue of the classical Otto engine in the presence of a perfectly reflecting boundary. A single qubit acts as the working substance interacting with a massless quantum scalar field, with the boundary obeying the Dirichlet condition. The quantum vacuum serves as a thermal bath through the Unruh effect. We observe that the response function of the qubit gets significantly modified by the presence of the reflecting boundary. From the structure of the correlation function, we find that three different cases emerge, namely, the intermediate boundary regime, the near boundary regime, and the far boundary regime. As expected, the correlation in the far boundary regime approaches that of the Unruh quantum Otto engine (UQOE) when the reflecting boundary goes to infinity. The effect of the reflecting boundary is manifested through the reduction of the critical excitation probability of the qubit and the work output of the engine. Inspite of the reduced work output, the efficiency of the engine remains unaltered even in the presence of the boundary.