Space-fractional quantum heat engine based on level degeneracy

In order to examine the work and efficiency of the space-fractional quantum heat engine, we consider a model of the space-fractional quantum heat engine which has a Stirling-like cycle with a single particle under infinite potential well as an example. We numerically compute the work and efficiency for various fractional exponents. We show the work and the efficiency of the engine depending on the length of the potential well and fractional exponent of the engine. Furthermore, we show that fractional exponent plays a substantial role in the operating range of the quantum heat engine. Thus, we conclude that the fractional parameter can be used as a tuning parameter to obtain positive work and efficiency for the large size of the quantum heat engine. Additionally, the numerical results and model imply that the size of the engine can be enlarged in the nano-scale by using fractional deformations. As a result, in this study, we have not only shown that fractional deformations in space play an important role on the work and efficiency of the quantum heat engines but also introduced the concept of fractional quantum heat engines to the literature.

Fermi energy in the q-deformed quantum mechanics

In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrödinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.

Quantum Lenoir Engine with a Single Particle System in a One Dimensional Infinite Potential Well

Lenoir engine based on the quantum system has been studied theoretically to increase the thermal efficiency of the ideal gas. The quantum system used is a single particle (as a working fluid instead of gas in a piston tube) in a one-dimensional infinite potential well with a wall that is free to move. The analogy of the appropriate variables between classical and quantum systems makes the three processes for the classical Lenoir engine applicable to the quantum system. The thermal efficiency of the quantum Lenoir engine is found to have the same formulation as the classical one. The higher heat capacity ratio in the quantum system increases the thermal efficiency of the quantum Lenoir engine by 56.29% over the classical version at the same compression ratio of 4.41.

Hole States in Spherical Quantum Nanoheterosystem with Intermediate Spin-Orbital Interaction

The hole energy spectrum has been studied for the spherical semiconductor nanoheterosystem with the cubic symmetry. The exact solutions of the Schrödinger equation for the ground and excited hole states are presented within the framework of the 6-band Luttinger Hamiltonian and the finite gap of bands with the corresponding boundary conditions. Dependence of the holes energies from the radius of the quantum dot has been calculated for the GaAs/AlAs heterostructure. Obtained results where compared with data obtained using the infinite potential well model, as well as the single-band model for heavy and light holes.

Quantum complexity associated with tunneling

We use a one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of a locally defined spatial entropy function defined by S=-\int |\Psi(x,t)|^2 \ln |\Psi(x,t)|^2 dx . We show that changing the square barrier by increasing the height or width of the barrier not only decreases the tunneling but also slows down the rapid rise of the entropy function, indicating that the locally defined entropy growth is an essentially quantum effect.

Construction of Dirac Delta Function from the Discrete Orthonormal Basis of the Function Space

Orthonormal basis of the function space can be used to construct Dirac delta function. In particular, set of eigenfunctions of the Hamiltonian operator of a particle in one dimensional infinite potential well forms a non-degenerate discrete orthonormal basis of the function space. Such a simple basis set is suitable to study closure property of the basis and various properties of Dirac delta function in Physics graduate lab.The Himalayan Physics Vol. 6 & 7, April 2017 (54-57)