Consumer myopia, compatibility and aftermarket monopolization

In this paper, I show that the standard Bertrand competition argument does not apply when firms compete for myopic consumers who optimize period-by-period. I develop the model in the context of aftermarket. With overlapping-generations of consumers, simultaneous product offerings in the primary market and aftermarket establishes a price floor for the primary good. This constraint prevents aftermarket rents from being dissipated by the primary market competition. Duopoly firms earn positive profits despite price competition with undifferentiated products. Nonetheless, government interventions to reinforce aftermarket competition such as a standardization requirement may lead to the partial collapse of the primary market.aftermarket, Bertrand competition, bounded rationality, standardization.

Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space

Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case

Investigating the quantum discord dynamics with a bipartite split of the multiqubit system in the correlated photon-matter model

In this paper, we try to study the quantum discord dynamics in a complex correlated photon-matter model, which is modified from the Tavis-Cummings-Hubbard model - a common cavity quantum electrodynamics model. The target model consists of two hydrogen atoms. A neutral hydrogen molecule can be obtained through an association reaction and disintegrated through dissociation reaction. The formation and breaking of covalent bond is accompanied by the creation and annihilation of phonon. Compared with previous efforts, studying the quantum discord dynamics of this complicated system is more challenging than it was for the simple quantum system, which consisted of a single two-level atom. For convenience, we adopt a bipartite split of the multiqubit system and the two-qubit von Neumann projective measurement on the observed subsystem. We attempt to examine the dissipative dynamics in open quantum system in addition to the unitary evolution of closed quantum system. We are dedicated to identifying the regularity of quantum correlation as the basis for future research on more complex quantum systems, specifically including the impacts of nuclei tunneling effect, covalent bond intensity, and dissipation strengths of photon and phonon on quantum discord.Comment: 20 pages, 15 figures, 2 table

Studying quantum entanglement and quantum discord in the cavity QED models

Based on the two-qubit Jaynes-Cummings model - a common cavity quantum electrodynamics model, and extending to modification of the three-qubit Tavis-Cummings model, we investigate the quantum correlation between light and matter in bipartite quantum systems. By resolving the quantum master equation, we are able to derive the dissipative dynamics in open systems. To gauge the degree of quantum entanglement in the two-qubit system, von Neumann entropy and concurrence are introduced. Quantum discord, which can properly measure the quantum correlation in both closed and open systems, is also introduced. In addition, consideration is given to the impacts of initial entanglement and dissipation strength on quantum discord. Finally we discussed two different cases of nuclei motion: quantum and classical.Comment: 12 pages, 9 figure

Modeling and simulating formation of neutral hydrogen molecule in Tavis-Cummings-Hubbard model

A finite-dimensional model of chemistry with two two-level artificial atoms on quantum dots placed in optical cavities, called the association-dissociation model of neutral hydrogen molecule, is described. The initial conditions for formation of the artificial analogue of the neutral hydrogen molecule are discussed. The motion of the nuclei can be represented in quantum form. The association of atoms in the molecule is simulated through a quantum master equation, containing hybridization of atomic orbitals into molecular - depending on the position of the nuclei. Electron spin transitions of electrons and spin-spin interactions between electrons and nuclei are also considered. The influence of temperature variation of photonic modes to unitary evolution and formation of neutral hydrogen molecule is investigated.Comment: 15 pages, 10 figure