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Register a new userEntangled state representations in noncommutative quantum mechanics
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We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled state representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.
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We study the effect of noncommutativity of space on the physics of a quantum interferometer located in a rotating disk in a gauge field background. To this end, we develop a path-integral approach which allows defining an effective action from which relevant physical quantities can be computed as in the usual commutative case. For the specific case of a constant magnetic field, we are able to compute, exactly, the noncommutative Lagrangian and the associated shift on the interference pattern for any value of $theta$.
A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincar{e}s magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.
We establish a relation between entanglement in simple quantum mechanical qubit systems and in wormhole physics as considered in the context of the AdS/CFT correspondence. We show that in both cases, states with the same entanglement structure, indistinguishable by any local measurement, nevertheless are characterized by a different Berry phase. This feature is experimentally accessible in coupled qubit systems where states with different Berry phase are related by unitary transformations. In the wormhole case, these transformations are identified with a time evolution of one of the two throats.
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature.
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