Abstract:
The Hamiltonian associated to the mass variable system is constructed from first principles through finding a constant of motion of the system. A comparison is made of the classical motion of a body with its mass position depending in the (x,v) space and (x,p) space which are defined by the constant of motion and the Hamiltonian, for a particular model of mass variation. As one could expected, these motion looks different on these spaces. The quantization of the harmonic oscillator with this mass variation is done, and a comparison is made by using the usual Hamiltonian approach with the proposed quantization of the constant of motion approach. This comparison is done at first order in perturbation theory, and one sees a difference between both approaches which can, in principle, be measured.

Abstract:
We study the phenomenon of decoherence during the operation of one qubit transformation, controlled-not (CNOT) and controlled-controlled-not (C^{2}NOT) quantum gates in a quantum computer model formed by a linear chain of three nuclear spins system. We make this study with different type of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of . We also study the behavior of the purity parameter for these gates and different environments and found linear or quadratic decays of this parameter depending on the type of environments.

We make a numerical study of decoherence on the teleportation algorithm implemented in a linear chain of three nuclear spins system. We study different types of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of γ≤4×10^{-4} for not thermalized case, which was determined by using the purity parameter calculated at the end of the algorithm. For the thermalized case the decoherence is stablished for very small dissipation parameter, making almost not possible to implement this algorithm for not zero temperature.

By removing a ^{12}C atom from the tetrahedral
configuration of the diamond, replacing it by a ^{13}C atom, and repeating
this in a linear direction, it is possible to have a linear chain of nuclear
spins one half and to build a solid state quantum computer. One qubit rotation,
controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are
obtained immediately from this configuration. CNOT and CCNOT quantum gates are
used to determined the design parameters of this quantum computer.

Abstract:
Classical
chaotic behavior in diatomic molecules is studied when chaos is driven by a
circularly polarized resonant electric field and expanding up to fourth order
of approximation the Morse’s potential and angular momentum of the system. On
this double resonant system, we find a weak and a strong stationary (or
critical) points where the chaotic characteristics are different with respect to
the initial conditions of the system. Chaotic behavior around the weak critical
point appears at much weaker intensity on the electric field than the electric
field needed for the chaotic behavior around the strong critical point. This
classical chaotic behavior is determined through Lyapunov exponent, separation
of two nearby trajectories, and Fourier transformation of the time evolution of
the system. The threshold of the amplitude of the electric field for appearing
the chaotic behavior near each critical point is different and is found for
several molecules.

Abstract:
We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear reso-nances associated to the vibrational and rotational motion. We solve the Schrödinger equation associated with the wave function expanded in term of proper stationary states, |n> |lm> (vibrational angular momentum states). Looking for quantum-classic correspondence, we consider the Liouville dynamics in the two dimensional phase space defined by the coherent-like state of vibrational states. We consider the rela-tionship between the overlapping of the classical resonances and the mixing of the quantum states, and it is found some similarities when the quantum dynamics is pictured in terms of number and phase operators.

We make an observation about Galilean transformation on a 1-D mass variable system which leads us to the right way to deal with mass variable systems. Then using this observation, we study two-body gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. For this system, a constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion, and the period of the body is studied using the constant of motion of the system. Our theoretical results are applied to Halley’s Comet.

Abstract:
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian
for relativistic particle moving in a dissipative medium characterized by a
force which depends on the square of the velocity of the particle is done. It
is shown that while the trajectories in the space (x,v), defined by the
constant of motion, look as one might expected, the trajectories in the space (x,p),
defined by the Hamiltonian, have an odd behavior.<

Abstract:
Through the study of the factorization conditions of a wave function made up of two, three and four qubits, we propose an analytical expression which can characterize entangled states in terms of the coefficients of the wave function and density matrix elements.

Abstract:
During the last years, many bisbibenzylic macrocyclic ethers were isolated and identified in Hepaticae. One of them is MARCHANTINQUINONE, a quinonic macrocycle with interesting biological activity. In the following report, we present the last steps of the total synthesis.