Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Modeling and manufacturability assessment of bistable quantum-dot cells

We have investigated the behavior of bistable cells made up of four quantum dots and occupied by two electrons, in the presence of realistic confinement potentials produced by depletion gates on top of a GaAs/AlGaAs heterostructure. Such a cell represents the basic building block for logic architectures based on the concept of quantum cellular automata (QCA) and of ground state computation, which have been proposed as an alternative to traditional transistor-based logic circuits. We have focused on the robustness of the operation of such cells with respect to asymmetries derived from fabrication tolerances. We have developed a two-dimensional model for the calculation of the electron density in a driven cell in response to the polarization state of a driver cell. Our method is based on the one-shot configuration-interaction technique, adapted from molecular chemistry. From the results of our simulations, we conclude that an implementation of QCA logic based on simple ¿hole arrays¿ is not feasible, because of the extreme sensitivity to fabrication tolerances. As an alternative, we propose cells defined by multiple gates, where geometrical asymmetries can be compensated for by adjusting the bias voltages. Even though not immediately applicable to the implementation of logic gates and not suitable for large scale integration, the proposed cell layout should allow an experimental demonstration of a chain of QCA cells.

Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

A parallel quantum histogram architecture

A parallel formulation of an algorithm for the histogram computation of n data items using an on-the-fly data decomposition and a novel quantum-like representation (QR) is developed. The QR transformation separates multiple data read operations from multiple bin update operations thereby making it easier to bind data items into their corresponding histogram bins. Under this model the steps required to compute the histogram is n/s + t steps, where s is a speedup factor and t is associated with pipeline latency. Here, we show that an overall speedup factor, s, is available for up to an eightfold acceleration. Our evaluation also shows that each one of these cells requires less area/time complexity compared to similar proposals found in the literature.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Normalization procedure for relaxation studies in NMR quantum information processing

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a ""loss of purity"" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.

Gravitational and quantum bounds on the photon mass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Quantum Aspects of Solitons and Deformations on Ad'S IND. 4'x C'P POT.3' ('S POT. 7')

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A novel self consistent calculation approach for the capacitance-voltage characteristics of semiconductor quantum wire transistors based on a split-gate configuration

Purpose - The purpose of this paper is to develop an efficient numerical algorithm for the self-consistent solution of Schrodinger and Poisson equations in one-dimensional systems. The goal is to compute the charge-control and capacitance-voltage characteristics of quantum wire transistors. Design/methodology/approach - The paper presents a numerical formulation employing a non-uniform finite difference discretization scheme, in which the wavefunctions and electronic energy levels are obtained by solving the Schrodinger equation through the split-operator method while a relaxation method in the FTCS scheme ("Forward Time Centered Space") is used to solve the two-dimensional Poisson equation. Findings - The numerical model is validated by taking previously published results as a benchmark and then applying them to yield the charge-control characteristics and the capacitance-voltage relationship for a split-gate quantum wire device. Originality/value - The paper helps to fulfill the need for C-V models of quantum wire device. To do so, the authors implemented a straightforward calculation method for the two-dimensional electronic carrier density n(x,y). The formulation reduces the computational procedure to a much simpler problem, similar to the one-dimensional quantization case, significantly diminishing running time.

Quantum state tomography and quantum logical operations in a three qubits NMR quadrupolar system

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP) and the various stages of each implementation were verified by quantum state tomography (QST). The results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms are presented here. Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.

Structure and electronic properties of hydrated mesityl oxide: a sequential quantum mechanics/molecular mechanics approach

The hydration of mesityl oxide (MOx) was investigated through a sequential quantum mechanics/molecular mechanics approach. Emphasis was placed on the analysis of the role played by water in the MOx syn-anti equilibrium and the electronic absorption spectrum. Results for the structure of the MOx-water solution, free energy of solvation and polarization effects are also reported. Our main conclusion was that in gas-phase and in low-polarity solvents, the MOx exists dominantly in syn-form and in aqueous solution in anti-form. This conclusion was supported by Gibbs free energy calculations in gas phase and in-water by quantum mechanical calculations with polarizable continuum model and thermodynamic perturbation theory in Monte Carlo simulations using a polarized MOx model. The consideration of the in-water polarization of the MOx is very important to correctly describe the solute-solvent electrostatic interaction. Our best estimate for the shift of the pi-pi* transition energy of MOx, when it changes from gas-phase to water solvent, shows a red-shift of -2,520 +/- 90 cm(-1), which is only 110 cm(-1) (0.014 eV) below the experimental extrapolation of -2,410 +/- 90 cm(-1). This red-shift of around -2,500 cm(-1) can be divided in two distinct and opposite contributions. One contribution is related to the syn -> anti conformational change leading to a blue-shift of similar to 1,700 cm(-1). Other contribution is the solvent effect on the electronic structure of the MOx leading to a red-shift of around -4,200 cm(-1). Additionally, this red-shift caused by the solvent effect on the electronic structure can by composed by approximately 60 % due to the electrostatic bulk effect, 10 % due to the explicit inclusion of the hydrogen-bonded water molecules and 30 % due to the explicit inclusion of the nearest water molecules.

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.