P. Girard

Bio: P. Girard is an academic researcher from Université de Montréal. The author has contributed to research in topics: Topological quantum computer & Path integral formulation. The author has an hindex of 2, co-authored 2 publications receiving 7 citations.

Altered Stats: Two anyons via path integrals for multiply connected spaces

Abstract: We apply the formalism of path integrals in multiply connected spaces to the problem of two anyons.

Quantum mechanical continuum solvation models.

Abstract: 6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

The stationary properties and the state transition of the tumor cell growth mode

Abstract: We study the stationary properties and the state transition of the tumor cell growth model (the logistic model) in presence of correlated noises for the case of nonzero correlation time. We derived an approximative Fokker-Planck equation and the stationary probability distribution (SPD) of the model. Based the SPD, we investigated the effects of both correlation strength ( $\lambda$ ) and correlation time ( $\tau$ ) of cross-correlated noises on the SPD, the mean of the tumor cell population and the normalized variance ( $\lambda_2$ ) of the system, and calculated the state transition rate of the system between two stable states. Our results indicate that: (i) $\lambda$ and $\tau$ play opposite roles in the stationary properties and the state transition of the system, i.e. increase of $\lambda$ can produce a smaller mean value of the cell population and slow down the state transition, but increase of $\tau$ can produce a larger mean value of the cell population and enhance state transition; (ii) For large $\lambda$ , there a peak structure on both $\lambda_2$ - $\lambda$ plot and $\lambda_2$ - $\tau$ plot. For the small $\lambda$ , $\lambda_2$ increases with increasing $\lambda$ , but $\lambda_2$ increases with decreasing $\tau$ .

Radiative and nonradiative decay rates of a molecule close to a metal particle of complex shape

Abstract: We present a model to evaluate the radiative and nonradiative lifetimes of electronic excited states of a molecule close to a metal particle of complex shape and, possibly, in the presence of a solvent. The molecule is treated quantum mechanically at Hartree-Fock (HF) or density-functional theory (DFT) level. The metal/solvent is considered as a continuous body, characterized by its frequency dependent local dielectric constant. For simple metal shapes (planar infinite surface and spherical particle) a version of the polarizable continuum model based on the integral equation formalism has been used, while an alternative methodology has been implemented to treat metal particles of arbitrary shape. In both cases, equations have been numerically solved using a boundary element method. Excitation energies and nonradiative decay rates due to the energy transfer from the molecule to the metal are evaluated exploiting the linear response theory (TDHF or TDDFT where TD--time dependent). The radiative decay rate of the whole system (molecule + metal/solvent) is calculated, still using a continuum model, in terms of the response of the surrounding to the molecular transition. The model presented has been applied to the study of the radiative and nonradiative lifetimes of a lissamine molecule in solution (water) and close to gold spherical nanoparticles of different radius. In addition, the influence of the metal shape has been analyzed by performing calculations on a system composed by a coumarin-type molecule close to silver aggregates of complex shape.

Path Integral Approach to Faraday's Law of Induction

Abstract: We derive a general form of the induced electromotive force due to a time-varying magnetic field. It is shown that the integral form of Faraday's law of induction is more conveniently written in the covering space. Thus the differential form is shown to relate the induced electric field in the nth winding number to the (n+1)th time-derivative of the magnetic field.