Nguyen Tri Lan

First, Second Quantization and Q-Deformed Harmonic Oscillator

Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.

On the fluctuation induced mass enhancement

The effective mass induced by the background fluctuation on particles is considered. The analytical results show that the effective mass depends only on the properties of fluctuation, and takes non-zero value when and only when fluctuation mean value is non-zero. The possible applications of the obtained results to complex systems such as biology and ecology where environmental factors lead to the changes of the information exchange ranges from long to short one are discussed, i.e. the possibility of using physical modeling techniques to investigate macroscopic behaviors of some complex systems under consideration.

Boltzmann-Gaussian Transition under Specific Noise Effect

It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.

Study of Hanoi and HoChiMinh Stock Exchange by Econophysics Methods

The econophysics methods are used to study the financial fluctuation of Hanoi Stock Exchange (HNX) and Hochiminh Stock Exchange (HSX) in comparison to Dow John Industrial Average’s one. The study has been made both on panic period (2007-2008) and on normal time of theses stocks. The results point out that for the period under consideration, the distribution of returns tends to be Student distribution. There exists an analogy between nonequilibrium phase transitions and financial market movement. Thus it is hypothesized that financial markets undergo self-organizing when the external volatility perception rises above some critical value, the distribution of signs of returns is to be similar to a second order phase transition. The results obtained by econophysics method have quite good agreement with the ones obtained by other economy analyzation methods.

Optically trapping cold atoms by using a silicon nanopillar

A new optical trapping model for cold atoms using a nanopillar is proposed. A strong electromagnetic wave is sent to the pillar to creat the existence of a stable bound state of cold atom. An evanescent wave is generated around the pillar and creates an effective attractive potential. The result will be compared to some recent trapping models.

Energy spectrum inverse problem of q-deformed harmonic oscillator and WBK approximation

Using the connection between q-deformed harmonic oscillator and Morse-like anharmonic potential we investigate the energy spectrum inverse problem. Consider some energy levels of energy spectrum of q-deformed harmonic oscillator are known, we construct the corresponding Morse-like potential then find out the deform parameter q. The application possibility of using the WKB approximation in the energy spectrum inverse problem was discussed for the cases of parabolic potential (harmonic oscillator), Morse-like potential (q-deformed harmonic oscillator). so we consider our deformed-three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. For practical problems, we propose the deformed- three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined.

On application of non—extensive statistical mechanics to studying ecological diversity

The concept of Tsallis entropy provides an extension of thermodynamics and statistical physics. In the ecology, Tsallis entropy is proposed to be a new class of diversity indices Sq which covers many common diversity indices found in ecological literature. As a new statistical model for the Whittaker plots describing species abundance distribution, the truncated exponential distribution is used to calculate the diversity and evenness indices. The obtained results in new model are graphically compared with those in previous publication in the same field of interests, and shows a good agreement. A further development of a thermodynamic theory of ecological systems that is consistent with entropic approach of statistical physics is motivated.

The possible conection between q-defomed hamornic oscillator formation and anharmonicity

In our previous article, the connection between q-deformed harmonic oscillation and Morse-like asymmetric potential is investigated. In present work, a possibility of the connection between q-deformed harmonic oscillator and anharmonic symmetric potential is in detail considered. For simplicity, we take the inverse square cosine-hyperbolic form of potential, i.e Poschl-Teller potential. The relation between the deformation parameter q and the set of parameters of anharmonic symmetric potential was found. The correspondence of two types of connections between q-deformed harmonic oscillator with asymmetric and symmetric potentials are discussed.

Simple Model for Gold Nano Particles Concentration Dependence of Resonance Energy Transfer Intensity

Gold nano particles (GNPs) concentration dependence of the energy transfer occurs between the fluorophores and GNPs is investigated. In the case of theses pairs, GNPs can enhance or quench the fluorescence of fluorophores depending upon the relative magnitudes of two energy transfer mechanisms: i) the plasmonic field enhancement at the fluorophores emission frequencies (plasmon coupled fluorescence enhancement) and ii) the localized plasmon coupled Forster energy transfer from fluorescent particles to gold particles, which quenches the fluorescence. The competition of these mechanisms is depending on the spectral overlap of fluorophores and GNPs, their relative concentration, excitation wavelength. Simple two branches surface plasmon polariton model for GNPs concentration dependence of the energy transfer is proposed. The experimental data and theoretical results confirm our findings.

Ginzburg-Landau functional for three order parameter problem

A model is presented utilizing a generic Hamiltonian with equal pairings in channels based on quantum field theory and functional integral formalism, to show the correlation among the order parameters which are described in multi-component Ginzburg-Landau functional. In the vicinity of the phase transition, the further perturbative expansions of the functional around the mean-field theory in the auxiliary fields are carried out with the aim of leading to a possible solution for the coexistence of many phases. The work is motivated by the recent theoretical researches and experimental evidences of the coexistence of superconductivity and ferromagnetism in U and Ce compounds.