Usualmente o potencial de Morseé estudado em contextos de mecânica quântica. Por outro lado, eleé relativamente pouco aplicado em problemas clássicos. Neste trabalho uma solução completaé encontrada para as equações de movimento clássicas para uma partícula submetida a esse potencial. Exemplos numéricos são apresentados para alguns valores fixos dos parâmetros. Palavras-chave: mecânica clássica, potencial de Morse, equação de movimento.Usually the Morse potential is studied in the quantum mechanics context. On the other hand, there are relatively few applications for classical problems. In this work, a complete solution for the classical equation of motion is found for a particle subject to this potential. Numerical examples are presented for a fixed set of parameters.
Abstract. In this work it is analyzed a one-dimensional lattice which is composed by massspring systems with one additional Rosen-Morse potential on site. This kind of lattice is used to study thermodynamic properties of DNA, especially its thermal denaturation. On the context of this work, the Rosen-Morse potential simulates hydrogen bonds between double strands of the molecule. From the graphic of the average stretching of base pairs versus temperature it is possible to observe the thermal denaturation of the system. This result shows that it is possible to obtain phase transition with an asymmetric potential without an infinite barrier.The Peyrard-Bishop (PB) model proposed in 1989 [1] has been used a lot to describe the thermal denaturation of DNA [2]. In the original model the double strand of DNA is described by two chains of particles, in which the harmonic potential simulates the stacking interactions. On the other hand, the Morse potential describes the hydrogen bonds that are one of the main interactions responsible for maintaining stable the double strand of the molecule. From this model, several dynamic and thermodynamic aspects of the DNA have been explored, for example, formation of domain wall [3,4], energy location [5], formation and stability of breathers [6][7][8].Several modifications have been proposed in the PB model in order to obtain a better description of the phase transition for a DNA molecule. One way to alter the model consists on the modification of stacking interaction. Originally, this interaction was taken as purely harmonic [1], but in more recent works [9][10][11], an exponential term was introduced with this harmonic term. Another way to alter the original model is to substitute the Morse potential for others potentials with different characteristics. This can be made by the addition of a new term to the Morse potential as it is done, for instance, in ref. [12]. In this reference, the additional term was interpreted as interactions of the macromolecule with the solvent.Concerning the general behavior of non-linear lattices of the type here studied, Angelani et all [13] show that phase transitions are related to topological changes occurred in the system. One important result indicated in reference [13] is that the system does not presents phase transition when the potential on site has a symmetrical well. This happens because these potential have symmetric waves functions, obtained in the Schrödinger-type equation that emerges from the formalism, and centered in the origin. Therefore, the average value of the stretching of base pairs is always zero, what results on the impossibility of existing phase transition. This result contrasts with the one obtained for potentials with infinite barrier in one extremity of the potential well, like the Morse potential, in which the transition happens. This property is emphasized in reference [3], in which the transition is discussed both by using the dynamical method of domain wall as by using statistic mechanic. Thus, when the potential th...
This paper presents a thermodynamic study of DNA through a Peyrard-Bishop one-dimensional lattice with an on-site "hump" potential. The transfer integral operator method was used to obtain the thermodynamic properties of the system and the solution of the Schrödinger-type equation that emerges from this formalism was determined by the variational method. With the parameters of the potential, commonly used in literature, the value obtained for the denaturation temperature was extremely high. This work suggests different parameters to describe the thermodynamics of DNA macromolecule.
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