In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Polsson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation(Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space,but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.
A novel structure of fiber optic biosensor and its principle are introduced.The sample is detected in microchannels of several microns diameter in fiber optic biosensors.The relation between the optic fiber tapered angle and the fluorescence incident angle is calculated in signal receiving part.As the sensor is a zero-order system,calculating formula of the static sensitivity is derived.When ZnSe nano-crystalline cluster is used for marking the molecules,the static sensitivity for fiber optic biosensors is calculated. At the same time,the relation between the static sensitivity and the ratio of exciting wavelength to fluorescence wavelength is presented.
