Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variabl...Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.展开更多
The correlation of the inhomogeneous broadening of the resonance transition at different time intervals and the efficiency of long-lived photon echo response locking by the action of standing waves of non-resonant las...The correlation of the inhomogeneous broadening of the resonance transition at different time intervals and the efficiency of long-lived photon echo response locking by the action of standing waves of non-resonant laser pulses are considered. It is shown that the long-lived photon echo response locking effect may be observed even at the angles of the relative orientation of the non-resonant standing wave laser pulses of less than one degree, due to the change in the correlation coefficient of inhomogeneous broadening at time intervals between the first and the second and after the third resonant laser pulses.展开更多
文摘Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.
文摘The correlation of the inhomogeneous broadening of the resonance transition at different time intervals and the efficiency of long-lived photon echo response locking by the action of standing waves of non-resonant laser pulses are considered. It is shown that the long-lived photon echo response locking effect may be observed even at the angles of the relative orientation of the non-resonant standing wave laser pulses of less than one degree, due to the change in the correlation coefficient of inhomogeneous broadening at time intervals between the first and the second and after the third resonant laser pulses.
