In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffu...In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic展开更多
We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,...We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,which shows that even though the two channels are independent of each other,since the two modes of the initial state are entangled with each other,the final state remains entangled.Nevertheless,although the squeezing(entanglement)between the two modes is weakened after the diffusion,it is not completely removed.We also highlight the law of photon number evolution.In the calculation process used in this paper,we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.展开更多
文摘In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic
基金supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents in College of Anhui Province,China(Grant No.gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2019A0688 and KJ2020A0638)。
文摘We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,which shows that even though the two channels are independent of each other,since the two modes of the initial state are entangled with each other,the final state remains entangled.Nevertheless,although the squeezing(entanglement)between the two modes is weakened after the diffusion,it is not completely removed.We also highlight the law of photon number evolution.In the calculation process used in this paper,we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.
