Abstract
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy dissipation. To this end, we discuss two different time-dependent methods. One is to introduce an effective time-dependent Hamiltonian, which leads to a classical equation of motion as a relationship among expectation values of quantum operators. We apply this method to a heavy-ion fusion reaction and discuss the role of dissipation on the penetrability of the Coulomb barrier. The other method is to start with a Hamiltonian with environmental degrees of freedom and derive an equation which the system degree of freedom obeys. For this, we present a new efficient method to solve coupled-channels equations, which can be easily applied even when the dimension of the coupled-channels equations is huge.
Highlights
Open quantum systems are ubiquitous in many branches of science
The couplings to the environmental degrees of freedom can strongly affect the dynamics of the system
It has been well known that a large amount of the relative energy and angular momentum is dissipated during collisions of heavy nuclei at energies close to the Coulomb barrier, known as deep inelastic collisions [3]
Summary
Open quantum systems are ubiquitous in many branches of science. In general, a system is never isolated but couples to other degrees of freedom, which are often referred to as the environment. One is to use a phenomenological quantum friction model in which the expectation values of operators obey the classical equation of motion with friction [14,15,16,17] We solved such quantum friction Hamiltonians with a time-dependent wave packet approach in order to discuss the effect of friction on quantum tunneling [18]. One can employ the Caldeira-Leggett Hamiltonian [1] since the classical Langevin equation can be derived from it [3, 4] This approach is more microscopic, and a computation would be more involved than the quantum friction model. We first discuss the phenomenological quantum friction models using a timedependent wave packet approach. One can modify the Schrödinger equation for ul (r, t) in the same way as Equation (3)
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