Coupled-channels density-matrix approach to low-energy nuclear collision dynamics: A technique for quantifying quantum decoherence effects on reaction observables
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulas of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for the low-energy collision of the $^{16}\mathrm{O}$ projectile on the $^{154}\mathrm{Sm}$ target.
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulas of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for the low-energy collision of the 16O projectile on the 154Sm target.
Atomic nuclei are complex, quantum many‐body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom. Collective modes (vibration and/or rotation) dominate at low energy (near the ground‐state). The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low‐energy reaction dynamics. However, excluded states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials. Is this a complete description of open system dynamics? Does it include effects of quantum decoherence? Can decoherence be manifested in reaction observables? In this contribution, I discuss these issues and the main ideas of a coupled‐channels density‐matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low‐energy nuclear reaction dynamics. Topical applications, which refer to understanding the astrophysically important collision 12C+12C and achieving a unified quantum dynamical description of relevant reaction processes of weakly‐bound nuclei, are highlighted.
Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom.Collective modes (vibration and/or rotation) dominate at low energy (near the ground-state).The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low-energy reaction dynamics.However, excluded non-collective states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials.Is this a complete description of open system dynamics?Does it include effects of quantum decoherence?Can decoherence be manifested in reaction observables?This paper discusses these issues and the main ideas of a coupled-channels density-matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low-energy nuclear reaction dynamics.Some topical applications are highlighted.
Model calculations that include the effects of irreversible, environmental couplings on top of a coupled-channels dynamical description of the collision of two complex nuclei are presented. The Liouville-von Neumann equation for the time evolution of the density matrix of a dissipative system is solved numerically providing a consistent transition from coherent to decoherent (and dissipative) dynamics during the collision. Quantum decoherence and dissipation are clearly manifested in the model calculations. Energy dissipation, due to the irreversible decay of giant-dipole vibrational states of the colliding nuclei, is shown to result in a hindrance of quantum tunneling and fusion.
Low-energy nuclear fusion reactions have been described using a dynamical coupled-channels density matrix method, based on the theory of open quantum systems. For the first time, this has been combined with an energy projection method, permitting the calculation of energy resolved fusion probabilities. The results are benchmarked against calculations using stationary Schrödinger dynamics and show excellent agreement. Calculations of entropy, energy dissipation and coherence were conducted, demonstrating the capability of this method. It is evident that the presence of quantum decoherence does not affect fusion probability. This framework provides a basis for quantum thermodynamic studies using thermal environments.
Time-dependent density-matrix propagation is used to demonstrate, in a schematic model of an open quantum system, that the complex potential approach and the Lindblad dissipative dynamics are not equivalent. While the former preserves coherence, it is destroyed in the Lindblad dissipative dynamics. Quantum decoherence is the key aspect that makes the difference between the two approaches, indicating that the complex potential model is inadequate for a consistent description of open quantum-system dynamics. It is suggested that quantum decoherence should always be explicitly included when modeling low-energy nuclear collision dynamics within a truncated model space of reaction channels.
Non-relativistic quantum scattering theory informs our broad understanding of nuclear collision processes. However, detailed theoretical insights into the dynamics of fusion, whereby the colliding nuclei form a compound nucleus, remain elusive with conventional approaches. Fundamentally, understanding the complex dissipative processes inherent to compound nucleus formation and when they occur during the collision remains challenging. This, for example, prevents a consistent description of heavy-ion fusion over a wide range of collision energies and hinders searches for new super-heavy elements. To understand these dynamics, we need time-dependent approaches to nuclear collisions. In this thesis, a non-relativistic, time-dependent wave packet theory for potential scattering of charged quantum particles (such as nuclei) has been developed. It formally extends the application of Tannor and Weeks's (1993) formulation of the scattering matrix theory to systems containing the long-range Coulomb potential, by utilising Dollard's (1964) Møller operators. Using the asymptotic localisation of wave packets, analytical theorems have been formulated that allow convenient numerical application of this method. Numerical tests illustrating the theory mark the first rigorous application of this method in nuclear physics. Further insights are gained through a novel analysis of the wave packet time-correlation function (which underlies the theory) to understand how different dynamical processes, such as the formation of long-lived, quasi-bound states, during scattering contribute to the scattering matrix. This provides guidance on using the time-correlation function to obtain fusion observables, along with the associated challenges. Furthermore, this analysis showed that time-correlation functions can be obtained from static calculations, opening numerous new possibilities for studying the dynamics of nuclear reactions, in general, using this approach. This work opens new avenues for studying the dynamics of compound nucleus formation and other dissipative processes in nuclear reactions.