Browsing by Author "Uken, Daniel Alexander."

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Computer simulation of nonadiabatic dynamics by means of the quantum-classical Liouville equation.
(2013) Uken, Daniel Alexander.; Sergi, Alessandro.
Simulation of quantum dynamics for many-body systems is an open area of research. For interacting many-body quantum systems, the computer memory necessary to perform calculations has an astronomical value, so that approximated models are needed to reduce the required computational resources. A useful approximation that can often be made is that of quantum-classical dynamics, where the majority of the degrees are treated classically, while a few of them must be treated quantum mechanically. When energy is exchanged very quickly between the quantum subsystem and classical environment, the dynamics is nonadiabatic. Most theories for nonadiabatic dynamics are unsatisfactory, as they fail to properly describe the quantum backreaction of the subsystem on the environment. However, an approach based on the quantum-classical Liouville equation solves this problem. Even so, nonadiabatic dynamics is di cult to implement on a computer, and longer simulation times are often inaccessible due to statistical error. There is thus a need for improved algorithms for nonadiabatic dynamics. In this thesis, two algorithms that utilise the quantum-classical Liouville equation will be qualitatively and quantitatively compared. In addition, stochastic sampling schemes for nonadiabatic transitions will be studied, and a new sampling scheme is introduced [D. A. Uken et al., Phys. Rev. E. 88, 033301 (2013)] which proves to have a dramatic advantage over existing techniques, allowing far longer simulation times to be calculated reliably.
Generalisation of theory and algorithms for the configurational temperature Nosé–Hoover thermostat.
(2015) Beckedahl, Derrick.; Sergi, Alessandro.; Petruccione, Francesco.; Uken, Daniel Alexander.
In this dissertation we reformulate the configurational temperature Nos`e-Hoover thermostat proposed by Braga and Travis (C. Braga and K.P. Travis, 2005), using the antisymmetric matrix formalism found in (A. Sergi, 2003). By exploiting the properties of this formalism, and utilising the concept behind the Nos`e-Hoover chain thermostat, we extend our reformulated thermostat to obtain a hybrid configurational-kinetic chain thermostat. This is done with a view to achieving an ergodic sampling of phase space. We derive an integration algorithm, based upon the symmetric Trotter factorisation of the Liouville operator, as well as symplectic position and velocity Verlet integrations schemes, for purposes of comparison. In the case of systems possessing non-harmonic and non-linear interaction potentials, a position-dependent harmonic approximation scheme is presented. The thermostats and integration schemes were tested on one-dimensional harmonic and quartic oscillators, where it was found that the hybrid configurational-kinetic temperature Nos`e-Hoover chain thermostat overcame the ergodicity problem, and the integration scheme based on the Trotter factorisation was the best performing.
Numerical sampling of nonadiabatic dynamics of quantum-classical systems.
(2010) Uken, Daniel Alexander.; Sergi, Alessandro.
The simulation of the dynamics of quantum systems is very di cult, due to the fact that, in general, it cannot be calculated exactly for interacting many-body systems. Brute force simulations of quantum dynamics are simply not feasible, and approximations need to be made. In many instances a quantum system can be approximated as a quantum-classical system, where only a subsystem of interest is treated quantum mechanically, and the rest is considered as a classical bath. When energy is free to be exchanged between the subsystem and its environment, the dynamics that occur is said to be nonadiabatic. This type of dynamics is challenging to calculate on a computer, as it can lead to large statistical errors at long times. Hence, there is a need for improved algorithms for nonadiabatic dynamics. In this thesis, a recently introduced nonadiabatic sampling scheme [A. Sergi and F. Petruccione, Phys. Rev. E 81, 032101 (2010)] is used to calculate the long-time dynamics of a model system comprising a quantum spin coupled to a bath of harmonic oscillators. Also, various technical aspects of the algorithm are investigated.