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The Global ETD Search service is a free service for researchers
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Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Isothermal quantum dynamics: Investigations for the harmonic oscillatorMentrup, Detlef 26 May 2003 (has links)
Thermostated time evolutions are on a firm ground and widely used in classical molecular dynamics (MD) simulations. Hamilton´s equations of motion are supplemented by time-dependent pseudofriction terms that convert the microcanonical isoenergetic time evolution into a canonical isothermal time evolution, thus permitting the calculation of canonical ensemble averages by time averaging. However, similar methods for quantum MD schemes are still lacking. Given the rich dynamical behavior of ultracold trapped quantum gases depending on the value of the s-wave scattering length, it is timely to investigate how classical thermostating methods can be combined with powerful approximate quantum dynamics schemes to deal with interacting quantum systems at finite temperature. In this work, the popular method of Nose and Hoover to create canonically distributed positions and momenta in classical MD simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states may be modified in a Nose-Hoover manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. The method is developed initially for a single particle and then generalized to the case of an arbitrary number of identical quantum particles, involving entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain additional terms leading to Bose-attraction and Pauli-blocking, respectively. Questions of ergodicity are discussed for different coupling schemes. In the many-particle case, the superiority of the Nose-Hoover technique to a Langevin approach is demonstrated. In addition, the work contains an investigation of the Grilli-Tosatti thermostating method applied to the harmonic oscillator, and calculations for quantum wavefunctions moving with a time-invariant shape in a harmonic potential.
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Investigation of the emergence of thermodynamic behavior in closed quantum systems and its relation to standard stochastic descriptionsSchmidtke, Daniel 20 August 2018 (has links)
Our everyday experiences teach us that any imbalance like temperature gradients, non-uniform particle-densities etc. will approach some equilibrium state if not subjected to any external force. Phenomenological descriptions of these empirical findings reach back to the 19th century where Fourier and Fick presented descriptions of relaxation for macroscopic systems by stochastic approaches. However, one of the main goals of thermodynamics remained the derivation of these phenomenological description from basic microscopic principles. This task has gained much attraction since the foundation of quantum mechanics about 100 years ago. However, up to now no such conclusive derivation is presented. In this dissertation we will investigate whether closed quantum systems may show equilibration, and if so, to what extend such dynamics are in accordance with standard thermodynamic behavior as described by stochastic approaches. To this end we consider i.a. Markovian dynamics, Fokker-Planck and diffusion equations. Furthermore, we consider fluctuation theorems as given e.g. by the Jarzynski relation beyond strict Gibbsian initial states. After all we find indeed good agreement for selected quantum systems.
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Application of Projection Operator Techniques to Transport Investigations in Closed Quantum SystemsSteinigeweg, Robin 28 August 2008 (has links)
The work at hand presents a novel approach to transport in closed quantum systems. To this end a method is introduced which is essentially based on projection operator techniques, in particular on the time-convolutionless (TCL) technique. The projection onto local densities of quantities such as energy, magnetization, particles, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. Especially, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems. The term modular basically corresponds to (quasi-) one-dimensional structures consisting of identical or at least similar many-level subunits. Modular quantum systems are demonstrated to represent many physical situations and several examples are given. In the context of these quantum systems lowest order TCL is shown as an efficient tool which also allows to investigate the dependence of transport on the considered length scale. In addition an estimation for the validity range of lowest order TCL is derived. As a first application a "design" model is considered for which a complete characterization of all available transport types as well as the transitions to each other is possible. For this model the relationship to quantum chaos and the validity of the Kubo formula is further discussed. As an example for a "real" system the Anderson model is finally analyzed. The results are partially verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization or approximative integrators.
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Das Verhältnis zwischen Journalismus und Public Relations. Ressort und Status der Informationsquelle als Einflussfaktoren. / Eine Fallstudie am Beispiel der Thüringer Allgemeine. / The relationship between journalism and public relations. Editorial departments and the status of information sources as influencing factors. / A case study of the Thüringer Allgemeine.Riesmeyer, Claudia 23 March 2006 (has links)
No description available.
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