Optimal protocols for Hamiltonian and Schr\"odinger dynamics

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schr\"odinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations of the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space.Comment: submitted to J. Stat. Mech.: Theor. Exp

Ginkgo biloba Extract EGb 761 Improves Vestibular Compensation and Modulates Cerebral Vestibular Networks in the Rat

Unilateral inner ear damage is followed by behavioral recovery due to central vestibular compensation. The dose-dependent therapeutic effect of Ginkgo biloba extract EGb 761 on vestibular compensation was investigated by behavioral testing and serial cerebral [18F]-Fluoro-desoxyglucose ([18F]-FDG)-μPET in a rat model of unilateral labyrinthectomy (UL). Five groups of 8 animals each were treated with EGb 761-supplemented food at doses of 75, 37.5 or 18.75 mg/kg body weight 6 weeks prior and 15 days post UL (groups A,B,C), control food prior and EGb 761-supplemented food (75 mg/kg) for 15 days post UL (group D), or control food throughout (group E). Plasma levels of EGb 761 components bilobalide, ginkgolide A and B were analyzed prior and 15 days post UL. Behavioral testing included clinical scoring of nystagmus, postural asymmetry, head roll tilt, body rotation during sensory perturbation and instrumental registration of mobility in an open field before and 1, 2, 3, 5, 7, 15 days after UL. Whole-brain [18F]-FDG-μPET was recorded before and 1, 3, 7, 15 days after UL. The EGb 761 group A (75 mg/kg prior/post UL) showed a significant reduction of nystagmus scores (day 3 post UL), of postural asymmetry (1, 3, 7 days post UL), and an increased mobility in the open field (day 7 post UL) as compared to controls (group E). Application of EGb 761 at doses of 37.5 and 18.75 mg/kg prior/post UL (groups B,C) resulted in faster recovery of postural asymmetry, but did not influence mobility relative to controls. Locomotor velocity increased with higher plasma levels of ginkgolide A and B. [18F]-FDG-μPET revealed a significant decrease of the regional cerebral glucose metabolism (rCGM) in the vestibular nuclei and cerebellum and an increase in the hippocampal formation with higher plasma levels of ginkgolides and bilobalide 1 and 3 days post UL. Decrease of rCGM in the vestibular nucleus area and increase in the hippocampal formation with higher plasma levels persisted until day 15 post UL. In conclusion, Ginkgo biloba extract EGb 761 improves vestibulo-ocular motor, vestibulo-spinal compensation, and mobility after UL. This rat study supports the translational approach to investigate EGb 761 at higher dosages for acceleration of vestibular compensation in acute vestibular loss

Ginkgo biloba Extract EGb 761 Improves Vestibular Compensation and Modulates Cerebral Vestibular Networks in the Rat

Unilateral inner ear damage is followed by behavioral recovery due to central vestibular compensation. The dose-dependent therapeutic effect of Ginkgo biloba extract EGb 761 on vestibular compensation was investigated by behavioral testing and serial cerebral [18F]-Fluoro-desoxyglucose ([18F]-FDG)-μPET in a rat model of unilateral labyrinthectomy (UL). Five groups of 8 animals each were treated with EGb 761-supplemented food at doses of 75, 37.5 or 18.75 mg/kg body weight 6 weeks prior and 15 days post UL (groups A,B,C), control food prior and EGb 761-supplemented food (75 mg/kg) for 15 days post UL (group D), or control food throughout (group E). Plasma levels of EGb 761 components bilobalide, ginkgolide A and B were analyzed prior and 15 days post UL. Behavioral testing included clinical scoring of nystagmus, postural asymmetry, head roll tilt, body rotation during sensory perturbation and instrumental registration of mobility in an open field before and 1, 2, 3, 5, 7, 15 days after UL. Whole-brain [18F]-FDG-μPET was recorded before and 1, 3, 7, 15 days after UL. The EGb 761 group A (75 mg/kg prior/post UL) showed a significant reduction of nystagmus scores (day 3 post UL), of postural asymmetry (1, 3, 7 days post UL), and an increased mobility in the open field (day 7 post UL) as compared to controls (group E). Application of EGb 761 at doses of 37.5 and 18.75 mg/kg prior/post UL (groups B,C) resulted in faster recovery of postural asymmetry, but did not influence mobility relative to controls. Locomotor velocity increased with higher plasma levels of ginkgolide A and B. [18F]-FDG-μPET revealed a significant decrease of the regional cerebral glucose metabolism (rCGM) in the vestibular nuclei and cerebellum and an increase in the hippocampal formation with higher plasma levels of ginkgolides and bilobalide 1 and 3 days post UL. Decrease of rCGM in the vestibular nucleus area and increase in the hippocampal formation with higher plasma levels persisted until day 15 post UL. In conclusion, Ginkgo biloba extract EGb 761 improves vestibulo-ocular motor, vestibulo-spinal compensation, and mobility after UL. This rat study supports the translational approach to investigate EGb 761 at higher dosages for acceleration of vestibular compensation in acute vestibular loss

Nichtgleichgewichtsdynamik der DNA-Entfaltung

In this thesis, the unfolding of DNA is used as a paradigm to address two topics in the field of the nonequilibrium thermodynamics of small systems. In the first project, a variety of systems is driven into a nonequilibrium steady state (NESS) to investigate whether these systems equilibrate with an effective temperature (see Chapter 4). The systems considered range from a colloidal particle in an optical trap to two-state and multiple-state DNA hairpins. For all systems, both experimental and theoretical results are available. The second project focuses on the feedback mechanism for the applied force in the DNA unfolding setup (see Chapter 5). Both experimental data and simulations are used to study the feedback-controlled dynamics, thus determining the set of feedback parameters for which the control of the force is optimized.In dieser Doktorarbeit wurde die Entfaltung von DNA als Paradigma für die Betrachtung von zwei Themen in dem Feld der Nichtgleichgewichtsthermodynamik von kleinen Systemen benutzt. In dem ersten Projekt wurde eine Vielfalt von Systemen in einen stationären Nichtgleichgewichtszustand (NESS) getrieben, um zu untersuchen, ob diese Systeme mit einer effektiven Temperatur equilibrieren (siehe Kapitel 4). Dabei reichen die betrachteten Systeme von einem kolloidalen Teilchen in einer optischen Falle hin zu DNA-Hairpins mit zwei oder vielen Zuständen. Für alle Systeme sind sowohl experimentelle als auch theoretische Ergebnisse verfügbar. Das zweite Projekt betrachtet den Feedback-Mechanismus für die angewendete Kraft in dem DNA-Entfaltungssetup (siehe Kapitel 5). Mit Hilfe von experimentellen Daten und Simulationen wird hier die Feedback-kontrollierte Dynamik untersucht und damit die Feedback-Parameter, für die die Kontrolle der Kraft optimiert ist, bestimmt