Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems

We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot, but shows potential for generalization. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. Importantly, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy and heat. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. Finally, we highlight several advantages of our approach in an exhaustive comparison with the Sinitsyn-Nemenmann full-counting statistics (FCS) approach to geometric pumping of an observable`s first moment. We explain how in the FCS approach an "adiabatic" approximation leads to a manifestly nonadiabatic result involving a finite retardation time of the response to parameter driving.Comment: Major changes: the text was reorganized and improved throughout. Several typos have been fixed: Note in particular in Eq. (87), (F3) and an important comment after (107). Throughout Sec V the initial time was incorrectly set to 0 instead of t_

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

Attractive and driven interactions in quantum dots: Mechanisms for geometric pumping

We analyze time-dependent transport through a quantum dot with electron-electron interaction that is statically tunable to both repulsive and attractive regimes, or even dynamically driven. Motivated by the recent experimental realization [A. Hamo et al., Nature (London) 535, 395 (2016)] of such a system in a static double quantum dot we compute the geometric pumping of charge in the limit of weak tunneling, high temperature, and slow driving. We analyze the responses for all possible pumping experiments or “driving protocols”, each defined by choosing a pair of driving parameters (gate voltage, bias voltage, tunnel coupling, electron-electron interaction). We show that such responses for different experiments can be governed by a common, underlying pumping mechanism, which is characterized by a set of effective parameters. The latter are nontrivial combinations of the experimentally driven parameters and other static parameters. If two different pumping experiments result in the same modulation of the effective parameters, i.e., the underlying mechanism is the same, then their responses will also be the same. Interestingly, for static attractive interaction we find a nonzero pumping response despite the attractive Coulomb blockade that hinders stationary transport. Furthermore, we identify a unique pumping response whose underlying mechanism relies on the interaction to be one of the driving parameters: it cannot be obtained with other sets of driving parameters. Finally, although a single-dot model with orbital pseudospin describes most of the physics of the mentioned experimental setup, it is crucial to account for the additional (real-)spin degeneracy of the double dot and the associated electron-hole symmetry breaking. This is necessary because the pumping response is more sensitive than dc transport measurements and detects this difference through pronounced qualitative effects