Duality for open fermion systems: energy-dependent weak coupling and quantum master equations

Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [Phys. Rev. B 93, 81411 (2016)] which allows for a drastic simplification of time-evolution calculations. In the weak-coupling limit, such a system can be associated with a unique dual physical system in which all energies are inverted, in particular the internal interaction. This paper generalizes this fermionic duality in two ways: we allow for weak coupling with arbitrary energy dependence and describe both occupations and coherences coupled by a quantum master equation for the density operator. We also show that whenever generalized detailed balance holds (Kolmogorov criterion), the stationary probabilities for the dual system can be expressed explicitly in terms of the stationary recurrence times of the original system, even at large bias. We illustrate the generalized duality by a detailed analysis of the rate equation for a quantum dot with strong onsite Coulomb repulsion, going beyond the commonly assumed wideband limit. We present predictions for (i) the decay rates for transient charge and heat currents after a gate-voltage quench and (ii) the thermoelectric linear response coefficients in the stationary limit. We show that even for pronouncedly energy-dependent coupling, all nontrivial parameter dependence in these problems is entirely captured by just two well-understood stationary variables, the average charge of the system and of the dual system. Remarkably, it is the latter that often dictates the most striking features of the measurable quantities (e.g., positions of resonances), underscoring the importance of the dual system for understanding the actual one.Comment: 25 pages + 2 pages appendix + 2 pages references, 7 figures. To be submitted to Phys. Rev.

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_

Shot noise of a mesoscopic two-particle collider

We investigate the shot noise generated by particle emission from a mesoscopic capacitor into an edge state reflected and transmitted at a quantum point contact (QPC). For a capacitor subject to a periodic voltage the resulting shot noise is proportional to the number of particles (both electrons and holes) emitted during a period. It is proportional to the product of transmission and reflection probability of the QPC independent of the applied voltage but proportional to the driving frequency. If two driven capacitors are coupled to a QPC at different sides then the resulting shot noise is maximally the sum of noises produced by each of the capacitors. However the noise is suppressed depending on the coincidence of the emission of two particles of the same kind.Comment: 4 pages, 2 figure

Fermion-parity duality and energy relaxation in interacting open systems

We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.Comment: 5 pages + 19 pages of Supplementary Materia

Acoustic measurements from a rotor blade-vortex interaction noise experiment in the German-Dutch Wind Tunnel (DNW)

Acoustic data are presented from a 40 percent scale model of the 4-bladed BO-105 helicopter main rotor, measured in the large European aeroacoustic wind tunnel, the DNW. Rotor blade-vortex interaction (BVI) noise data in the low speed flight range were acquired using a traversing in-flow microphone array. The experimental apparatus, testing procedures, calibration results, and experimental objectives are fully described. A large representative set of averaged acoustic signals is presented

Advancing-side directivity and retreating-side interactions of model rotor blade-vortex interaction noise

Acoustic data are presented from a 40 percent scale model of the four-bladed BO-105 helicopter main rotor, tested in a large aerodynamic wind tunnel. Rotor blade-vortex interaction (BVI) noise data in the low-speed flight range were acquired using a traversing in-flow microphone array. Acoustic results presented are used to assess the acoustic far field of BVI noise, to map the directivity and temporal characteristics of BVI impulsive noise, and to show the existence of retreating-side BVI signals. The characterics of the acoustic radiation patterns, which can often be strongly focused, are found to be very dependent on rotor operating condition. The acoustic signals exhibit multiple blade-vortex interactions per blade with broad impulsive content at lower speeds, while at higher speeds, they exhibit fewer interactions per blade, with much sharper, higher amplitude acoustic signals. Moderate-amplitude BVI acoustic signals measured under the aft retreating quadrant of the rotor are shown to originate from the retreating side of the rotor

Model helicopter rotor high-speed impulsive noise: Measured acoustics and blade pressures

A 1/17-scale research model of the AH-1 series helicopter main rotor was tested. Model-rotor acoustic and simultaneous blade pressure data were recorded at high speeds where full-scale helicopter high-speed impulsive noise levels are known to be dominant. Model-rotor measurements of the peak acoustic pressure levels, waveform shapes, and directively patterns are directly compared with full-scale investigations, using an equivalent in-flight technique. Model acoustic data are shown to scale remarkably well in shape and in amplitude with full-scale results. Model rotor-blade pressures are presented for rotor operating conditions both with and without shock-like discontinuities in the radiated acoustic waveform. Acoustically, both model and full-scale measurements support current evidence that above certain high subsonic advancing-tip Mach numbers, local shock waves that exist on the rotor blades ""delocalize'' and radiate to the acoustic far-field

Helicopter model rotor-blade vortex interaction impulsive noise: Scalability and parametric variations

Acoustic data taken in the anechoic Deutsch-Niederlaendischer Windkanal (DNW) have documented the blade vortex interaction (BVI) impulsive noise radiated from a 1/7-scale model main rotor of the AH-1 series helicopter. Averaged model scale data were compared with averaged full scale, inflight acoustic data under similar nondimensional test conditions. At low advance ratios (mu = 0.164 to 0.194), the data scale remarkable well in level and waveform shape, and also duplicate the directivity pattern of BVI impulsive noise. At moderate advance ratios (mu = 0.224 to 0.270), the scaling deteriorates, suggesting that the model scale rotor is not adequately simulating the full scale BVI noise; presently, no proved explanation of this discrepancy exists. Carefully performed parametric variations over a complete matrix of testing conditions have shown that all of the four governing nondimensional parameters - tip Mach number at hover, advance ratio, local inflow ratio, and thrust coefficient - are highly sensitive to BVI noise radiation

Wake Geometry Effects on Rotor Blade-Vortex Interaction Noise Directivity

Acoustic measurements from a model rotor wind tunnel test are presented which show that the directionality of rotor blade vortex interaction (BVI) noise is strongly dependent on the rotor advance ratio and disk attitude. A rotor free wake analysis is used to show that the general locus of interactions on the rotor disk is also strongly dependent on advance ratio and disk attitude. A comparison of the changing directionality of the BVI noise with changes in the interaction locations shows that the strongest noise radiation occurs in the direction of motion normal to the blade span at the time of interaction, for both advancing and retreating side BVI. For advancing side interactions, the BVI radiation angle down from the tip-path plane appears relatively insensitive to rotor operating condition and is typically between 40 and 55 deg below the disk. However, the azimuthal radiation direction shows a clear trend with descent speed, moving towards the right of the flight path with increasing descent speed. The movement of the strongest radiation direction is attributed to the movement of the interaction locations on the rotor disk with increasing descent speed