Coherent Quantum Ratchets Driven by Tunnel Oscillations

We demonstrate that the tunnel oscillations of a biased double quantum dot can be employed as driving source for a quantum ratchet. As a model, we use two capacitively coupled double quantum dots. One double dot is voltage biased and provides the ac force, while the other experiences the ac force and acts as coherent quantum ratchet. The current is obtained from a Bloch-Redfield master equation which ensures a proper equilibrium limit. We find that the two-electron states of the coupled ratchet-drive Hamiltonian lead to unexpected steps in the ratchet current.Comment: 4 pages, 4 figure

A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options

Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time. Our approach is to recursively compute the so-called continuation values. They are defined as regression functions of the cash flow, which would occur over a series of subsequent time periods, if the approximated optimal exercise strategy is applied. We use nonparametric least squares regression estimates to approximate the continuation values from a set of sample paths which we simulate from the underlying stochastic process. The parameters of the regression estimates and the regression problems are chosen in a data-dependent manner. We present results concerning the consistency and rate of convergence of the new algorithm. Finally, we illustrate its performance by pricing high-dimensional Bermudan basket options with strangle-spread payoff based on the average of the underlying assets.Comment: Published in at http://dx.doi.org/10.1214/105051607000000249 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transport, shot noise, and topology in AC-driven dimer arrays

We analyze an AC-driven dimer chain connected to a strongly biased electron source and drain. It turns out that the resulting transport exhibits fingerprints of topology. They are particularly visible in the driving-induced current suppression and the Fano factor. Thus, shot noise measurements provide a topological phase diagram as a function of the driving parameters. The observed phenomena can be explained physically by a mapping to an effective time-independent Hamiltonian and the emergence of edge states. Moreover, by considering quantum dissipation, we determine the requirements for the coherence properties in a possible experimental realization. For the computation of the zero-frequency noise, we develop an efficient method based on matrix-continued fractions.Comment: 8 pages, 6 figure

Nonadiabatic Electron Pumping: Maximal Current with Minimal Noise

The noise properties of pump currents through an open double quantum dot setup with non-adiabatic ac driving are investigated. Driving frequencies close to the internal resonances of the double dot-system mark the optimal working points at which the pump current assumes a maximum while its noise power possesses a remarkably low minimum. A rotating-wave approximation provides analytical expressions for the current and its noise power and allows to optimize the noise characteristics. The analytical results are compared to numerical results from a Floquet transport theory.Comment: 4 pages, 3 figures, replaced Fig. 1, added new inset in Fig. 2, extended paragraph on symmetry consideration

Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF."Comment: Contains corrections to the published versio

Phase-matched coherent hard x-rays from relativistic high-order harmonic generation

High-order harmonic generation (HHG) with relativistically strong laser pulses is considered employing electron ionization-recollisions from multiply charged ions in counterpropagating, linearly polarized attosecond pulse trains. The propagation of the harmonics through the medium and the scaling of HHG into the multi-kilo-electronvolt regime are investigated. We show that the phase mismatch caused by the free electron background can be compensated by an additional phase of the emitted harmonics specific to the considered setup which depends on the delay time between the pulse trains. This renders feasible the phase-matched emission of harmonics with photon energies of several tens of kilo-electronvolt from an underdense plasma

Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descent

Estimation of a regression function from independent and identically distributed random variables is considered. The $L_2$ error with integration with respect to the design measure is used as an error criterion. Over-parametrized deep neural network estimates are defined where all the weights are learned by the gradient descent. It is shown that the expected $L_2$ error of these estimates converges to zero with the rate close to $n^{-1/(1+d)}$ in case that the regression function is H\"older smooth with H\"older exponent $p \in [1/2,1]$. In case of an interaction model where the regression function is assumed to be a sum of H\"older smooth functions where each of the functions depends only on $d^*$ many of $d$ components of the design variable, it is shown that these estimates achieve the corresponding $d^*$-dimensional rate of convergence