Christian Bracher

Zalando SE, Berlin · Zalando Research

Attention is a general reasoning mechanism than can flexibly deal with image information, but its memory requirements had made it so far impractical for high resolution image generation. We present Grid Partitioned Attention (GPA), a new approximate attention algorithm that leverages a sparse inductive bias for higher computational and memory effic...

Visual search, in particular the street-to-shop task of matching fashion items displayed in everyday images with similar articles, is a challenging and commercially important task in computer vision. Building on our successful Studio2Shop model [20], we report results on Street2Fashion2Shop, a pipeline architecture that stacks Studio2Fashion, a seg...

Online fashion sales present a challenging use case for personalized recommendation: Stores offer a huge variety of items in multiple sizes. Small stocks, high return rates, seasonality, and changing trends cause continuous turnover of articles for sale on all time scales. Customers tend to shop rarely, but often buy multiple items at once. We repo...

We present a method to determine Fashion DNA, coordinate vectors locating fashion items in an abstract space. Our approach is based on a deep neural network architecture that ingests curated article information such as tags and images, and is trained to predict sales for a large set of frequent customers. In the process, a dual space of customer st...

This paper considers the probability density and current distributions generated by a pointlike, isotropic source of monoenergetic charges embedded in a uniform magnetic field environment. Electron sources of this kind have been realized in recent photodetachment microscopy experiments. Unlike the total photocurrent cross section, which is largely...

Near-threshold photodetachment of negative ions provides a practical means to operate an almost point-like, coherent, monochromatic source of electrons. Due to their charge, the emitted electron matter-waves are easily manipulated by external electromagnetic fields. In our contribution, we present the influence of a homogeneous magnetic field on th...

I reexamine Heisenberg's uncertainty relation for two- and three-dimensional wave packets with fixed angular momentum quantum numbers m or l. A simple proof shows that the product of the average extent Deltar and Deltap of a two-dimensional wave packet in position and momentum space is bounded from below by DeltarDeltap>=ℏ(|m|+1). The minimu...

Near-threshold photodetachment of negative atomic ions provides an almost monochromatic, nearly pointlike source of electrons that can be used to probe the quantum dynamics of electrons in externally applied electromagnetic fields. These fields cause modulations both in the observed photocurrent spectrum, and the spatial distribution of the emitted...

Progress in manufacturing technology has allowed us to probe the behavior of devices on a smaller and faster scale than ever before. With increasing miniaturization, quantum effects come to dominate the transport properties of these devices, between collisions, carriers undergo ballistic motion under the influence of local electric and magnetic fie...

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symme...

Progress in manufacturing technology has allowed us to probe the behavior of devices on a smaller and faster scale than ever before. With increasing miniaturization, quantum effects come to dominate the transport properties of these devices; between collisions, carriers undergo ballistic motion under the influence of local electric and magnetic fie...

In the present study, we develop a kinetic lattice gas model for hopping in an inhomogeneous one-dimensional adsorbate system with nearest-neighbor interactions and periodic boundary conditions. From the matrices of the associated equations of motion, we can calculate adsorbate correlation functions in momentum space exactly on all time and length...

Near-threshold photodetachment from negative atomic ions provides a virtually pointlike source of electrons, and is ideally suited to study electron dynamics in externally applied electric and magnetic fields. These fields govern the motion of the emitted electron wave, and lead to characteristic modulations both in the total photocurrent and in th...

Negative ions undergoing near-threshold photodetachment in a weak laser field provide an almost pointlike, isotropic source of low-energy electrons. External fields exert forces on the emitted coherent electron wave and direct its motion. Here, we examine the spatial distribution of photodetached electrons in uniform, parallel electric and magnetic...

Atoms and negative ions interacting with laser photons yield a coherent source of photoelectrons. Applying external fields to photoelectrons gives rise to interesting and valuable interference phenomena. We analyze the spatial distribution of the photocurrent using elementary quantum methods. The photoelectric effect is shown to be an interesting e...

The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadraticpolynomialinthepositionsandmomenta. The corresponding quantummechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well-known....

We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the class...

Real-space observation of single atoms and electron surface states lies at the heart of scanning tunneling microscopy. The resolution of atomic structures depends on quantum mechanical features such as three-dimensional tunneling, the Pauli principle, the possibility of electron resonances, and the importance of multiple scattering events, which al...

We predict photodetachment cross sections and spatial photoelectron distributions in parallel electric and magnetic fields. Near-threshold photodetachment cross-sections of negative ions in strong external electric fields show oscillations related to interference of outgoing with returning electron waves. The interference pattern can also be imaged...

The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a step depends on the relative orientation towards the preceding step. For all but the shortest walks, the prop...

We have investigated photodetachment from negative ions in a homogeneous 1.0-Tesla magnetic field and a parallel ac electric field of ˜ 10 V/cm. A brief theoretical model for detachment in combined fields is presented. Calculations show that a field of 10 V/cm or more should considerably diminish the Landau structure in the detachment cross section...

The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding quantum-mechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well...

We analyse the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field-induced quantum mechanical drift motion of (i) single electrons and (ii) a dilute Fermi gas of electrons. The method yields the drift current and, at...

Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are introduced into the Schrödinger equation. The source formalism yields direct access to the scattering wavefunction, pa...

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely prop...

Tunneling problems are characterized by different quantum time scales of motion. In this paper, we identify a tunneling time scale, which is based on a simple variational principle. The method utilizes the stationary eigenfunctions for a given one-dimensional potential structure, and it provides a truly local definition of the tunneling time, indep...

Im Rahmen dieser Arbeit wird das Konzept der stationären Multipolquelle als Modell für Streuprozesse in der Quantenmechanik eingeführt und auf das geschlossen lösbare Problem des homogenen Kraftfeldes in drei räumlichen Dimensionen angewandt. Die dabei erhaltenen ballistischen Multipol-Wellenfunktionen eröffnen einen einfachen und erfolgversprechen...

Backscattering of atomic beams above a given surface yields information similar to the one obtained from scanning the same surface with a scanning tunneling microscope (STM): In both cases the experimentally accessible quantity is the local density of states (LDOS) n(r,E) of the surface. For the case of backscattering, the LDOS at the turning point...

Starting out with the dwell time approach by Smith for stationary one-dimensional tunneling problems, we introduce the notion of the minimum tunneling time required for traversal through an arbitrary potential barrier. The newly devised time scale is based on a simple variational principle and presents a strictly local quantity not depending on the...

Starting out with the dwell time approach by Smith for stationary one‐dimensional tunneling problems, we introduce the notion of the minimum tunneling time required for traversal through an arbitrary potential barrier. The newly devised time scale is based on a simple variational principle and presents a strictly local quantity not depending on the...

We discuss a novel source-theoretical description of the STM based on the concepts of quantum-mechanical scattering theory. As an application of the formalism, we study how the presence of a crystalline adsorbate layer alters the tunneling current for a simplified one-dimensional surface model.

We provide an elementary case study of field-induced quantum tunneling in a realistic three-dimensional environment which exhibits both tunneling and classically allowed motion. An analytic description is presented for ballistic motion in a uniform electric field. From there we derive simple expressions concerning the wave function for field emissi...

We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the tip of a scanning tunneling microscope. The method is based on propagators (or Green functions) for quasistationary scattering with the tip being an electron source (or sink). The results for the tunneling current generalize the Tersoff-Hamann approach...

The interaction of light and matter provides a `clock' which allows us to extract characteristic timescales of quantum motion. Two-level atoms temporarily subjected to a radiation field will undergo Rabi oscillations, and the rotation angle of the corresponding Bloch vector serves as a measure of the interaction time. The approach is closely relate...

this report, we present a simple geometric generation principle

this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to find the roots of a complex cubic. We show that a modified Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of...

Starting with wave packets, an eigenvalue equation is derived for the amount of time a particle needs for reflection from an impermeable potential barrier. The corresponding Hermitian operator TR is linear and diagonal in energy space. The eigenvalues are given by τ2(E) = ℏ , where ρ(E) is the phase shift for stationary reflection at fixed scatteri...