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Alexej Schelle

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Published work

4 published item(s)

preprint2026arXiv

Fault tolerance estimation in digital circuits with visualised generative networks

We propose a new numerical method to estimate the fault tolerance of failure modes in digital circuit structures with a generative network sampling technique. From a random input of generated bitwise configurations of ideally digitalised analog currents in the digital circuit design with classical logical gates, expected output currents are compared to the realistic signals of a numerical experiment at the discriminator part of the Generative Adversarial Network (GAN) to calculate the deviation from ideal digital electronic signals, including various error modes, such as missing or interchanged logical devices. From the present analysis of a representation of the GAN in terms of complex variables, it is possible to evaluate the robustness in electronic designs by differentiating the impact of failure modes associated with different classical logical elements in the circuit.

preprint2016arXiv

Spontaneously broken gauge symmetry in a Bose gas with constant particle number

The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose-Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.

preprint2011arXiv

Transition of a mesoscopic bosonic gas into a Bose-Einstein condensate

The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.

preprint2010arXiv

Number-conserving master equation theory for a dilute Bose-Einstein condensate

We describe the transition of $N$ weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and non-condensate thermalization, we derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of $N$ non-interacting atoms.