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Alexej Schelle

Publications and source records attributed to Alexej Schelle.

9 recordsLinked to original sources
arXiv2026

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.

cs.AR↗
arXiv2025

Secure Text Mail Encryption with Generative Adversarial Networks

This work presents an encryption model based on Generative Adversarial Networks (GANs). Encryption of RTF-8 data is realized by dynamically generating decimal numbers that lead to the encryption and decryption of alphabetic strings in integer representation by simple addition rules, the modulus of the dimension of the considered alphabet. The binary numbers for the private dynamic keys correspond to the binary numbers of public reference keys, as defined by a specific GAN configuration. For reversible encryption with a bijective mapping between dynamic and reference keys, as defined by the GAN encryptor, secure text encryption can be achieved by transferring a GAN-encrypted public key along with the encrypted text from a sender to a receiver. Using the technique described above, secure text mail transfer can be realized through component-wise encryption and decryption of text mail strings, with total key sizes of up to $10^{8}$ bits that define random decimal numbers generated by the GAN. From the present model, we assert that encrypted texts can be transmitted more efficiently and securely than from RSA encryption, as long as users of the specific configuration of the GAN encryption model are unaware of the GAN encryptor circuit and configuration, respectively.

cs.CR↗
arXiv2024

Physical aspects of symmetry breaking in Bose gases at thermal equilibrium

The theory of non-interacting Bose gases is supplemented by a numerical quantum field description with a two-dimensional non-local order parameter that allows the modeling of wave-like atomic correlations and interference effects in the limit of low atomic densities. From the present model, it is possible to explain symmetry aspects of non-interacting and very weakly interacting Bose gases in the limit of fluctuating particle numbers, like the forward propagation of time and the relation to the breaking and preservation of phase gauge symmetry in solids. In the present formalism, the propagation of one-directional time arises from the pre-defined and equivalent convergence of independent quantum fields towards the Boltzmann equilibrium, and it is shown that Glauber coherent states are related to the definition of the quantized field. Coherently coupling condensate and non-condensate parts as a direct consequence of the increasing quantum coherence time between the different quantum field components in the Bose gas from cooling to below the critical temperature, the present model describes symmetry breaking, which is originally known from the definition of a specific gauge field from Elitzur's theorem for local gauge fields, as a global physical rather than a purely formal mathematical process.

cond-mat.quant-gas↗
arXiv2024

Josephson oscillations of two weakly coupled Bose-Einstein condensates

A numerical experiment based on a particle number-conserving quantum field theory is performed for two initially independent Bose-Einstein condensates that are coherently coupled at two temperatures. The present model illustrates ab initio that the initial phase of each of the two condensates doesn't remain random at the Boltzmann equilibrium, but is distributed around integer multiple values of $2\pi$ from the interference and thermalization of forward and backward propagating matter waves. The thermalization inside the atomic vapors can be understood as an intrinsic measurement process that defines a temperature for the two condensates and projects the quantum states to an average wave field with zero (relative) phases. Following this approach, focus is put on the original thought experiment of Anderson on whether a Josephson current between two initially separated Bose-Einstein condensates occurs in a deterministic way or not, depending on the initial phase distribution.

cond-mat.quant-gas↗
arXiv2022

Finite phase coherence time of a bosonic quantum field at the Boltzmann equilibrium

A quantitative quantum field approach with non-local order parameters is presented for a very weakly interacting, dilute Bose gas. Within the presented model, which assumes the constraint of particle number conservation at constant average energy in the canonical ensemble, it is shown that both coherent oscillations, as well as decay times of quantum coherence for the forward and backward propagating components of the quantum field created by the atomic cloud of a very weakly interacting Bose-Einstein condensate, are defined by a unique time variable. Within the present numerical theory, a quantitative estimate for the unit time scale for time propagation of a particle in a very weakly interacting Bose gas is derived from the coherence time of the wave field and it is illustrated that this time scale defines a unit time for transitions between different realizations of the Boltzmann equilibrium as defined by the maximum entropy from the vanishing of the chemical potential.

cond-mat.quant-gas↗
arXiv2014

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.

cond-mat.quant-gas↗
arXiv2011

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.

quant-ph↗
arXiv2010

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.

quant-ph↗