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This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also…
Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…
Present atomic theory provides accurate and reliable results for atoms with a small number of valence electrons. However, most current methods of calculations fail when the number of valence electrons exceeds four or five. This means that…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
Nuclei are prototypes of many-body open quantum systems. Complex aggregates of protons and neutrons that interact through forces arising from quantum chromo-dynamics, nuclei exhibit both bound and unbound states, which can be strongly…
Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster…
Quantum mechanics is characterized by quantum coherence and entanglement. After having discovered how these fundamental concepts govern physical reality, scientists have been devoting intense efforts to harness them to shape future science…
A method is proposed for evaluation of single and double layer potentials of the Laplace and Helmholtz equations on piecewise smooth manifold boundary elements with constant densities. The method is based on a novel two-term decomposition…
The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the…
Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyse this…
We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…
In classical mechanics, a procedure for simultaneous synchronization in all inertial frames is consistent with the Galilean transformation. However, if one attempts to achieve such a synchronization utilizing light signals, he will be…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
The ability to control the motion of mechanical systems through its interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…
We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to…
Nuclear lattice effective field theory has become an important framework for quantum many-body calculations in nuclear physics, yet its classical implementation remains increasingly challenging for more general interactions and larger…