Related papers: Complexified phase spaces, initial value represent…
Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term…
A simplified mathematical model is suggested to describe the dynamics of a quasi-monochromatic optical wave in the bulk of an effectively isotropic metamaterial with averaged dielectrical permittivity near zero (ENZ medium), in the presence…
We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincar\'e generators explicitly from field operators and show that in the vector spaces for the…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
In this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equation and the associated linearized Cahn-Hilliard (C-H) model…
Let $L$ be the function field of a projective space ${\mathbb P}^n_k$ over an algebraically closed field $k$ of characteristic zero, and $H$ be the group of projective transformations. An $H$-sheaf ${\mathcal V}$ on ${\mathbb P}^n_k$ is a…
Classical vector waves can possess intricate spin angular momenta (SAM), which are \emph{perpendicular} to the propagation direction, as revealed by the recent recognition of surprisingly transverse SAM in electromagnetic (EM) fields. In…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
Vector quantization approaches (VQ-VAE, VQ-GAN) learn discrete neural representations of images, but these representations are inherently position-dependent: codes are spatially arranged and contextually entangled, requiring autoregressive…
Charge ordering induced by strong short-range repulsion in itinerant fermion systems typically follows a two-sites alternation pattern. However, the covariance matrix spectrum of the one-dimensional, half-filled, spinless $t$-$V$ model…
Following Epstein-Glaser's work we show how a QFT formulation based on operator valued distributions (OPVD) with adequate test functions treats original singularities of propagators on the diagonal in a mathematically rigourous way.Thereby…
In this study, we present a comprehensive global spectral analysis of the convection dispersion equation, which is also referred to in specific contexts as the Korteweg de Vries (KdV) equation, to investigate the behaviour of high order…
A class of Fourier Integral Operators which converge to the unitary group of the Schroedinger equation in semiclassical limit $\eps\to 0$ is constructed. The convergence is in the uniform operator norm and allows for an error bound of order…
We present a detailed derivation of the semiclassical propagator in the SU(n) coherent state representation. In order to provide support for immediate physical applications, we restrict this work to the fully symmetric irreducible…
We systematically apply semisimplification functors in modular representation theory. Motivated by the Duflo--Serganova functor in Lie superalgebras, we construct various functors of interest. In the setting of finite groups, we refine the…
The recently introduced mixed time-averaging semiclassical initial value representation molecular dynamics method for spectroscopic calculations [M. Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is applied to…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…
Transmission through potential barriers is a fundamental problem in quantum mechanics. While semiclassical methods can approximate certain aspects of transmission, they fail to capture the intrinsically quantum interference associated with…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…