Related papers: Embedded Representations and Quasi-Dynamical Symme…
Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…
Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic…
Based on the boson realization of the Euclidean algebras, it is shown that the five-dimensional Euclidean dynamical symmetry may emerge at the triple point of the shape phase diagram of the interacting boson model, which thus offers a…
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…
Incorporating symmetries into the numerical solution of differential equations has been a mainstay of research over the last 40 years, however, one aspect is less known and under-utilised: discretisations of partial differential equations…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
Supersymmetry is one of the most plausible and theoretically motivated frameworks for extending the Standard Model. However, any supersymmetry in Nature must be a broken symmetry. Dynamical supersymmetry breaking (DSB) is an attractive idea…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell-model of nuclei and shown to be…
Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
In the late 1980's Sullivan initiated a programme to prove quasisymmetric rigidity in one-dimensional dynamics: interval or circle maps that are topologically conjugate are quasisymmetrically conjugate (provided some obvious necessary…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…