相关论文: A canonical transformation theory from extended no…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
Light-cone perturbation theory is a powerful tool for calculating high-energy scattering amplitudes, particularly for quantum particles such as electrons, photons, or protons scattering off heavy nuclei, a process analogous to potential…
This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem…
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…
We present a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables. We provide physical semantics to our approach in terms of quantum clocks and quantisation of time. We…
This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback.…
We apply the transcorrelated method to problems of multireference character. For this, we show that the choice of reference wavefunction during the Jastrow optimisation procedure is vital, and we propose a workflow wherein we use…
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
Canonical quantisation gives a new and convenient finite-temperature perturbation theory in covariant gauges, and solves the problem of the zero-frequency mode in the temporal gauge. [Talk at Workshop on Thermal Field Theories and their…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
The ion-induced long-range orientational order between water molecules recently observed in second harmonic scattering experiments and illustrated with large scale molecular dynamics simulations is quantitatively explained using the…
The simplified Lennard-Jones (LJ) potential minimization problem is $f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\frac{1}{\tau_{ij}^6} -\frac{1}{\tau_{ij}^3}) {subject to} x\in \mathbb{R}^n,$ where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2…
We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…
This paper mainly addresses the Monge mass transfer problem in the 1-D case. Through an ingenious approximation mechanism, one transforms the Monge problem into a sequence of minimization problems, which can be converted into a sequence of…
The well-known gyrokinetic problem regards the perturbative expansion related to the dynamics of a charged particle subject to fast gyration motion due to the presence of a strong magnetic field. Although a variety of approaches have been…
Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering,…
While rule-based attribution methods have proven useful for providing local explanations for Deep Neural Networks, explaining modern and more varied network architectures yields new challenges in generating trustworthy explanations, since…