Related papers: KW-models for (multivariate) linear differential s…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…
In this paper we propose a Kronecker-based modeling for identifying the spatial-temporal dynamics of large sensor arrays. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its…
This work discusses quantum states defined in a finite-dimensional Hilbert space. In particular, after the presentation of some of them and their basic properties the work concentrates on the group of the quantum optical models that can be…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
The Lee-Wick Standard Model assumes a minimal set of higher-derivative quadratic terms that produce a negative-norm partner for each Standard Model particle. Here we introduce additional terms of one higher order in the derivative expansion…
Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and…