Related papers: Symplectic Coarse-Grained Classical and Semi-Class…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
We study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the Hilbert space $L^2(\rz^d)\otimes\kz^n$ into a finite number of almost invariant subspaces. For…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a Hamiltonian dynamics in an intrinsic time $\tau$ which samples a…
We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian $\mathsf H$ is given, as sum of quadratic forms, by $\mathsf H=…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…
Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We will present a consistent description of Hamiltonian dynamics on the ``symplectic extended phase space'' that is analogous to that of a time-\underline{in}dependent Hamiltonian system on the conventional symplectic phase space. The…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of an absolute space and time in which the physical objects are located and…
We compute numerically the time evolution of simple semiclassical states describing homogeneous and isotropic spatial geometries in quantum-reduced loop gravity under a deparametrized formulation of the dynamics, in which a reference matter…
We present here the first lattice simulation of symplectic quantization, a new functional approach to quantum field theory which allows to define an algorithm to numerically sample the quantum fluctuations of fields directly in Minkowski…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
Within the framework of Weyl calculus we establish a quantum-classical correspondence for the time evolution of observables generated by a Dirac-Hamiltonian. This includes a semiclassical separation of particles and antiparticles. We then…
The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in…
We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…