Related papers: Towards the topological quantization of classical …
Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Topological properties of quantum systems are one of the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
A canonical quantisation of the coordinates of the spacetime within the general relativity theory is proposed. This quantisation will depend on the observer but it provides an interesting perspective on the problem of relating the…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…