Related papers: Topological quantum mechanics and the first Chern …
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
We briefly review the advanced mathematical language of fiber bundle structures and how they can be used to classify two-level quantum systems based on the analysis of the topological properties of their sets of state vectors. The…
We show that wavefunctions in a two-dimensional (2D) electron system with spin-orbit coupling can be characterized by a topological quantity--the Chern integer due to the existence of the intrinsic Kramers degeneracy. The…
The experimental shock wave, discovery in quantum systems is the important one through last years. This effect has several phenomenological explanations. It seems to us there is interesting, especially from the systematical point of view,…
We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these two approaches yields nontrivial…
Topological quantum error-correcting codes (QECC) encode a variety of topological invariants in their code space. A classic structure that has not been encoded directly is that of obstruction classes of a fiber bundle, such as the Chern or…
Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered. A quantum system with positions in the profinite group ${\mathbb Z}_p$ and momenta in the group ${\mathbb Q}_p/{\mathbb Z}_p$; and a…
The measurement problem of quantum mechanics concerns the question under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem…
Using the Madelung fluid picture of Schr\"odinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to…
We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of…
The Chern number has been widely used to describe the topological properties of periodic structures in the momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new…
Topological invariants are fundamental characteristics reflecting global properties of quantum systems, yet their exploration has predominantly been limited to the static (DC) transport and transverse (Hall) channel. In this work, we extend…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
We presented the topological current of Ehrenfest definition of phase transition. It is shown that different topology of the configuration space corresponds to different phase transition, it is marked by the Euler number of the interaction…
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…