Related papers: Topological quantum mechanics and the first Chern …
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
Quantum rings have emerged as a playground for quantum mechanics and topological physics, with promising technological applications. Experimentally realizable quantum rings, albeit at the scale of a few nanometers, are 3D nanostructures.…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
The quantum transition between shifted zero-mode wave functions is shown to be induced by the systematic deformation of topological and non-topological defects that support the $1$-dim double-well (DW) potential tunneling dynamics. The…
We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…
Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important…
For quantum systems described by Schr\"odinger operators on the half-space $\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy is topologically quantised provided the Fermi energy lies in a gap of the bulk…
Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to…
By the application of $\phi$-mapping topological theory, the properties of vortices in quantum R\"ontgen effect is thoroughly studied. The explicit expression of the vorticity is obtained, wherein which the $\delta$ function indicates that…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
Different topological phases of quantum systems has become areas of increased focus in recent decades. In particular, the question of how to realize and manipulate systems with non-trivial first Chern number is pursued both experimentally…
The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…