Related papers: The Garden of Quantum Spheres
The convex hull on three points in two dimensional euclidean space of three flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the area of space is performed. It is shown that it reproduces exactly the equidistant…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented.
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three…
Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.
Quantum dots can confine single electrons or holes to define spin qubits that can be operated with high fidelity. Experimental work has progressed from linear to two-dimensional arrays of quantum dots, enabling qubit interactions that are…
A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are…
Let us consider a sphere $S^{n-1}$ of radius $r$ in $\mathbb{R}^n$, where we have fixed poles $N$ and $S$. Suppose that $K$ is a set in $\mathbb{R}^n$ containing a translated copy of each meridian (that is an $S^{n-2}$-sphere) of $S^{n-1}$.…
In this paper we define $q$-spherical surfaces as the surfaces that contain the absolute conic of the Euclidean space as a $q-$fold curve. Particular attention is paid to the surfaces with singular points of the highest order. Two classes…
We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is "easy",…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
This is a brief, popular-level introduction to holographic entanglement. It was published in the newsletter of the International Centre for Theoretical Sciences, Bangalore.
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
The scalar matter and gravity are unified into the geometric scalar matter and quantized. The quantum with a definite 3-metric has definite energy but does not have well-defined momentum. The quantum theory resolves singularities.
An integral lattice which is generated by some vectors of norm $q$ is called $q$-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices…
A survey of results on quantum Poincare groups and quantum Minkowski spaces is presented.
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…
In three dimensional Euclidean space, a raspberry is defined to be an arrangement of spheres with pairwise disjoint interiors, where all spheres are tangent to a central unit sphere and such that the contact graph of the non-central spheres…
Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific…