Related papers: Geometrical and Algebraic Structures in Quantum Ha…
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a K\"{a}hler structure. We find an explicit relation…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
In this note, we explore some recent advancements in enumerative algebraic geometry, focusing particularly on the role of quantum K-theory of quiver varieties as viewed through the lens of integrable systems. We highlight a number of…
We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces…
We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…
This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…