Related papers: Quantum differential systems and some applications…
The derivation of a quantum Markovian model for an opto-mechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is difficult problem which ultimately involves the…
The imposition of symmetry upon the nature and structure of quantum observables has recently been extensively studied, with quantum reference frames playing a crucial role. In this paper, we extend this work to quantum transformations,…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
A liaison between quantum logics and non-commutative differential geometry is outlined: a class of quantum logics are proved to possess the structure of discrete differential manifolds. We show that the set of proper elements of an…
Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
Given a smooth projective variety $X$ with a smooth anticanonical divisor $D$, we study mirror symmetry for the log Calabi--Yau pair $(X,D)$ without assuming that $D$ is nef. We consider the mirror proper Landau--Ginzburg model $(\check…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
In this paper, we propose a new way to approach qudit systems using toric geometry and related topics including the local mirror symmetry used in the string theory compactification. We refer to such systems as (n,d) quantum systems where…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere - which, with additional structures, we identify with the quantum projective line.…
We develop a quantum circuit model describing unitary interactions between quantum fields and a uniformly accelerated object, and apply it to a semi-transparent mirror which uniformly accelerates in the Minkowski vacuum. The reflection…
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of…
In this article we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology,…
The generalized notion of noncontextuality provides an avenue to explore the fundamental departure of quantum theory from a classical explanation. Recently, extracting a different form of quantum advantage in various information processing…
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…