Related papers: Topological structure of projective Hilbert spaces…
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasi-strings and quasi-membranes in their bulk states. In this study, we investigate the physics of these topological…
The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…
Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper…
We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
In this paper we elaborate on the structure of the continuous-time histories description of quantum theory, which stems from the consistent histories scheme. In particular, we examine the construction of history Hilbert space, the…
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…