Related papers: Singular vector structure of quantum curves
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…
We consider the motivic Hall algebra of coherent sheaves over an irreducible reduced projective curve of arithmetic genus $1$. We introduce the composition subalgebra in the singular curve case, and show that it is isomorphic to the…
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
We introduce a new notion of a curvature of a superconnection, different from the one obtained by a purely algebraic analogy with the curvature of a linear connection. The naturalness of this new notion of a curvature of a superconnection…
For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to…
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…
The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure with singularities on the diagonal of the square of the curve.
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras.…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…