Related papers: Integer characteristic polynomial factorization an…

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional…

This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…

The eigenstate thermalization hypothesis describes how isolated many-body quantum systems reach thermal equilibrium. However, quantum many-body scars and Hilbert space fragmentation violate this hypothesis and cause nonthermal behavior. We…

Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…

The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio,…

Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function $f$ in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization…

This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…

Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under…

We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in…

A central problem in formulating a theory of quantum gravity is to determine the size and structure of the Hilbert space of black holes. Here we use a quantum dynamical Krylov complexity approach to calculate the Hilbert space dimension of…

We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific…

A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1)D anti-de Sitter, Minkowskian and de Sitter…

We discuss rather systematically the principle, implicit in earlier works, that for a "random" element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the splitting field of the characteristic…

We compute the Hilbert series of the space of $n=3$ variable quasi-invariant polynomials in characteristic $2$ and $3$, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the…

Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…

Free fermions in disguise (FFD) Hamiltonians describe spin chains which can be mapped to free fermions, but not via a Jordan-Wigner transformation. Although the mapping gives access to the full Hamiltonian spectrum, the computation of spin…

We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain…

We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we…

The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…