Related papers: Mayet-Godowski Hilbert Lattice Equations
We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…
This article introduces several new relations among related Hilbert space operators. In particular, we prove some L\"{o}ewner partial orderings among $T, |T|, \mathcal{R}T, \mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new…
In this paper, we focus on the fixed-circle problem on metric spaces by means of the multivalued mappings. We introduce new multivalued contractions using Wardowski's techniques and obtain new fixed-circle results related to multivalued…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
A first-order elliptic-hyperbolic system in extended projective space is shown to possess strong solutions to a natural class of Guderley-Morawetz-Keldysh problems on a typical domain.
Computing correlation functions in strongly-interacting quantum systems is one of the most important challenges of modern condensed matter theory, due to their importance in the description of many physical observables. Simultaneously, this…
An integrable spin-ladder model with nearest-neighbor exchanges and biquadratic interactions is proposed. With the Bethe ansatz solutions of the model hamiltonian, it is found that there are three possible phases in the ground state, i.e.,…
The Bethe Ansatz equations for the one-dimensional Hubbard model are reexamined. A new procedure is introduced to properly include bound states. The corrected equations lead to new elementary excitations away from half-filling.
Motived by the study of motion in a random environment we introduce and investigate a variant of the Temperley-Lieb algebra. This algebra is very rich, providing us three classes of solutions of the Yang-Baxter equation. This allows us to…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can…
A remarkable progress has been made in the understanding of the hot and dense QCD matter using lattice gauge theory. The issues which are very well understood as well those which require both conceptual as well as algorithmic advances are…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…
We show that finite lattices with arbitrary boundaries may support large degenerate subspaces, stemming from the underlying translational symmetry of the lattice. When the lattice is coupled to an environment, a potentially large number of…
We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the…