Related papers: Analytical solutions of basic models in quantum op…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
These notes, intended to be self contained and tutorial, present a direct, macroscopic approach to quantizing light inside a linear-response dielectric material when both spectral dispersion and spatial nonuniformity are present, but the…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T-Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend this problem to differential equations having an…
The desire to understand the interaction between light and matter has stimulated centuries of research, leading to technological achievements that have shaped our world. One contemporary frontier of research into light-matter interaction…
We extend the Quantum Memory Matrix (QMM) framework, originally developed to reconcile quantum mechanics and general relativity by treating space-time as a dynamic information reservoir, to incorporate the full suite of Standard Model gauge…
A rigorous treatment of light-matter interactions typically requires an interacting quantum field theory. However, most applications of interest are handled using classical or semiclassical models, which are valid only when quantum-field…
We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic…
The focus of this work is a correspondence between the Hilbert space operators on one hand, and doubly periodic generalized functions on the other. The linear map that implements it, referred to as the Q-transform, enables a direct…
We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is coupled to a dark-matter perfect fluid in the spatially flat Friedmann-Robertson-Walker Universe. This allows an energy exchange in…
Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
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…
We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay.…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
Effective nonlinear optical interactions are essential for many applications in modern photonics. In this paper, we investigate the role of the nonlinear response of a material to improve quantum metrology. In particular, the collective…
We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaitre-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via…