相关论文: A Few Exactly Solvable Models For Riccati Type Equ…

The discovery of chaotic quantum circuits with (partially) solvable dynamics has played a key role in our understanding of non-equilibrium quantum matter and, at the same time, has helped the development of concrete platforms for quantum…

One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…

A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples…

We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…

In this note we establish a relation between two exactly-solvable problems on circle, namely singular Coulomb and singular oscillator systems.

In this paper we first consider a linear time invariant systems with almost periodic forcing term. We propose a new deterministic quadratic control problem, motivated by Da-Prato. With the help of associated degenerate Riccati equation we…

The stability of a recently developed piecewise flat Ricci flow is investigated, using a linear stability analysis and numerical simulations, and a class of piecewise flat approximations of smooth manifolds is adapted to avoid an inherent…

This paper discusses the discrete-time mean-field stochastic linear quadratic optimal control problems, whose weighting matrices in the cost functional are not assumed to be definite. The open-loop solvability is characterized by the…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…

The Riccati equation method is used to establish some new oscillatory criteria for the hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the hamiltonian system.…

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of…

An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati…

The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time invariant control systems. Eigenvalue perturbation theory for the Hamiltonian…

We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…

This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in…

It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…

A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward…

We give a complete solution of the scattering problem for Jacobi matrices from a class which was recently introduced by E. Ryckman. We characterize the scattering data for this class and illustrate the inverse scattering on some simple…

We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by multiscale state equations. The multiscale nature of the problem can be leveraged to reformulate the associated…