Related papers: On Functionally Commutative Quantum Systems
In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.
We have used the homotopy analysis method to obtain solutions of linear and nonlinear fractional partial differential differential equations with initial conditions. We replace the first order time derivative by $\psi$-Caputo fractional…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
We introduce a type of quantum dissipation -- local quantum friction -- by adding to the Hamiltonian a local potential that breaks time-reversal invariance so as to cool the system. Unlike the Kossakowski-Lindblad master equation, local…
In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with a nonlinear deterministic clock.
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$ symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…