Related papers: Numerical Evolution from the Hamiltonian
The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
In this paper, we discuss time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics. we give the time evolving equation for a class of $PT$-symmetric Hamiltonians and some conditions of the adiabatic approximation for…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
We present an algorithm for constructing analytically approximate integrals of motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
Evolutionary computation offers a variety of tools to solve complex real-world optimization problems. However, research often focuses on smaller, simplified problems and optimization algorithms that sometimes miss expectations in real-world…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…