Related papers: Hahn's Symmetric Quantum Variational Calculus
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar…
We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential…
Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
Following a recently introduced approach to approximate Lie symmetries of differential equations which is consistent with the principles of perturbative analysis of differential equations containing small terms, we analyze the case of…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems,…
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of…
In this paper, we use the quantum variational calculus related to Hahn's discrete time derivative construct the deformed version for the classical mechanics related to the Hahn's calculus. We deal with the deformed dynamics such as the…
We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing…
We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…