Related papers: Invariants for time-dependent Hamiltonian systems

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…

In this article, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic…

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…

By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic…

The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic…

It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…

Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…

A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant…

There exist a number of typical and interesting systems or models which possess three-generator Lie-algebraic structure in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator…

A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic…

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…

${\cal C}$-operators were introduced as involution operators in non-Hermitian theories that commute with the time-independent Hamiltonians and the parity/time-reversal operator. Here we propose a definition for time-dependent ${\cal…

We show that any Hamiltonian system with one degree of freedom is invariant under a $w_\infty$ algebra of symmetries.

We develop a general optimization strategy for performing a chosen unitary or non-unitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a…

Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…

Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…

The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…