Related papers: Time Dependent Quantum Mechanics
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (tdependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical…
We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…
We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
It is shown that the time-dependent equations (Schr\"odinger and Dirac) for a quantum system can be always derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…