Related papers: Formulation of general dynamical invariants and th…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems.…
We revise the Lewis-Riesenfeld invariant method for solving the quantum time-dependent harmonic oscillator in light of the Quantum Arnold Transformation previously introduced and its recent generalization to the Quantum…
Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators, one of which is the Hamiltonian. We show that…
Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath…
We construct Lewis-Riesenfeld invariants from two dimensional point transformations for two oscillators that are coupled to each other in space in a PT-symmetrical and time-dependent fashion. The non-Hermitian Hamiltonian of the model is…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the…
Starting with a time-independent Hamiltonian $h$ and an appropriately chosen solution of the von Neumann equation $i\dot\rho(t)=[ h,\rho(t)]$ we construct its binary-Darboux partner $h_1(t)$ and an exact scattering solution of…
A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to…
In this paper, we first analyze a parametric oscillator with both mass and frequency time-dependent. We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
The unitary operator corresponding to the classical canonical transformation that connects a general closed system to an open system under adiabatic conditions is found. The quantum invariant operator of the adiabatic open system is derived…
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realises a required quantum process or task, under the influence of a prevailing `background' Hamiltonian that cannot be manipulated. When the task…
We introduce algebraic approach for superoperators that might be useful tool for investigation of quantum (bosonic) multi-mode systems and its dynamics. In order to demonstrate potential of proposed method we consider multi-mode Liouvillian…