Related papers: Applications of Canonical Transformations
A system of linearly coupled quantum harmonic oscillators can be diagonalized when the system is dynamically stable using a Bogoliubov canonical transformation. However, this is just a particular case of more general canonical…
We consider the process of changing reference frames in the case where the reference frames are quantum systems. We find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system…
Canonical methods of quasiclassical dynamics make it possible to go beyond a strict background approximation for cosmological perturbations by including independent fields such as correlation degrees of freedom. New models are introduced…
We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be…
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is…
We investigate two prototypical dissipative bosonic systems under slow driving and arbitrary system-bath coupling strength, recovering their dynamic evolution as well as the heat and work rates, and we verify that thermodynamic laws are…
Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…
A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a…
We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…
A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical…