Related papers: Applications of Canonical Transformations
We investigate the intricate dynamics of quantum coherence and non-classical correlations in a two-qubit open quantum system coupled to a squeezed thermal reservoir. By exploring the correlations between spatially separated qubits, we…
We study dynamical systems which admit action-angle variables at leading order which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical…
We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which…
In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinate based approach are described in detail. In particular,…
We introduce nonlinear canonical transformations that yield effective Hamiltonians of multiphoton down conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton…
In this paper we consider the classical and quantum control of squeezed states of harmonic oscillators. This provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated systems in…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behavior. Exactly solvable examples are the Brownian motion of a quantum…
In the scheme of a quantum nondemolition (QND) measurement, an observable is measured without perturbing its evolution. In the context of studies of decoherence in quantum computing, we examine the `open' quantum system of a two-level atom,…
Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
We show that a squeezed bath, that acts on the central element of a harmonic chain, can drive the whole system to a steady state featuring a series of nested entangled pairs of oscillators that, ideally, covers the whole chain regardless of…
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…
The effect of chaotic bath dynamics on the decoherence of a quantum system is examined for the vibrational degrees of freedom of a diatomic molecule in a realistic, constant temperature collisional bath. As an example, the specific case of…
Collisional models are a category of microscopic framework designed to study open quantum systems. The framework involves a system sequentially interacting with a bath comprised of identically prepared units. In this regard, quantum…
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…