Related papers: Wigner functional theory for quantum optics
A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any…
For quantum systems with two dimensional configuration space we construct a physical radial momentum observable. Rescaling the radius we find the dilatonic degrees of freedom form a Weyl algebra. With this we construct the radial Wigner…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…
The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this…
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
Traditional theories of electron transport in crystals are based on the Boltzmann equation and do not capture physics arising from quantum coherence. We introduce a transport formalism based on ''orbital Wigner functions'', which accurately…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation, and measurement techniques, in particular, by the…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
The formal solution of a general stargenvalue equation is presented, its properties studied and a geometrical interpretation given in terms of star-hypersurfaces in quantum phase space. Our approach deals with discrete and continuous…
Higher (2nd)-order Wigner distribution function in quantum phase space for entangled bi-modal coherent states, a representative of higher (2nd)-order optical-polarization, is introduced by generalizing kernel (transiting) operator in…