Related papers: Study on a Phase Space Representation of Quantum T…
We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…
Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is…
Introduction Phase space methods in quantum mechanics - The Wigner function - The Husimi function - Inverse participation ratio Anderson model in phase space - Husimi functions - Inverse participation ratios
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with 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…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
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…
The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$,…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…
We study a class of optical circuits with vacuum input states consisting of Gaussian sources without coherent displacements such as down-converters and squeezers, together with detectors and passive interferometry (beam-splitters,…