Related papers: Phase Space Correspondence between Classical Optic…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
Quantum optics with quantum gases represents a new field, where the quantum nature of both light and ultracold matter plays equally important role. Only very recently this ultimate quantum limit of light-matter interaction became feasible…
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
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…
Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features -- for which no classical explanation exist -- and their interrelations is of foundational interest. Moreover, recognizing non-classical…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
The close analogy between geometrical optics and the classical theories of charged-particle beam optics have been known for a very long time. In recent years, quantum theories of charged-particle beam optics have been presented with the…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that,…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information…
It is well known that in classical optics, the visibility of interference, in a two-beam light interference, is related to the optical coherence of the two beams. A wave-particle duality relation can be derived using this mutual coherence.…
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
The correspondence principle bridges the quantum and classical worlds by establishing a direct link between their dynamics. This well-accepted tenant of quantum physics has been explored in quantum systems wherein the number of particles is…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…