Related papers: Quantum mechanics in phase space: First order comp…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter…
We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\tfrac{1}{2}$ systems. We develop a…
Topological strings on toric Calabi--Yau threefolds can be defined non-perturbatively in terms of a free Fermi gas of N particles. Using this approach, we propose a definition of quantum mirror curves as quantum distributions on phase…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
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…
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…
We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…
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…
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
We consider a system of quantum degenerate spin polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
We consider the real time dynamics of $N$ noninteracting fermions in $d=1$. They evolve in a trapping potential $V(x)$, starting from the equilibrium state in a potential $V_0(x)$. We study the time evolution of the Wigner function…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…