Wigner Functions – Systems and Generalizations  

Specific Types of Systems > s.a. wigner functions / quantum systems [including particle on a circle].
@ General references: Dias & Prata JMP(02)qp/00 [with boundaries]; Curtright et al PLA(02)ht/01, Polkovnikov AP(10)-a0905 [many-body]; Tilma et al a1601 [for arbitrary quantum systems].
@ Qubits: Klimov et al AP(09)-a0806 [n qubits]; Barry & Drummond PRA(08)-a0808 [qubits, SU(n) coherent states]; Kijowski et al a1512 [one qubit].
@ Other discrete systems: Leonhardt PRL(95), PRA(96) [and tomography]; Atakishiyev et al JMP(98) [finite data sets]; Bianucci et al PLA(02) [e.g., quantum computers]; Luís PRA(04) [states on single phase-space points]; Gibbons et al PRA(04)qp [based on finite fields]; Galvão PRA(05)qp/04 [and computation]; Argüelles & Dittrich PhyA(05)qp; Cormick et al PRA(06)qp/05 [classicality]; Chaturvedi et al Pra(05)qp [algebraic]; Franco & Penna JPA(06)qp/05 [2 qubits, entanglement]; Ruzzi et al JPA(05) [Cahill-Glauber formalism]; Gross JMP(06)qp [non-negative]; Klimov et al qp/06-ln; Cormick & Paz PRA(06)qp [interference]; Wootters & Sussman a0704-proc [and minimum uncertainty states]; Gross & Eisert QIC(08)-a0710 [quantum Margulis expander map]; Casaccino et al PRA(08) [extrema]; Livine a0906; Adam et al JRLR-a1312 [qubits, and tomography].
@ Particle on a lattice: Takami et al PRA(01)hl/00; Hinarejos et al NJP(12)-a1205, NJP(15)-a1405 [infinite lattice].
@ H atom, Coulomb potential: Holstein AJP(95)aug; Nouri PRA(98); Praxmeyer et al JPA(06)qp/05.
@ Infinite potential walls: Belloni et al AJP(04)sep, Dong et al PS(04) [square well]; Walton AP(07)qp/06.
@ Damped systems: Chruściński mp/02; Belchev & Walton AP(09)-a0810 [and deformation quantization].
@ And tunneling: Heim et al PLA(13)-a1302 [through a parabolic barrier]; Lin & Dahlsten a1607 [negative Wigner function].
@ Angle and angular momentum: Kastrup PRA(16)-a1601; Kastrup a1702 [angle and orbital angular momentum].
@ Other systems: Lee PLA(90) [potential step, quantum potential]; Diósi & Kiefer JPA(02)qp/01 [Markovian open system]; Horvat & Prosen JPA(03), qp/06-proc [classically chaotic]; O'Connell JOB(03)qp [dissipative, decoherence]; Genovese et al qp/05 [open boundary, failure]; Regniers & Van der Jeugt JMP(10)-a1011 [simple 1D Hamiltonians]; Benavides-Riveros & Gracia-Bondía PRA(13)-a1207 [fermions and bosons]; Harland et al PRA(12)-a1210 [ensemble of spins or qubits]; Fischer et al NJP(13)-a1210 [for the orientation state of extended quantum objects]; Sels & Brosens PRE(13)-a1307 [system coupled to an external quantum system].
@ Field theory: Ochs & Heinz AP(98) [covariant]; Amorim et al PhyA(09); Giese et al proc(14)-a1402 [intro, and gravity]; > s.a. quantum cosmology; quantum dirac fields; quantum field theory in curved spacetime; spacetime geometry in quantum gravity.
> Related topics: see Kerr State; photon; quantum oscillator; spinning quantum particle.

Variations, Generalizations > s.a. deformation quantization [including constrained systems]; representations in quantum theory.
@ Relativistic: Sonego PRA(91); Morgan PLA(04)qp/03; Dragoman a0803 [and localization]; Campos et al PRA(14)-a1402 [non-classicality].
@ Discrete phase space: Gudder JMP(86); Bang & Berger PRA(09) [wave packets]; Hadhrami & Vourdas PRA(09) [fourth-order interference]; Marchiolli & Ruzzi AP(12); Van der Jeugt JPA(13)-a1310, Oste & Van der Jeugt JPA(14) [finite oscillator systems]; Zhu PRL(16)-a1504 [and permutation symmetry]; Przanowski & Tosiek a1609 [and number-phase Wigner function]; > s.a. random walk.
@ And deformation: Zachos IJMPA(02)ht/01; Costa Dias & Prata MPLA(05)ht-proc; Błaszak & Domański AP(12)-a1009 [rev].
@ Other phase spaces: Antonsen gq/97-proc; Alonso et al JMP(02)qp [hyperboloids], JMP(03) [spheres]; Gneiting et al PRA(13)-a1309 [curved configuration space]; Ligabò a1409 [torus phase space].
@ In non-commutative quantum mechanics: Wang et al a0908; Chowdhury & Twareque Ali JMP(15)-a1506 [group-representation based].
@ Other variations: Cohen JMP(66) [more general quasi-probability distribution functions]; Fairlie CSF(99)ht/98 [generalized Wigner function]; Hakioglu & Tepedelenlioglu JPA(00) [action-angle Wigner function]; Włodarz PLA(01); Curtright & Veitia JMP(07)qp [quasi-hermitian]; Ibort et al JPA(09) [on the space of irreducible representations of the Weyl-Heisenberg group]; Hu & Fan PRA(09) [generalized phase-space representation]; Beck & Sergi JPA(13) [partial Wigner picture]; Utz et al a1405 [extended, for particles with internal degrees of freedom].
> Related topics: see Fermi Function.


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