Phenomenology of Quantum Uncertainties  

Configuration-Momentum Uncertainty Relation > s.a. equivalence principle; uncertainty relations [theoretical aspects].
@ Mixed states / density matrices: Park JMP(05)mp/04; Luo PRA(05); de Gosson & Luef PLA(07)qp.
@ Discrete observables: Brody & Meister JPA(99); Barchielli et al CMP(18)-a1608 [relative-entropy formulation].
@ Other states / systems: Trifonov JOSA(00)qp [coherent-squeezed states]; Trifonov PW(01)phy [minimizing states]; Kowalski & Rembieliński JPA(03)qp [on S1]; Fujikawa PTP(10)-a1009 [with periodic boundary conditions]; Miyadera JMP(11)-a1104 [finite-dimensional systems]; Al-Hashimi & Wiese AP(12) [particle in a box]; Dorsch & Nogueira IJMPA(12) [maximally localized states]; > s.a. coherent states.
@ System preparation / measurement: Park & Band FP(92); Krenn et al PRA(00)qp/95; de Muynck FP(00)qp/99; Werner qp/04-fs [joint measurement].
@ Violations, ways to beat it: Ozawa PLA(03)qp/02; Hall PRA(04)qp/03 [with prior information]; Kitano a0803 [not really violated]; Hänggi & Wehner nComm(12)-a1205 [and violations of the second law of thermodyamics]; > s.a. lines [open timelike curves].
@ Measurement of error and disturbance: news pw(12)jan [test of error-and-disturbance formulation]; Mochizuki JModP(13)-a1203 [measurability]; Rozema et al PRL(12)-a1208 [violation of Heisenberg's "measurement-disturbance relationship" by weak measurements]; Kaneda et al PRL(14) [experimental test].
@ Experimental tests: Görlich et al a0812; Chernega PS(12)-a1201-conf [homodyne photon state detection]; Ma et al PRL(16)-a1512 [based on statistical distances]; > s.a. Popper's Experiment.
@ Field theories: Moayedi et al IJMPA(11)-a1105 [spinor field with Quesne-Tkachuk algebra]; Husain et al PRD(13)-a1208 [free scalar field, Green's function]; > s.a. QED [fluxes] and modified QED; types of quantum field theory.

Other Uncertainties in Quantum Mechanics > s.a. modified uncertainty relations [other observables and types of relations]; quantum fluctuations.
@ Systems: Barros e Sá JMP(01) [SU(2)-invariant, \(\hbar\)2j ≤ Δ ≤ \(\hbar\)2j(j+1)]; Trifonov JPA(03) [particle on a circle]; Białynicki-Birula & Białynicka-Birula PRL(12)-a1110, PRA(12)-a1205, comment Wang et al PRL(12)-a1207 [for photons]; > s.a. spinors in field theory.
@ Entropic / information version: Sánchez-Ruíz PRA(98) [single- and double-slit]; Hiesmayr JPCS(11)-a1103 [decaying systems and CP violation].
@ Related topics: Soucek qp/04 [tests, with Δt ~ 10–12 s]; Bastos et al PRD(12)-a1207 [violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics].

GUP and Gravitational Systems > s.a. modified general relativity [neighbors, signature change]; modified lorentz symmetry.
@ Compact stars: Wang et al PLB(12)-a1110 [cores]; Farag Ali & Tawfik IJMPD(13)-a1301; Rashidi AP(16)-a1512, Mathew & Nandy a1712 [white dwarfs].
@ Black holes: Brout et al PRD(99)ht/98; Scardigli PLB(99)ht [micro-black holes]; Maziashvili PLB(06) [remnants]; Carr et al a1107; Maziashvili JCAP(13)-a1208 [remnants]; Casadio & Scardigli EPJC(14)-a1310 [horizon wave function, quantum black hole decay]; Dutta & Gangopadhyay GRG(14)-a1402 [entropy and remnant mass]; Carr a1402-proc [Black Hole Uncertainty Principle correspondence]; Scardigli & Casadio EPJC(14)-a1407 [and setting parameter bounds]; Tawfik & Diab IJMPA(15)-a1502; Carr et al JHEP-a1504 [sub-Planckian black holes].
@ Black hole thermodynamics: Xiang & Shen MPLA(04); Stetsko IJMPA(13)-a1205; Gangopadhyay et al GRG(14)-a1307; Tawfik & El Dahab IJMPA(15)-a1501 [entropy corrections]; > s.a. black-hole entropy, information and thermodynamics; specific types of black holes.
@ Other astrophysics: Majumder a1105 [perihelion precession of Mercury]; Maziashvili PRD(12)-a1206 [light incoherence in stellar interferometry].
@ Inflation: Hassan & Sloth NPB(03)ht/02; Nozari & Akhshabi IJMPD(10)-a0910; Tawfik et al GRG(13)-a1208 [and early-universe thermodynamics]; Tawfik & Diab EJTP-a1410 [and BICEP2 observations]; Gangopadhyay et al EPL(15)-a1501 [constraints on the GUP].
@ Other cosmological models: Rama PLB(01)ht; Nozari & Fazlpour GRG(06)gq [early-universe thermodynamics]; Battisti & Montani PLB(09)-a0808 [mixmaster universe]; Shalyt-Margolin a0807-proc [for cosmological-constant–spacetime-volume]; Vakili IJMPD(09)-a0811 [effects on classical and quantum dS/AdS]; Zhu et al PLB(09)-a0811 [thermodynamics]; Rashidi ASS(13)-a1209 [avoiding the big-bang singularity]; Miao & Zhao IJMPD(14)-a1312 [and the cosmological constant problem]; Jalalzadeh et al PRD(14)-a1403; Pedram PRD(15)-a1502 [Wheeler-DeWitt equation for FLRW with conformally coupled scalar field]; > s.a. bianchi-I quantum cosmology; friedmann equation.
@ Other systems: Feng et al PLB(17)-a1610 [gravitational wave propagation].
@ Strings: Capozziello et al IJTP(00)gq/99; Yoneya PTP(00)ht, IJMPA(01)ht/00; Benczik et al PRD(02)ht; Hossenfelder et al PLB(03)ht; Chang et al AHEP(11)-a1106.
@ Non-commutative geometry: Carlen & Vilela Mendes PLA(01); Brandenberger & Ho PRD(02)ht; Bolonek & Kosiński PLB(02)ht, APPB(03)ht/02 [non-commutative quantum mechanics]; > s.a. non-commutative spacetime.
> Other quantum gravity: see hořava-lifshitz gravity; locality; quantum-gravity phenomenology and effects on matter.

Other GUP Phenomenology > s.a. deformed uncertainty relations; discrete spacetime; fine-structure constant; geodesics; Polymer Representation.
* Idea: The various forms of the gravity-motivated Generalized Uncertainty Principle and its variants also have consequences for other areas of physics.
@ Harmonic oscillator: Kempf JPA(97)ht/96; Brau JPA(99)qp [and H atom]; Pedram EPL(10)-a1003 [and particle in a box]; Farag Ali et al PRD(11) [and corrections to the Lamb shift, Landau levels, etc]; Khalil AHEP(14)-a1309 [and H atom, Lorentz force]; Sadeghnezhad ChJP(16)-a1603 [energy spectrum and coherent states]; Bosso et al PRD(17)-a1704 [coherent and squeezed states]; > s.a. quantum oscillator.
@ H atom: Akhoury & Yao PLB(03)hp; Benczik et al PRA(05); Stetsko & Tkachuk PRA(06); Bouaziz & Ferkous PRA(10)-a1009; Pedram JPA(12)-a1203, EPL(13)-a1205 [1D]; Francisco et al BJP(14)-a1402 [relativistic approach].
@ Other quantum-mechanical systems: Nozari & Azizi GRG(06)qp/05 [free particle + box]; Nozari & Mehdipour GRG(05)qp [wave packet dispersion]; Bang & Berger PRD(06) [minimum uncertainty wave packets]; Bouaziz & Bawin PRA(07)-a0711 [inverse-square potential]; Das & Vagenas PRL(10)-a0810, CJP(09)-a0901-conf [Lamb shift, reflection and transmission coefficients, ...]; Pedram IJMPD(10) [a class of solutions]; Nozari & Pedram EPL(10)-a1011 [bouncing particle]; Pedram et al JHEP(11) [ultracold neutrons in a gravitational field]; Pedram IJTP(12)-a1201 [quantum bouncer]; Majhi & Vagenas PLB(13)-a1307 [photons, modified dispersion relation]; Ma & Zhao JMP(14) [square well]; Conti PRA(14) [simulation by non-paraxial non-linear optics]; Blado et al EJP(16)-a1509 [tunneling]; Chen et al a1602 [ion trap]; Bosso & Das AP(17)-a1607 [corrections to angular momentum eigenvalues]; Gao & Zhan PRA(16)-a1607 [cold atoms]; Gusson et al a1704 [Dirac δ-function potential in quasiposition representation]; Blado et al a1706 [entangled particles]; > s.a. Dirac Oscillator.
@ Thermodynamics / statistical physics: Rama PLB(02)ht [Planck spectrum, etc]; Nozari & Mehdipour CSF(07)ht/06, Shababi JTP-a1310 [ideal gas]; Vakili & Gorji JSTAT(12)-a1207 [statistical mechanics]; Shababi JTP-a1310 [thermodynamics of black-body radiation]; Abbasiyan-Motlaq & Pedram JSM(14)-a1406 [quantum partition function]; Zhang & Tian ChPL(15)-a1410 [Bose-Einstein condensation of a relativistic ideal Bose gas].
@ Other systems: Kober PRD(10)-a1008 [gauge theories]; Das & Mann PLB(11)-a1109 [superconductivity and quantum Hall effect].

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