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]; news PhysOrg(13)feb, ns(13)feb [macroscopic demonstration]; Ma et al PRL(16)-a1512 [based on statistical distances]; Bosso et al PLB(18)-a1804 [in advanced LIGO]; news cosmos(19)jun; > 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.
@ Relativistic particles: Białynicki-Birula & Białynicka-Birula PRL(12)-a1110, PRA(12)-a1205, comment Wang et al PRL(12)-a1207 [photons]; Nanni PE(16)-a1501; Białynicki-Birula & Białynicka-Birula NJP(19)-a1903; Białynicki-Birula & Prystupiuk a2103 [relativistic bosons].
@ Other systems: Barros e Sá JMP(01) [SU(2)-invariant, \(\hbar\)2j ≤ Δ ≤ \(\hbar\)2j(j+1)]; Trifonov JPA(03) [particle on a circle]; > 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 \(\Delta t \sim 10^{-12}\) 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. casimir effect; 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 AP(18)-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]; Neves EPJC(20)-a1906 [black-hole shadows]; Tamburini et al a2103 [M87*].
@ 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]; Buoninfante et al a1903 [and the corpuscular theory of gravity]; Buoninfante et al a2009 [and the Bekenstein bound]; > s.a. black-hole entropy, information and thermodynamics; rainbow gravity; specific types of black holes.
@ Other astrophysics: Majumder a1105 [perihelion precession of Mercury]; Maziashvili PRD(12)-a1206 [light incoherence in stellar interferometry]; Buoninfante et al a2001 [GUP stars]; Ökcü & Aydiner NPB-a2101 [classical tests of general reativity]; > s.a. Jeans Mass.
@ 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]; Kouwn a1805; Bosso & Obregón CQG(20)-a1904 [Kantowski-Sachs model]; Giardino & Salzano a2006; > s.a. bianchi-I quantum cosmology; friedmann equation.
@ Gravitational waves: Feng et al PLB(17)-a1610 [propagation]; Bosso et al PLB(18)-a1804 [in the advanced LIGO experiment]; Bhattacharyya et al a2005 [resonant detectors]; Das et al a2101 [GW150914 and GW190521].
@ 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, effects on matter and effects on particles.

Other GUP Phenomenology > s.a. deformed uncertainty relations; discrete spacetime and phenomenology; Polymer Representation.
* Idea: The various forms of the gravity-motivated Generalized Uncertainty Principle and its variants also have consequences for other areas of physics.
@ Particles, fields: Nozari & Azizi GRG(06)qp/05 [free particle + box]; 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 IJTP(12)-a1201 [quantum bouncer]; Ma & Zhao JMP(14) [square well]; Blado et al EJP(16)-a1509 [tunneling]; Bosso & Das AP(17)-a1607 [corrections to angular momentum eigenvalues]; Gusson et al EPJC(18)-a1704 [Dirac δ-function potential in quasiposition representation]; Blado et al a1706 [entangled particles]; Marcucci & Conti a1805 [orbital precession]; Gangopadhyay & Bhattacharyya PRD(19)-a1901 [path integral, and non-commutativity]; Yesiltas a1904 [Dirac fields in curved spacetime]; Park & Jung a2001 [inequivalence of Schrödinger and Feynman path-integral approach]; Bosso et al a2005 [scalar electrodynamics], a2005 [quantum electrodynamics]; > s.a. Dirac Oscillator; fermions [exotic]; No-Cloning Theorem.
@ 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]; Bushev et al a1903 [amplitude-frequency effect]; > 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].
@ Photons: Majhi & Vagenas PLB(13)-a1307, Araújo & Petrov a2105 [photon gas with modified dispersion relation]; Conti a1805 [spectral features].
@ Experimental systems: Pedram et al JHEP(11) [ultracold neutrons in a gravitational field]; Conti PRA(14) [simulation by non-paraxial non-linear optics]; Chen et al a1602 [ion trap]; Gao & Zhan PRA(16)-a1607 [cold atoms].
@ Wave packets: Nozari & Mehdipour GRG(05)qp [dispersion]; Bang & Berger PRD(06) [minimum uncertainty]; Villalpando & Modak PRD(19)-a1812, Das & Modak a2102 [broadening]
@ 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]; > s.a. fine-structure constant; geodesics; Raychaudhuri Equation; unruh effect.

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