Minimal length effect on the broadening of free wave packets and its physical implications
Abstract
We study the generalized uncertainty principle (GUP) modified time evolution for the width of wave packets for a scalar potential. The free particle case is solved exactly where the wavepacket broadening is modified by a coupling between the GUP parameter and higherorder moments in the probability distribution in momentum space. We consider two popular forms of deformations widely used in the literature—one of which modifies the commutator with a quadratic term in momentum, while the other modifies it with terms both linear and quadratic in momentum. Unlike the standard case, satisfying Heisenberg uncertainty, here the GUP modified broadening rates, for both deformations, not only depend on the initial size (in both position and momentum space) of the wave packet but also on the initial probability distribution and momentum of the particle. The new rates of wavepacket broadening, for both situations, are modified by a handful of new terms—such as the skewness and kurtosis coefficients, as well as the (constant) momentum of the particle. Comparisons with the standard Heisenberg uncertainty principle–based results show potentially measurable differences in the rates of free wavepacket broadening for physical systems such as the C60 and C176 molecules, and more so for large organic molecular wavemore »
 Authors:

 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. de Colima (Mexico)
 Univ. de Colima (Mexico)
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1523427
 Report Number(s):
 arXiv:1812.06112; FERMILABPUB18704
Journal ID: ISSN 24700010; PRVDAQ; 1709339
 Grant/Contract Number:
 AC0207CH11359
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 2; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Villalpando, Carlos, and Modak, Sujoy K. Minimal length effect on the broadening of free wave packets and its physical implications. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.024054.
Villalpando, Carlos, & Modak, Sujoy K. Minimal length effect on the broadening of free wave packets and its physical implications. United States. https://doi.org/10.1103/PhysRevD.100.024054
Villalpando, Carlos, and Modak, Sujoy K. Fri .
"Minimal length effect on the broadening of free wave packets and its physical implications". United States. https://doi.org/10.1103/PhysRevD.100.024054. https://www.osti.gov/servlets/purl/1523427.
@article{osti_1523427,
title = {Minimal length effect on the broadening of free wave packets and its physical implications},
author = {Villalpando, Carlos and Modak, Sujoy K.},
abstractNote = {We study the generalized uncertainty principle (GUP) modified time evolution for the width of wave packets for a scalar potential. The free particle case is solved exactly where the wavepacket broadening is modified by a coupling between the GUP parameter and higherorder moments in the probability distribution in momentum space. We consider two popular forms of deformations widely used in the literature—one of which modifies the commutator with a quadratic term in momentum, while the other modifies it with terms both linear and quadratic in momentum. Unlike the standard case, satisfying Heisenberg uncertainty, here the GUP modified broadening rates, for both deformations, not only depend on the initial size (in both position and momentum space) of the wave packet but also on the initial probability distribution and momentum of the particle. The new rates of wavepacket broadening, for both situations, are modified by a handful of new terms—such as the skewness and kurtosis coefficients, as well as the (constant) momentum of the particle. Comparisons with the standard Heisenberg uncertainty principle–based results show potentially measurable differences in the rates of free wavepacket broadening for physical systems such as the C60 and C176 molecules, and more so for large organic molecular wave packets. In doing so, we open a path to scan the GUP parameter space by several orders of magnitude inside the best existing upper bounds for both forms of GUP.},
doi = {10.1103/PhysRevD.100.024054},
journal = {Physical Review D},
number = 2,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Quantum Gravity and Minimum Length
journal, January 1995
 Garay, Luis J.
 International Journal of Modern Physics A, Vol. 10, Issue 02
Can spacetime be probed below the string size?
journal, January 1989
 Amati, D.; Ciafaloni, M.; Veneziano, G.
 Physics Letters B, Vol. 216, Issue 12
New generalized uncertainty principle from the doubly special relativity
journal, October 2018
 Chung, Won Sang; Hassanabadi, Hassan
 Physics Letters B, Vol. 785
Lorentz violation and generalized uncertainty principle
journal, April 2018
 Lambiase, Gaetano; Scardigli, Fabio
 Physical Review D, Vol. 97, Issue 7
Generalized Uncertainty Principle in Quantum Cosmology for the Maximally Symmetric Space
journal, February 2019
 Kuzmichev, V. E.; Kuzmichev, V. V.
 Ukrainian Journal of Physics, Vol. 64, Issue 2
Constraining the generalized uncertainty principle with cold atoms
journal, July 2016
 Gao, Dongfeng; Zhan, Mingsheng
 Physical Review A, Vol. 94, Issue 1
String theory, scale relativity and the generalized uncertainty principle
journal, June 1997
 Castro, Carlos
 Foundations of Physics Letters, Vol. 10, Issue 3
Minimal Length Scale Scenarios for Quantum Gravity
journal, January 2013
 Hossenfelder, Sabine
 Living Reviews in Relativity, Vol. 16, Issue 1
Quantum gravity, shadow states and quantum mechanics
journal, February 2003
 Ashtekar, Abhay; Fairhurst, Stephen; Willis, Joshua L.
 Classical and Quantum Gravity, Vol. 20, Issue 6
On Gravity and the Uncertainty Principle
journal, June 1999
 Adler, Ronald J.; Santiago, David I.
 Modern Physics Letters A, Vol. 14, Issue 20
Generalized uncertainty principle in quantum gravity from microblack hole gedanken experiment
journal, April 1999
 Scardigli, Fabio
 Physics Letters B, Vol. 452, Issue 12
On Gravity's role in Quantum State Reduction
journal, May 1996
 Penrose, Roger
 General Relativity and Gravitation, Vol. 28, Issue 5
Potential tests of the generalized uncertainty principle in the advanced LIGO experiment
journal, October 2018
 Bosso, Pasquale; Das, Saurya; Mann, Robert B.
 Physics Letters B, Vol. 785
Minimal length, maximal momentum, and Hilbert space representation of quantum mechanics
journal, May 2012
 Nozari, Kourosh; Etemadi, Amir
 Physical Review D, Vol. 85, Issue 10
Hydrogenatom spectrum under a minimallength hypothesis
journal, July 2005
 Benczik, Sándor; Chang, Lay Nam; Minic, Djordje
 Physical Review A, Vol. 72, Issue 1
Probing Planckscale physics with quantum optics
journal, March 2012
 Pikovski, Igor; Vanner, Michael R.; Aspelmeyer, Markus
 Nature Physics, Vol. 8, Issue 5
“Stringy” coherent states inspired by generalized uncertainty principle
journal, May 2012
 Ghosh, Subir; Roy, Pinaki
 Physics Letters B, Vol. 711, Issue 5
Probing deformed commutators with macroscopic harmonic oscillators
journal, June 2015
 Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele
 Nature Communications, Vol. 6, Issue 1
Generalized uncertainty principle: Approaches and applications
journal, October 2014
 Tawfik, A.; Diab, A.
 International Journal of Modern Physics D, Vol. 23, Issue 12
The highenergy behavior of string scattering amplitudes
journal, October 1987
 Gross, David J.; Mende, Paul F.
 Physics Letters B, Vol. 197, Issue 12
Some aspects of Planck scale quantum optics
journal, November 2005
 Nozari, Kourosh
 Physics Letters B, Vol. 629, Issue 1
Generalized uncertainty principle as a consequence of the effective field theory
journal, February 2017
 Faizal, Mir; Ali, Ahmed Farag; Nassar, Ali
 Physics Letters B, Vol. 765
Backgroundindependent quantization and the uncertainty principle
journal, July 2010
 Hossain, Golam Mortuza; Husain, Viqar; Seahra, Sanjeev S.
 Classical and Quantum Gravity, Vol. 27, Issue 16
Minimum physical length and the generalized uncertainty principle in string theory
journal, January 1990
 Konishi, Kenichi; Paffuti, Giampiero; Provero, Paolo
 Physics Letters B, Vol. 234, Issue 3
Discreteness of space from the generalized uncertainty principle
journal, August 2009
 Ali, Ahmed Farag; Das, Saurya; Vagenas, Elias C.
 Physics Letters B, Vol. 678, Issue 5
A generalized uncertainty principle in quantum gravity
journal, April 1993
 Maggiore, Michele
 Physics Letters B, Vol. 304, Issue 12
The quantum structure of spacetime at the Planck scale and quantum fields
journal, August 1995
 Doplicher, Sergio; Fredenhagen, Klaus; Roberts, John E.
 Communications in Mathematical Physics, Vol. 172, Issue 1
SubPlanckian black holes and the Generalized Uncertainty Principle
journal, July 2015
 Carr, Bernard; Mureika, Jonas; Nicolini, Piero
 Journal of High Energy Physics, Vol. 2015, Issue 7
Modified commutation relationships from the BerryKeating program
journal, January 2019
 Bishop, Michael; Aiken, Erick; Singleton, Douglas
 Physical Review D, Vol. 99, Issue 2
Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
journal, June 2002
 Chang, Lay Nam; Minic, Djordje; Okamura, Naotoshi
 Physical Review D, Vol. 65, Issue 12
Quantum uncertainty in doubly special relativity
journal, March 2005
 Cortés, J. L.; Gamboa, J.
 Physical Review D, Vol. 71, Issue 6
Generalized Lorentz invariance with an invariant energy scale
journal, February 2003
 Magueijo, João; Smolin, Lee
 Physical Review D, Vol. 67, Issue 4
Physics on the smallest scales: an introduction to minimal length phenomenology
journal, May 2012
 Sprenger, Martin; Nicolini, Piero; Bleicher, Marcus
 European Journal of Physics, Vol. 33, Issue 4
Relativity in Spacetimes with ShortDistance Structure Governed by an ObserverIndependent (Planckian) Length Scale
journal, January 2002
 AmelinoCamelia, Giovanni
 International Journal of Modern Physics D, Vol. 11, Issue 01
The algebraic structure of the generalized uncertainty principle
journal, December 1993
 Maggiore, Michele
 Physics Letters B, Vol. 319, Issue 13
Generalized uncertainty principle, extra dimensions and holography
journal, August 2003
 Scardigli, Fabio; Casadio, Roberto
 Classical and Quantum Gravity, Vol. 20, Issue 18
Universality of Quantum Gravity Corrections
journal, November 2008
 Das, Saurya; Vagenas, Elias C.
 Physical Review Letters, Vol. 101, Issue 22
String theory beyond the Planck scale
journal, July 1988
 Gross, David J.; Mende, Paul F.
 Nuclear Physics B, Vol. 303, Issue 3
Quantum groups, gravity, and the generalized uncertainty principle
journal, May 1994
 Maggiore, Michele
 Physical Review D, Vol. 49, Issue 10
A higher order GUP with minimal length uncertainty and maximal momentum
journal, August 2012
 Pedram, Pouria
 Physics Letters B, Vol. 714, Issue 25
GUP parameter from quantum corrections to the Newtonian potential
journal, April 2017
 Scardigli, Fabio; Lambiase, Gaetano; Vagenas, Elias C.
 Physics Letters B, Vol. 767
Proposal for testing quantum gravity in the lab
journal, August 2011
 Ali, Ahmed Farag; Das, Saurya; Vagenas, Elias C.
 Physical Review D, Vol. 84, Issue 4
Gravitational tests of the generalized uncertainty principle
journal, September 2015
 Scardigli, Fabio; Casadio, Roberto
 The European Physical Journal C, Vol. 75, Issue 9
Relativistic corrections to the algebra of position variables and spinorbital interaction
journal, October 2016
 Deriglazov, Alexei A.; PupasovMaksimov, Andrey M.
 Physics Letters B, Vol. 761
Quantum gravity effects in geodesic motion and predictions of equivalence principle violation
journal, December 2013
 Ghosh, Subir
 Classical and Quantum Gravity, Vol. 31, Issue 2
Wave–particle duality of C60 molecules
journal, October 1999
 Arndt, Markus; Nairz, Olaf; VosAndreae, Julian
 Nature, Vol. 401, Issue 6754
Constraining the generalized uncertainty principle with the gravitational wave event GW150914
journal, May 2017
 Feng, ZhongWen; Yang, ShuZheng; Li, HuiLing
 Physics Letters B, Vol. 768
Quantum spaces are modular
journal, November 2016
 Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
 Physical Review D, Vol. 94, Issue 10
Wave packets propagation in quantum gravity
journal, October 2005
 Nozari, Kourosh; Mehdipour, S. Hamid
 General Relativity and Gravitation, Vol. 37, Issue 12
Quantum interference of large organic molecules
journal, April 2011
 Gerlich, Stefan; Eibenberger, Sandra; Tomandl, Mathias
 Nature Communications, Vol. 2, Issue 1
Hilbert space representation of the minimal length uncertainty relation
journal, July 1995
 Kempf, Achim; Mangano, Gianpiero; Mann, Robert B.
 Physical Review D, Vol. 52, Issue 2
Size analysis of single fullerene molecules by electron microscopy
journal, January 2004
 Goel, Anish; Howard, Jack B.; Vander Sande, John B.
 Carbon, Vol. 42, Issue 10, p. 19071915
Generalized Uncertainty Principle and angular momentum
journal, August 2017
 Bosso, Pasquale; Das, Saurya
 Annals of Physics, Vol. 383
Figures / Tables found in this record: