Exact quantum decay of an interacting many-particle system: the Calogero–Sutherland model
Open accessAbstract
The exact quantum decay of a one-dimensional Bose gas with inverse-square interactions is presented. The system is equivalent to a gas of particles obeying generalized exclusion statistics. We consider the expansion dynamics of a cloud initially confined in a harmonic trap that is suddenly switched off. The decay is characterized by analyzing the fidelity between the initial and the time-evolving states, also known as the survival probability. It exhibits early on a quadratic dependence on time that turns into a power-law decay, during the course of the evolution. It is shown that the particle number and the strength of interactions determine the power-law exponent in the latter regime, as recently conjectured. The nonexponential character of the decay is linked to the many-particle reconstruction of the initial state from the decaying products.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Under quite general conditions, a power-law decay holds.
“Under quite general conditions, a power-law decay holds, as has been demonstrated in single-particle [23], few-body [30] and many-body systems [25, 31-33].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [31]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Zur Quantentheorie des Atomkernes
Gamow, G. (1928) · The European Physical Journal A · doi:10.1007/bf01343196 · Cited by 2,336 · see citing works
The Zeno’s paradox in quantum theory
Misra, B., & Sudarshan, E. C. G. (1977) · Journal of Mathematical Physics · doi:10.1063/1.523304 · Cited by 2,246 · see citing works
Fidelity for Mixed Quantum States
Jozsa, R. (1994) · Journal of Modern Optics · doi:10.1080/09500349414552171 · Cited by 1,911 · see citing works
Berechnung der nat�rlichen Linienbreite auf Grund der Diracschen Lichttheorie
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01336768 · Cited by 1,803 · see citing works
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
Girardeau, M. D. (1960) · Journal of Mathematical Physics · doi:10.1063/1.1703687 · Cited by 1,753 · see citing works
Calogero, F. (1971) · Journal of Mathematical Physics · doi:10.1063/1.1665604 · Cited by 1,399 · see citing works
Quantum many-body systems out of equilibrium
Eisert, J., Friesdorf, M., & Gogolin, C. (2015) · Nature Physics · doi:10.1038/nphys3215 · Cited by 1,255 · see citing works
‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle
Haldane, F. D. M. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.937 · Cited by 988 · see citing works
Log-Gases and Random MatricesPreprint
Forrester, P. J. (2010) · Princeton University Press eBooks · doi:10.1515/9781400835416 · Cited by 797 · see citing works
Quantum Many-Body Problem in One Dimension: Ground State
Sutherland, B. (1971) · Journal of Mathematical Physics · doi:10.1063/1.1665584 · Cited by 699 · see citing works
Decay theory of unstable quantum systems
Fonda, L., Ghirardi, G. C., & Rimini, A. (1978) · Reports on Progress in Physics · doi:10.1088/0034-4885/41/4/003 · Cited by 627 · see citing works
Dynamics of Loschmidt echoes and fidelity decay
Gorin, T., Prosen, T., Seligman, T. H., & Žnidarič, M. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.09.003 · Cited by 623 · see citing works
Muga, J. G., Palao, J. P., Navarro, B., & Egusquiza, I. L. (2004) · Physics Reports · doi:10.1016/j.physrep.2004.03.002 · Cited by 516 · see citing works
Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles
Wu, Y.-S. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.922 · Cited by 488 · see citing works
Strongly correlated quantum walks in optical lattices
Preiss, P. M., Ma, R., Tai, M. E., Lukin, A., Rispoli, M., Zupancic, P., Lahini, Y., Islam, R., & Greiner, M. (2015) · Science · doi:10.1126/science.1260364 · Cited by 437 · see citing works
�ber die nat�rliche Linienbreite in der Strahlung des harmonischen Oszillators
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01397406 · Cited by 435 · see citing works
Quantum Mechanics and Radioactive Disintegration
Gurney, R. W., & Condon, E. U. (1929) · Physical Review · doi:10.1103/physrev.33.127 · Cited by 420 · see citing works
Fermionization of Two Distinguishable Fermions
Zürn, G., Serwane, F., Lompe, T., Wenz, A. N., Ries, M. G., Bohn, J. E., & Jochim, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.075303 · Cited by 315 · see citing works
Expansion Dynamics of Interacting Bosons in Homogeneous Lattices in One and Two Dimensions
Ronzheimer, J. P., Schreiber, M., Braun, S., Hodgman, S. S., Langer, S., McCulloch, I. P., Heidrich‐Meisner, F., Bloch, I., & Schneider, U. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.205301 · Cited by 301 · see citing works
The Calogero-Sutherland Model and Generalized Classical Polynomials
Baker, T. H., & Forrester, P. J. (1997) · Communications in Mathematical Physics · doi:10.1007/s002200050161 · Cited by 281 · see citing works
Breathing modes and hidden symmetry of trapped atoms in two dimensions
Питаевский, Л. П., & Rosch, A. (1997) · Physical Review A · doi:10.1103/physreva.55.r853 · Cited by 270 · see citing works
Exact Coherent States of a Harmonically Confined Tonks-Girardeau Gas
Minguzzi, A., & Gangardt, D. M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.240404 · Cited by 223 · see citing works
A unitarity bound on the evolution of nonstationary states
Fleming, G. N. (1973) · Il Nuovo Cimento A · doi:10.1007/bf02819419 · Cited by 218 · see citing works
Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap
Girardeau, M. D., Wright, E. M., & Triscari, J. M. (2001) · Physical Review A · doi:10.1103/physreva.63.033601 · Cited by 216 · see citing works
Thermodynamics of a One-Dimensional Ideal Gas with Fractional Exclusion Statistics
Murthy, M. V. N., & Shankar, R. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.3331 · Cited by 185 · see citing works
Violation of the Exponential-Decay Law at Long Times
Rothe, C., Hintschich, S. I., & Monkman, A. P. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.163601 · Cited by 180 · see citing works
Uncertain turtle relationships
Wilkinson, M., Thorley, J., & Benton, M. J. (1997) · Nature · doi:10.1038/387466a0 · Cited by 177 · see citing works
Dynamics at the many-body localization transition
Torres-Herrera, E. J., & dos Santos, L. F. (2015) · Physical Review B · doi:10.1103/physrevb.92.014208 · Cited by 169 · see citing works
Minguzzi, A. (2004) · Physics Reports · doi:10.1016/j.physrep.2004.02.001 · Cited by 141 · see citing works
Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas
Goold, J., Fogarty, T., Gullo, N. L., Paternostro, M., & Busch, T. (2011) · Physical Review A · doi:10.1103/physreva.84.063632 · Cited by 123 · see citing works
Quench Dynamics of the Interacting Bose Gas in One Dimension
Iyer, D., & Andrei, N. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.115304 · Cited by 115 · see citing works
Example of a Quantum Anomaly in the Physics of Ultracold Gases
Olshanii, M., Perrin, H., & Lorent, V. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.095302 · Cited by 106 · see citing works
Fermionization and bosonization of expanding one-dimensional anyonic fluids
del Campo, A. (2008) · Physical Review A · doi:10.1103/physreva.78.045602 · Cited by 101 · see citing works
Self-citationLong-time behavior of many-particle quantum decay
del Campo, A. (2011) · Physical Review A · doi:10.1103/physreva.84.012113 · Cited by 82 · see citing works
Exact Coherent States of a One-Dimensional Quantum Fluid in a Time-Dependent Trapping Potential
Sutherland, B. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.3678 · Cited by 74 · see citing works
Fermi-Bose Transformation for the Time-Dependent Lieb-Liniger Gas
Buljan, H., Pezer, R., & Gasenzer, T. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.080406 · Cited by 73 · see citing works
Particle Statistics Affects Quantum Decay and Fano Interference
Crespi, A., Sansoni, L., Valle, G. D., Ciamei, A., Ramponi, R., Sciarrino, F., Mataloni, P., Longhi, S., & Osellame, R. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.090201 · Cited by 68 · see citing works
Exact Relaxation Dynamics of a Localized Many-Body State in the 1D Bose Gas
Sato, J., Kanamoto, R., Kaminishi, E., et al. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.110401 · Cited by 66 · see citing works
Gambardella, P. J. (1975) · Journal of Mathematical Physics · doi:10.1063/1.522651 · Cited by 62 · see citing works
Tunneling Theory of Two Interacting Atoms in a Trap
Rontani, M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.115302 · Cited by 57 · see citing works
Decay by tunneling of bosonic and fermionic Tonks-Girardeau gases
del Campo, A., Delgado, F. S., García‐Calderón, G., Muga, J. G., & Raizen, M. G. (2006) · Physical Review A · doi:10.1103/physreva.74.013605 · Cited by 55 · see citing works
Self-citationKrauss, L. M., & Dent, J. B. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.171301 · Cited by 49 · see citing works
Nonexponential fidelity decay in isolated interacting quantum systems
Torres-Herrera, E. J., & dos Santos, L. F. (2014) · Physical Review A · doi:10.1103/physreva.90.033623 · Cited by 49 · see citing works
Fidelity of fermionic-atom number states subjected to tunneling decay
Pons, M. L., Sokolovski, D., & del Campo, A. (2012) · Physical Review A · doi:10.1103/physreva.85.022107 · Cited by 43 · see citing works
Self-citationSome remarks on the origin of the deviations from the exponential decay law of an unstable particle
Fonda, L., & Ghirardi, G. C. (1972) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02728686 · Cited by 42 · see citing works
Hunn, S., Zimmermann, K. D., Hiller, M., & Buchleitner, A. (2013) · Physical Review A · doi:10.1103/physreva.87.043626 · Cited by 39 · see citing works
Time evolution of decay of two identical quantum particles
García‐Calderón, G., & Mendoza‐Luna, L. G. (2011) · Physical Review A · doi:10.1103/physreva.84.032106 · Cited by 33 · see citing works
Escape behavior of quantum two-particle systems with Coulomb interactions
Taniguchi, T., & Sawada, S.-I. (2011) · Physical Review E · doi:10.1103/physreve.83.026208 · Cited by 30 · see citing works
Role of initial state reconstruction in short- and long-time deviations from exponential decay
Muga, J. G., Delgado, F. S., del Campo, A., & García‐Calderón, G. (2006) · Physical Review A · doi:10.1103/physreva.73.052112 · Cited by 29 · see citing works
Self-citationExclusion Statistics in a Trapped Two-Dimensional Bose Gas
Hansson, T., Leinaas, J. M., & Viefers, S. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2930 · Cited by 26 · see citing works
Eigenfunctions for SU( nu ) particles with 1/r2interaction in harmonic confinement
Vacek, K., Okiji, A., & Kawakami, N. (1994) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/27/7/002 · Cited by 23 · see citing works
Many-particle quantum decay and trapping: The role of statistics and Fano resonances
Longhi, S., & Valle, G. D. (2012) · Physical Review A · doi:10.1103/physreva.86.012112 · Cited by 21 · see citing works
Jump Time and Passage Time: The Duration ofs a Quantum Transition
Schulman, L. S. (2007) · Springer eBooks · doi:10.1007/978-3-540-73473-4_4 · Cited by 20 · see citing works
Analytical study of quadratic and nonquadratic short-time behavior of quantum decay
Cordero, S., & García‐Calderón, G. (2012) · Physical Review A · doi:10.1103/physreva.86.062116 · Cited by 16 · see citing works
Energetically constrained co-tunneling of cold atoms
Kolovsky, A. R., Link, J. M., & Wimberger, S. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/7/075002 · Cited by 14 · see citing works
Loschmidt echo in one-dimensional interacting Bose gases
Lelas, K., Ševa, T., & Buljan, H. (2011) · Physical Review A · doi:10.1103/physreva.84.063601 · Cited by 11 · see citing works
Role of quantum statistics in multi-particle decay dynamics
Marchewka, A., & Granot, E. (2015) · Annals of Physics · doi:10.1016/j.aop.2015.02.022 · Cited by 11 · see citing works
Escape dynamics of a Bose-Hubbard dimer out of a trap
Максимов, Д. Н., & Kolovsky, A. R. (2014) · Physical Review A · doi:10.1103/physreva.89.063612 · Cited by 8 · see citing works
Anomalous Zeno effect for sharply localized atomic states
Sokolovski, D., Pons, M. L., & Kamalov, T. F. (2012) · Physical Review A · doi:10.1103/physreva.86.022110 · Cited by 7 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- Gogolin C and Eisert J 2015 in preparation (arXiv:1503.07538) · arXiv
- Kim S and Brand J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 195301 · DOI
- del Campo A 2011 Phys. Rev. A 84 031606(R) · DOI · Paper page
Cited by
Sorted by citations
Scrambling the spectral form factor: Unitarity constraints and exact results
del Campo, A., Molina-Vilaplana, J., & Sonner, J. (2017) · Physical Review D · doi:10.1103/physrevd.95.126008 · Cited by 133 · see citing works
Nonexponential quantum decay under environmental decoherence
Beau, M., Kiukas, J., Egusquiza, I. L., & del Campo, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.130401 · Cited by 70 · see citing works
Power-law decay exponents: A dynamical criterion for predicting thermalization
Távora, M., Torres-Herrera, E. J., & Santos, L. F. (2017) · Physical Review A · doi:10.1103/physreva.95.013604 · Cited by 53 · see citing works
- Authors
- Campo, A. D.
- Affiliations
- University of Massachusetts Boston (US)
- Corresponding author
- Campo, Adolfo del
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2016-01-19
- Volume
- 18
- Issue
- 1
- Pages
- 015014
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W3124058778
- Cited by
- 49
- References
- 59
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 3 · 2023: 2 · 2022: 4 · 2021: 4 · 2020: 10 · 2019: 2 · 2018: 7 · 2017: 9 · 2016: 3
- FWCI
- 3.31
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Funders
- University of Massachusetts (P20150000029279)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- Calogero-Sutherland model, inverse-square interaction, quantum decay, survival probability, fidelity, one-dimensional Bose gas, power-law decay, non-exponential decay, exact solutions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
