Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation

Bulgac, Aurel

doi:10.1103/physrevc.105.l021601

Title: Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation

Journal Article · Wed Feb 09 00:00:00 EST 2022 · Physical Review. C

DOI:https://doi.org/10.1103/physrevc.105.l021601· OSTI ID:1979888

^[1]

University of Washington, Seattle, WA (United States)

The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A semiclassical extension of this approach to quantum many-body systems was suggested by Uehling and Uhlenbeck in 1933 for both Fermi and Bose statistics, and many further developments of this approach are known as the Boltzmann-Uehling-Uhlenbeck (BUU) equations. In this paper I introduce a pure quantum version of the BUU type of equations, which is mathematically equivalent to a generalized time-dependent density functional theory extended to superfluid systems. As expected, during nonequilibrium processes the quantum Boltzmann one-body entropy increases during evolution.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Washington, Seattle, WA (United States); Texas A & M Univ., College Station, TX (United States); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: FG02-97ER41014; NA0003841

OSTI ID:: 1979888

Journal Information:: Physical Review. C, Vol. 105, Issue 2; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (50)

Shell effects in nuclear masses and deformation energies Strutinsky, V. M. Nuclear Physics A, Vol. 95, Issue 2 https://doi.org/10.1016/0375-9474(67)90510-6	journal	April 1967
Fission dynamics of ${}^{240}{Pu}$ from saddle to scission and beyond Bulgac, Aurel; Jin, Shi; Roche, Kenneth J. Physical Review C, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevC.100.034615	journal	September 2019
A guide to microscopic models for intermediate energy heavy ion collisions Bertsch, G. F.; Das Gupta, S. Physics Reports, Vol. 160, Issue 4 https://doi.org/10.1016/0370-1573(88)90170-6	journal	March 1988
Collective aspects deduced from time-dependent microscopic mean-field with pairing: Application to the fission process Tanimura, Yusuke; Lacroix, Denis; Scamps, Guillaume Physical Review C, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevC.92.034601	journal	September 2015
Isospin Properties of Nuclear Pair Correlations from the Level Structure of the Self-Conjugate Nucleus ${}^{88}{Ru}$ Cederwall, B.; Liu, X.; Aktas, Ö. Physical Review Letters, Vol. 124, Issue 6 https://doi.org/10.1103/PhysRevLett.124.062501	journal	February 2020
Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission Goddard, Philip; Stevenson, Paul; Rios, Arnau Physical Review C, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevC.92.054610	journal	November 2015
Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I Uehling, E. A.; Uhlenbeck, G. E. Physical Review, Vol. 43, Issue 7 https://doi.org/10.1103/PhysRev.43.552	journal	April 1933
Nonempirical Interactions for the Nuclear Shell Model: An Update Stroberg, S. Ragnar; Hergert, Heiko; Bogner, Scott K. Annual Review of Nuclear and Particle Science, Vol. 69, Issue 1 https://doi.org/10.1146/annurev-nucl-101917-021120	journal	October 2019
Unitary evolution with fluctuations and dissipation Bulgac, Aurel; Jin, Shi; Stetcu, Ionel Physical Review C, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevC.100.014615	journal	July 2019
Superfluid dynamics of ${}^{258}{Fm}$ fission Scamps, Guillaume; Simenel, Cédric; Lacroix, Denis Physical Review C, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevC.92.011602	journal	July 2015
Model nuclear energy density functionals derived from ab initio calculations Salvioni, G.; Dobaczewski, J.; Barbieri, C. Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 8 https://doi.org/10.1088/1361-6471/ab8d8e	journal	July 2020
Spin-triplet pairing in large nuclei Bertsch, G. F.; Luo, Y. Physical Review C, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevC.81.064320	journal	June 2010
Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process Brack, M.; Damgaard, Jens; Jensen, A. S. Reviews of Modern Physics, Vol. 44, Issue 2 https://doi.org/10.1103/RevModPhys.44.320	journal	April 1972
Collision Dynamics of Two ${}^{238}U$ Atomic Nuclei Golabek, Cédric; Simenel, Cédric Physical Review Letters, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevLett.103.042701	journal	July 2009
Large momentum part of a strongly correlated Fermi gas Tan, Shina Annals of Physics, Vol. 323, Issue 12 https://doi.org/10.1016/j.aop.2008.03.005	journal	December 2008
Minimal nuclear energy density functional Bulgac, Aurel; Forbes, Michael McNeil; Jin, Shi Physical Review C, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevC.97.044313	journal	April 2018
The long journey from ab initio calculations to density functional theory for nuclear large amplitude collective motion Bulgac, Aurel Journal of Physics G: Nuclear and Particle Physics, Vol. 37, Issue 6 https://doi.org/10.1088/0954-3899/37/6/064006	journal	March 2010
Nuclear Constitution and the Interpretation of Fission Phenomena Hill, David Lawrence; Wheeler, John Archibald Physical Review, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRev.89.1102	journal	March 1953
The nuclear density of states in the space of nuclear shapes Bertsch, G. Physics Letters B, Vol. 95, Issue 2 https://doi.org/10.1016/0370-2693(80)90458-X	journal	September 1980
The Effect of the Image Force on the Emission and Reflexion of Electrons by Metals Nordheim, L. W. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 121, Issue 788 https://doi.org/10.1098/rspa.1928.0222	journal	December 1928
Overview of neutron–proton pairing Frauendorf, S.; Macchiavelli, A. O. Progress in Particle and Nuclear Physics, Vol. 78 https://doi.org/10.1016/j.ppnp.2014.07.001	journal	September 2014
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids Bulgac, Aurel Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170631	journal	October 2013
Mixed-Spin Pairing Condensates in Heavy Nuclei Gezerlis, Alexandros; Bertsch, G. F.; Luo, Y. L. Physical Review Letters, Vol. 106, Issue 25 https://doi.org/10.1103/PhysRevLett.106.252502	journal	June 2011
Local density approximation for proton-neutron pairing correlations: Formalism Perlińska, E.; Rohoziński, S. G.; Dobaczewski, J. Physical Review C, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevC.69.014316	journal	January 2004
The Mechanism of Nuclear Fission Bohr, Niels; Wheeler, John Archibald Physical Review, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRev.56.426	journal	September 1939
Comment on “Spontaneous Fission: A Kinetic Approach” Bertsch, George F.; Bulgac, Aurel Physical Review Letters, Vol. 79, Issue 18 https://doi.org/10.1103/PhysRevLett.79.3539	journal	November 1997
Restoring broken symmetries for nuclei and reaction fragments Bulgac, Aurel Physical Review C, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevC.104.054601	journal	November 2021
The Time-Dependent Generator Coordinate Method in Nuclear Physics Verriere, Marc; Regnier, David Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00233	journal	July 2020
Pairing dynamics in particle transport Scamps, Guillaume; Lacroix, Denis; Bertsch, G. F. Physical Review C, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevC.85.034328	journal	March 2012
The LISE package: Solvers for static and time-dependent superfluid local density approximation equations in three dimensions Jin, Shi; Roche, Kenneth J.; Stetcu, Ionel Computer Physics Communications, Vol. 269 https://doi.org/10.1016/j.cpc.2021.108130	journal	December 2021
The shapes of nuclei Bertsch, G. F. International Journal of Modern Physics E, Vol. 26, Issue 01n02 https://doi.org/10.1142/S0218301317400018	journal	January 2017
Collective Motions in Nuclei by the Method of Generator Coordinates Griffin, James J.; Wheeler, John A. Physical Review, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRev.108.311	journal	October 1957
Symmetry restoration in the mean-field description of proton-neutron pairing Romero, A. M.; Dobaczewski, J.; Pastore, A. Physics Letters B, Vol. 795 https://doi.org/10.1016/j.physletb.2019.06.032	journal	August 2019
Microscopic theory of nuclear fission: a review Schunck, N.; Robledo, L. M. Reports on Progress in Physics, Vol. 79, Issue 11 https://doi.org/10.1088/0034-4885/79/11/116301	journal	October 2016
Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors Yang, C. N. Reviews of Modern Physics, Vol. 34, Issue 4 https://doi.org/10.1103/RevModPhys.34.694	journal	October 1962
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction Meitner, Lise; Frisch, O. R. Nature, Vol. 143, Issue 3615 https://doi.org/10.1038/143239a0	journal	February 1939
Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method Jin, Shi; Bulgac, Aurel; Roche, Kenneth Physical Review C, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevC.95.044302	journal	April 2017
Self-consistent mean-field models for nuclear structure Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard Reviews of Modern Physics, Vol. 75, Issue 1 https://doi.org/10.1103/RevModPhys.75.121	journal	January 2003
Fission dynamics within time-dependent Hartree-Fock. II. Boost-induced fission Goddard, Philip; Stevenson, Paul; Rios, Arnau Physical Review C, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevC.93.014620	journal	January 2016
Self-energy, momentum distribution, and effective masses of a dilute Fermi gas Sartor, R.; Mahaux, C. Physical Review C, Vol. 21, Issue 4 https://doi.org/10.1103/PhysRevC.21.1546	journal	April 1980
Large-amplitude motion in superfluid fermi droplets Barranco, F.; Bertsch, G. F.; Broglia, R. A. Nuclear Physics A, Vol. 512, Issue 2 https://doi.org/10.1016/0375-9474(90)93232-U	journal	January 1990
Induced Fission of ${}^{240}{Pu}$ within a Real-Time Microscopic Framework Bulgac, Aurel; Magierski, Piotr; Roche, Kenneth J. Physical Review Letters, Vol. 116, Issue 12 https://doi.org/10.1103/PhysRevLett.116.122504	journal	March 2016
Isovector giant dipole resonance from the 3D time-dependent density functional theory for superfluid nuclei Stetcu, I.; Bulgac, A.; Magierski, P. Physical Review C, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevC.84.051309	journal	November 2011
Nuclear Fission Dynamics: Past, Present, Needs, and Future Bulgac, Aurel; Jin, Shi; Stetcu, Ionel Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00063	journal	March 2020
Time‐Dependent Density Functional Theory for Fermionic Superfluids: From Cold Atomic Gases − To Nuclei and Neutron Stars Crust Bulgac, Aurel physica status solidi (b), Vol. 256, Issue 7 https://doi.org/10.1002/pssb.201800592	journal	February 2019
Applications of Time-Dependent Density-Matrix Approach Tohyama, Mitsuru Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00067	journal	March 2020
Momentum sharing in imbalanced Fermi systems Hen, O.; Sargsian, M.; Weinstein, L. B. Science, Vol. 346, Issue 6209 https://doi.org/10.1126/science.1256785	journal	October 2014
Theory of Nuclear Fission Krappe, Hans J.; Pomorski, Krzysztof Lecture Notes in Physics https://doi.org/10.1007/978-3-642-23515-3	book	January 2012

Similar Records

Nuclear flow inversion in the Boltzmann-Uehling-Uhlenbeck model

Journal Article · Tue Nov 10 00:00:00 EST 1998 · AIP Conference Proceedings · OSTI ID:1979888

Persram, D; Gale, C

Intensity-interferometric test of nuclear collision geometries obtained from the Boltzmann-Uehling-Uhlenbeck equation

Journal Article · Mon Oct 22 00:00:00 EDT 1990 · Physical Review Letters; (USA) · OSTI ID:1979888

Gong, W G; Bauer, W; Gelbke, C K; +15 more

Vlasov-Uehling-Uhlenbeck theory of medium energy heavy ion reactions: Role of mean field dynamics and two body collisions

Journal Article · Wed May 01 00:00:00 EDT 1985 · Phys. Rev. C; (United States) · OSTI ID:1979888

Kruse, H; Jacak, B V; Molitoris, J J; +2 more

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
density functional calculations
density functional theory
nuclear density functional theory
nuclear reactions

Title: Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation

Citation Formats

References (50)

Similar Records

Related Subjects