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Table representation of search results timeline featuring number of search results per year.

Year Number of Results
1965 1
1970 1
1975 1
1977 2
1979 1
1982 2
1984 1
1985 2
1986 4
1987 3
1988 2
1989 2
1990 2
1992 5
1993 3
1994 2
1995 3
1996 2
1998 1
1999 7
2000 4
2001 4
2002 7
2003 13
2004 14
2005 28
2006 29
2007 14
2008 19
2009 21
2010 15
2011 33
2012 23
2013 24
2014 29
2015 22
2016 30
2017 27
2018 32
2019 29
2020 33
2021 25
2022 13
2023 32
2024 8

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557 results

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Page 1
Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling.
Toutounji M. Toutounji M. J Chem Theory Comput. 2023 Jul 11;19(13):3779-3797. doi: 10.1021/acs.jctc.2c01225. Epub 2023 Jun 26. J Chem Theory Comput. 2023. PMID: 37365487 Review.
This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. ...
This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equa …
Stochastic Liouville equation for particles driven by dichotomous environmental noise.
Bressloff PC. Bressloff PC. Phys Rev E. 2017 Jan;95(1-1):012124. doi: 10.1103/PhysRevE.95.012124. Epub 2017 Jan 17. Phys Rev E. 2017. PMID: 28208333
The population density of particle states evolves according to a stochastic Liouville equation with respect to different realizations of the DMNP. We then exploit the connection with previous work on diffusion in randomly switching environments, in order to derive m …
The population density of particle states evolves according to a stochastic Liouville equation with respect to different reali …
Destructive relativity.
Przybylska M, Szumiński W, Maciejewski AJ. Przybylska M, et al. Chaos. 2023 Jun 1;33(6):063156. doi: 10.1063/5.0140633. Chaos. 2023. PMID: 37368038
The description of dynamics for high-energy particles requires an application of the special relativity theory framework, and analysis of properties of the corresponding equations of motion is very important. Here, we analyze Hamilton equations of motion in the limi …
The description of dynamics for high-energy particles requires an application of the special relativity theory framework, and analysis of pr …
Exact solution to a Liouville equation with Stuart vortex distribution on the surface of a torus.
Sakajo T. Sakajo T. Proc Math Phys Eng Sci. 2019 Apr;475(2224):20180666. doi: 10.1098/rspa.2018.0666. Epub 2019 Apr 3. Proc Math Phys Eng Sci. 2019. PMID: 31105449 Free PMC article.
A steady solution of the incompressible Euler equation on a toroidal surface TR,r of major radius R and minor radius r is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, TR,r2psi = c edpsi + (8/d)kappa , wh …
A steady solution of the incompressible Euler equation on a toroidal surface TR,r of major radius R and minor radius r is provided. I …
Non-Equilibrium Liouville and Wigner Equations: Classical Statistical Mechanics and Chemical Reactions for Long Times.
Álvarez-Estrada RF. Álvarez-Estrada RF. Entropy (Basel). 2019 Feb 14;21(2):179. doi: 10.3390/e21020179. Entropy (Basel). 2019. PMID: 33266895 Free PMC article. Review.
We treat classical closed three-dimensional many-particle interacting systems without any "heat bath" (h b), evolving through the Liouville equation for the non-equilibrium classical distribution W c, with initial states describing thermal equilibrium at large dista …
We treat classical closed three-dimensional many-particle interacting systems without any "heat bath" (h b), evolving through the Liouvil …
Boltzmann stochastic thermodynamics.
de Oliveira MJ. de Oliveira MJ. Phys Rev E. 2019 May;99(5-1):052138. doi: 10.1103/PhysRevE.99.052138. Phys Rev E. 2019. PMID: 31212577
The stochastic evolution yields a generation of entropy, leading to an increase of Gibbs entropy, in contrast to a Hamiltonian dynamics, described by the Liouville equation, for which the entropy is constant in time. By considering transition rates corresponding to …
The stochastic evolution yields a generation of entropy, leading to an increase of Gibbs entropy, in contrast to a Hamiltonian dynamics, des …
Liouville-von Neumann molecular dynamics.
Jakowski J, Morokuma K. Jakowski J, et al. J Chem Phys. 2009 Jun 14;130(22):224106. doi: 10.1063/1.3152120. J Chem Phys. 2009. PMID: 19530761
We present a novel first principles molecular dynamics scheme, called Liouville-von Neumann molecular dynamics, based on Liouville-von Neumann equation for density matrices propagation and Magnus expansion of the time-evolution operator. ...The method require …
We present a novel first principles molecular dynamics scheme, called Liouville-von Neumann molecular dynamics, based on Liouville …
Fractional Langevin equation and Riemann-Liouville fractional derivative.
Sau Fa K. Sau Fa K. Eur Phys J E Soft Matter. 2007 Oct;24(2):139-43. doi: 10.1140/epje/i2007-10224-2. Epub 2007 Oct 22. Eur Phys J E Soft Matter. 2007. PMID: 17955164
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. ...We also compare them with the results obtained f …
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifi …
Spectral properties of an impulsive Sturm-Liouville operator.
Bairamov E, Erdal I, Yardimci S. Bairamov E, et al. J Inequal Appl. 2018;2018(1):191. doi: 10.1186/s13660-018-1781-0. Epub 2018 Jul 27. J Inequal Appl. 2018. PMID: 30137919 Free PMC article.
This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm-Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of the mentioned operato …
This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm-Lio …
Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum-classical Liouville equation.
Kim HW, Rhee YM. Kim HW, et al. J Chem Phys. 2020 Dec 7;153(21):214103. doi: 10.1063/5.0027799. J Chem Phys. 2020. PMID: 33291890
Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using two oscillators for each electronic state. ...
Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using …
557 results