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Quantum Liouville-space trajectories for dissipative systems [article]

Jeremy B. Maddox, Eric R. Bittner
2001 arXiv   pre-print
Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum equations-of-motion for Liouville-space trajectories for a generalized system coupled to  ...  In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems.  ...  This approach opens a clear avenue to a number of new semi-classical and quantum-classical approximations for the quantum density matrix.  ... 
arXiv:quant-ph/0102055v1 fatcat:7mwhx7ix2jd7vj73clh4wyuinu

Multidimensional classical Liouville dynamics with quantum initial conditions

Illia Horenko, Burkhard Schmidt, Christof Schütte
2002 Journal of Chemical Physics  
A simple and numerically efficient approach to Wigner transforms and classical Liouville dynamics in phase space is presented. ͑1͒ The Wigner transform can be obtained with a given accuracy by optimal  ...  decomposition of an initial quantum-mechanical wave function in terms of a minimal set of Gaussian wave packets. ͑2͒ The solution of the classical Liouville equation within the locally quadratic approximation  ...  INTRODUCTION The classical Liouville equation ͑CLE͒ represents the conceptually most straightforward approach to the classical approximation of quantum dynamics.  ... 
doi:10.1063/1.1498467 fatcat:rje2ukahsbbnzb7slbkcg5rsha

Time Irreversibility Problem and Functional Formulation of Classical Mechanics [article]

Igor V. Volovich
2009 arXiv   pre-print
In the approach presented in this paper the physical meaning is attributed not to an individual trajectory but only to a bunch of trajectories or to the distribution function on the phase space.  ...  The fundamental equation of the microscopic dynamics in the proposed "functional" approach is not the Newton equation but the Liouville equation for the distribution function of a single particle.  ...  Acknowledgements The author expresses his sincere thanks to G.A. Alexeev, I.Ya  ... 
arXiv:0907.2445v1 fatcat:iovlbexpzrhnpjw3borsnq3cty

Page 5778 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region.  ...  Summary: “The Liouville-Bloch equation for a general spin j in time-dependent external fields is solved as a unitary product of exponential operators.  ... 

A theoretical model for molecules interacting with intense laser pulses: The Floquet-based quantum-classical Liouville equation

Illia Horenko, Burkhard Schmidt, Christof Schütte
2001 Journal of Chemical Physics  
The Floquet-based quantum-classical Liouville equation ͑F-QCLE͒ is presented as a novel theoretical model for the interaction of molecules with intense laser pulses.  ...  A numerical scheme to solve the F-QCLE is based on a Trotter splitting of the time evolution.  ...  Floquet-based quantum-classical Liouville equation In order to obtain a quantum-classical equation of motion for the system under consideration, we have to calculate the partial Wigner transform of the  ... 
doi:10.1063/1.1398577 fatcat:25lgcf4t7zg75arcxlyn6blepi

Phase-space description of the coherent state dynamics in a small one-dimensional system

Urszula Kaczor, Bogusław Klimas, Dominik Szydłowski, Maciej Wołoszyn, Bartłomiej J. Spisak
2016 Open Physics  
Quantum trajectories in the phase space are computed for different kinetic energies of the initial wave packet in the Wigner form. The results are compared with the classical trajectories.  ...  AbstractThe Wigner-Moyal approach is applied to investigate the dynamics of the Gaussian wave packet moving in a double-well potential in the 'Mexican hat' form.  ...  Acknowledgment This work was supported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research.  ... 
doi:10.1515/phys-2016-0036 fatcat:pmestkxzt5b6nhdisc23ydlxz4

Simulation of quantum processes using entangled trajectory molecular dynamics

Arnaldo Donoso, Yujun Zheng, Craig C. Martens
2003 Journal of Chemical Physics  
The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space.  ...  The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution.  ...  This work was supported by the National Science Foundation.  ... 
doi:10.1063/1.1597496 fatcat:6o64z2wjdfeu7jiv6vzyqw4bvm

The Liouville Dynamics of the q-Deformed 1-D Classical Harmonic Oscillator [article]

A. S. Mahmood, M. A. Z. Habeeb
2016 arXiv   pre-print
The resulting Liouville equation is solved by using the method of characteristics in order to obtain the classical probability distribution function for this system.  ...  The Liouville equation for the q-deformed 1-D classical harmonic oscillator is derived for two definitions of q-deformation.  ...  Solving these equations of motion gives the equations of trajectories for the q-deformed classical harmonic oscillator in the complex   ,   phase space:             0 ; 1, 2. 0 it q te  ... 
arXiv:1611.03682v1 fatcat:gnhluiosenbyjp7dynrzykcymm

The Liouville Dynamics of the q-Deformed 1-D Classical Harmonic Oscillator

A. S. Mahmood, M. A. Z. Habeeb
2016 Al-Nahrain Journal of Science  
The resulting Liouville equation is solved by using the method of characteristics in order to obtain the classical probability distribution function for this system.  ...  The Liouville equation for the q-deformed 1-D classical harmonic oscillator is derived for two definitions of q-deformation.  ...  Solving these equations of motion gives the equations of trajectories for the q-deformed classical harmonic oscillator in the complex   ,   phase space:             0 ; 1, 2. 0 it q t  ... 
doi:10.22401/jnus.19.1.14 fatcat:4bnv5l7qkbab7fru72hbp7nyqu

Quantum-classical Liouville approach to molecular dynamics: Surface hopping Gaussian phase-space packets

Illia Horenko, Christian Salzmann, Burkhard Schmidt, Christof Schütte
2002 Journal of Chemical Physics  
Such models can be systematically derived as a first-order approximation to the partial Wigner transform of the quantum Liouville-von Neumann equation.  ...  The resulting adiabatic quantum-classical Liouville equation ͑QCLE͒ can be decomposed into three individual propagators by means of a Trotter splitting: ͑1͒ phase oscillations of the coherences resulting  ...  Quantum-classical Liouville equation In order to obtain a quantum-classical equation of motion for the system under consideration, we have to calculate a partial Wigner transform of the quantum Liouville  ... 
doi:10.1063/1.1522712 fatcat:gn3k5teckrf7rnbdlpivn47rtm

Mixed quantum-classical molecular dynamics: Aspects of the multithreads algorithm

Chun-Cheng Wan, Jeremy Schofield
2000 Journal of Chemical Physics  
The mixed quantum-classical Liouville equation is derived from a semiclassical perspective starting from the full quantum Schrödinger equation.  ...  An asymptotic numerical scheme for solving the equation is discussed which relies on propagating swarms of interacting "threads" which represent the density matrix or other observable.  ...  Coker for his quantum dynamics code and P. J. Rossky for providing the MFSH data for the model systems. The authors would also like to thank R. Van Zon for useful discussions.  ... 
doi:10.1063/1.1313525 fatcat:xicxb6lo5nepbbsnundrhh6urm

Quantum irreversibility and chaos

Luca Bonci, Roberto Roncaglia, Bruce J. West, Paolo Grigolini
1991 Physical Review Letters  
We obtain quantum averages by numerically integrating the appropriate Liouville-Von Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semi-classical  ...  However, the quantum averages are shown to be dissipative as measured by the entropy of the spin subsystem and to suppress the phenomenon of "revivals".  ...  We refer to the calculations based on the study of the single trajectory solutions of the nonlinear dynamic equations as the semiclassical predictions.  ... 
doi:10.1103/physrevlett.67.2593 pmid:10044468 fatcat:4sqnbws4ojguzaf6efrvmsqvwm

Nonadiabatic dynamics in the semiclassical Liouville representation: Locality, transformation theory, and the energy budget

Craig C. Martens
2016 Chemical Physics  
In this paper, we revisit the semiclassical Liouville approach to describing molecular dynamics with electronic transitions using classical trajectories.  ...  The representation dependence of the coupled semiclassical Liouville equations in the diabatic and adiabatic bases are discussed and new results for the transformation theory of the Wigner functions representing  ...  Acknowledgments We are grateful to Shaul Mukamel, Vladimir Mandelshtam, and Greg Ezra for helpful discussions.  ... 
doi:10.1016/j.chemphys.2016.06.013 fatcat:76olmcnlsvgzldlk7wmykocx3q

Quantum Irreversibility and Chaos

Bruce J. West, Paolo Grigolini, Luca Bonci, Roberto Roncaglia
1997 Zeitschrift fur Naturforschung A-A Journal of Physical Sciences  
We obtain quantum averages by numerically integrating the appropriate Liouville-Von Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semi-classical  ...  However, the quantum averages are shown to be dissipative as measured by the entropy of the spin subsystem and to suppress the phenomenon of "revivals".  ...  We refer to the calculations based on the study of the single trajectory solutions of the nonlinear dynamic equations as the semiclassical predictions.  ... 
doi:10.1515/zna-1997-1-215 fatcat:myfj6z7urvdehklehucu6objja

Quantum-classical Liouville description of multidimensional nonadiabatic molecular dynamics

Mark Santer, Uwe Manthe, Gerhard Stock
2001 Journal of Chemical Physics  
In particular, the approach is shown to provide a correct quantum-classical description of the electronic coherence.  ...  Liouville equation.  ...  This work has been supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.  ... 
doi:10.1063/1.1336576 fatcat:3qrlzf35zregxdt5fuomiwtayi
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