Journal of the Physical Society of Japan, ISSN 0031-9015, 2006, Volume 75, Issue 8, pp. 082001 - 1"-"082001-39

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9...

NMR | Stochastic Liouville equation | quantum Fokker-Planck equation | 2D spectroscopy | Quantum Fokker-Planck equation

NMR | Stochastic Liouville equation | quantum Fokker-Planck equation | 2D spectroscopy | Quantum Fokker-Planck equation

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 01/2015, Volume 142, Issue 2, p. 024115

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a...

MOLECULAR-DYNAMICS | LASER-PULSES | MULTIPHOTON INTRAPULSE INTERFERENCE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | STRUCTURAL EVOLUTION | CHEMISTRY, PHYSICAL | MODEL | EXCITED-STATE DYNAMICS | PROTON-TRANSFER | Models, Theoretical | Spectrum Analysis, Raman | Stochastic Processes | Time Factors | Femtosecond | Coupling (molecular) | Time resolved | Nuclear magnetic resonance--NMR | Broadband | Computer simulation | Spectrum analysis | Liouville equations | Raman spectroscopy | Narrowband | ARTICLES

MOLECULAR-DYNAMICS | LASER-PULSES | MULTIPHOTON INTRAPULSE INTERFERENCE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | STRUCTURAL EVOLUTION | CHEMISTRY, PHYSICAL | MODEL | EXCITED-STATE DYNAMICS | PROTON-TRANSFER | Models, Theoretical | Spectrum Analysis, Raman | Stochastic Processes | Time Factors | Femtosecond | Coupling (molecular) | Time resolved | Nuclear magnetic resonance--NMR | Broadband | Computer simulation | Spectrum analysis | Liouville equations | Raman spectroscopy | Narrowband | ARTICLES

Journal Article

Stochastic Environmental Research and Risk Assessment, ISSN 1436-3240, 10/2015, Volume 29, Issue 7, pp. 1867 - 1880

Long-term shoreline evolution due to longshore sediment transport is one of the key processes that need to be addressed in coastal engineering design and...

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Math. Appl. in Environmental Science | Computational Intelligence | Total variation diminishing | Shoreline evolution | Liouville equation | Probability density function | Environment | Probability Theory and Stochastic Processes | Earth Sciences, general | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | BEACH | DIFFERENTIAL-EQUATION | STATISTICS & PROBABILITY | WATER RESOURCES | COASTAL REGIONS | COASTLINE | PRINCIPLE | 3RD-GENERATION WAVE MODEL | PREDICTION | PRESERVATION | ENVIRONMENTAL SCIENCES | PROBABILITY | ENGINEERING, CIVIL | ENGINEERING, ENVIRONMENTAL | UNCERTAINTY | Waterfront development | Monte Carlo method | Algorithms | Beach erosion | Analysis | Sediment transport | Shorelines | Coastal engineering | Computer simulation | Mathematical analysis | Evolution | Mathematical models | Beaches | Stochasticity

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Math. Appl. in Environmental Science | Computational Intelligence | Total variation diminishing | Shoreline evolution | Liouville equation | Probability density function | Environment | Probability Theory and Stochastic Processes | Earth Sciences, general | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | BEACH | DIFFERENTIAL-EQUATION | STATISTICS & PROBABILITY | WATER RESOURCES | COASTAL REGIONS | COASTLINE | PRINCIPLE | 3RD-GENERATION WAVE MODEL | PREDICTION | PRESERVATION | ENVIRONMENTAL SCIENCES | PROBABILITY | ENGINEERING, CIVIL | ENGINEERING, ENVIRONMENTAL | UNCERTAINTY | Waterfront development | Monte Carlo method | Algorithms | Beach erosion | Analysis | Sediment transport | Shorelines | Coastal engineering | Computer simulation | Mathematical analysis | Evolution | Mathematical models | Beaches | Stochasticity

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 01/2015, Volume 142, Issue 2

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a...

VARIATIONS | STOCHASTIC PROCESSES | VIBRATIONAL STATES | ELECTRONS | NUCLEAR MAGNETIC RESONANCE | TIME RESOLUTION | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | BOLTZMANN-VLASOV EQUATION | RAMAN SPECTROSCOPY | COUPLING | MOLECULES

VARIATIONS | STOCHASTIC PROCESSES | VIBRATIONAL STATES | ELECTRONS | NUCLEAR MAGNETIC RESONANCE | TIME RESOLUTION | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | BOLTZMANN-VLASOV EQUATION | RAMAN SPECTROSCOPY | COUPLING | MOLECULES

Journal Article

Physical Review A - Atomic, Molecular, and Optical Physics, ISSN 1050-2947, 08/2010, Volume 82, Issue 2

Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation....

BROWNIAN-MOTION | STATES | ENTANGLEMENT | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | MODEL | OPTICS | DIFFERENTIAL EQUATIONS | VARIATIONS | STOCHASTIC PROCESSES | MARKOV PROCESS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INFORMATION | ATOMIC AND MOLECULAR PHYSICS | BOLTZMANN-VLASOV EQUATION | EQUATIONS | RELAXATION | CORRELATIONS | QUANTUM ENTANGLEMENT | QUANTUM STATES | ENERGY LEVELS | QUBITS | QUANTUM INFORMATION | PARTIAL DIFFERENTIAL EQUATIONS | FLUCTUATIONS | TIME DEPENDENCE

BROWNIAN-MOTION | STATES | ENTANGLEMENT | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | MODEL | OPTICS | DIFFERENTIAL EQUATIONS | VARIATIONS | STOCHASTIC PROCESSES | MARKOV PROCESS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INFORMATION | ATOMIC AND MOLECULAR PHYSICS | BOLTZMANN-VLASOV EQUATION | EQUATIONS | RELAXATION | CORRELATIONS | QUANTUM ENTANGLEMENT | QUANTUM STATES | ENERGY LEVELS | QUBITS | QUANTUM INFORMATION | PARTIAL DIFFERENTIAL EQUATIONS | FLUCTUATIONS | TIME DEPENDENCE

Journal Article

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, ISSN 0022-0434, 07/2010, Volume 132, Issue 4, pp. 1 - 4

This technical brief shows that given a system and its abstraction, the evolution of uncertain initial conditions in the original system is, in some sense,...

dynamics | INSTRUMENTS & INSTRUMENTATION | mechanical engineering | uncertain systems | DYNAMICAL-SYSTEMS | POLYNOMIAL CHAOS | Liouville equation | AUTOMATION & CONTROL SYSTEMS | PREDICTION | Usage | Mathematical models | Design and construction | Stochastic systems | Mechanical ability | Analysis

dynamics | INSTRUMENTS & INSTRUMENTATION | mechanical engineering | uncertain systems | DYNAMICAL-SYSTEMS | POLYNOMIAL CHAOS | Liouville equation | AUTOMATION & CONTROL SYSTEMS | PREDICTION | Usage | Mathematical models | Design and construction | Stochastic systems | Mechanical ability | Analysis

Journal Article

The Journal of Physical Chemistry B, ISSN 1520-6106, 11/2008, Volume 112, Issue 45, pp. 14212 - 14220

Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer...

B: Statistical Mechanics, Thermodynamics, Medium Effects | ELECTRON-TRANSFER | HYDROGEN-BOND | FLUCTUATIONS | DYNAMICS | CHEMISTRY, PHYSICAL | ENERGY-TRANSFER | TIME | SIMULATION | FEMTOSECOND SPECTROSCOPY | Models, Chemical | Stochastic Processes | Time Factors | Photons | Diffusion | Spectrum Analysis | Dimerization | Normal Distribution | Exciton theory | Evaluation | Usage | Optical properties | Stochastic processes | Chemical properties | Vibrational spectra

B: Statistical Mechanics, Thermodynamics, Medium Effects | ELECTRON-TRANSFER | HYDROGEN-BOND | FLUCTUATIONS | DYNAMICS | CHEMISTRY, PHYSICAL | ENERGY-TRANSFER | TIME | SIMULATION | FEMTOSECOND SPECTROSCOPY | Models, Chemical | Stochastic Processes | Time Factors | Photons | Diffusion | Spectrum Analysis | Dimerization | Normal Distribution | Exciton theory | Evaluation | Usage | Optical properties | Stochastic processes | Chemical properties | Vibrational spectra

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 2004, Volume 340, Issue 1, pp. 283 - 291

The non-Markovian variant of the stochastic Liouville equation (SLE) based and the continuous time random walk approach (CTRWA) is proposed. This SLE turns out...

Stochastic Lioville equation | Anomalous diffusion | DIFFUSION | anomalous diffusion | PHYSICS, MULTIDISCIPLINARY | stochastic Lioville equation | WELL

Stochastic Lioville equation | Anomalous diffusion | DIFFUSION | anomalous diffusion | PHYSICS, MULTIDISCIPLINARY | stochastic Lioville equation | WELL

Journal Article

Journal of Shanghai Jiaotong University/Shanghai Jiaotong Daxue Xuebao, ISSN 1006-2467, 01/2014, Volume 48, Issue 1, pp. 81 - 85

The offshore platform tubular joint fatigue life reliability prediction was achieved by employing the Liouville probability density evolution equation to...

Fatigue life | Mathematical analysis | Stochastic processes | Evolution | Mathematical models | Density | Probability density functions | Crack propagation

Fatigue life | Mathematical analysis | Stochastic processes | Evolution | Mathematical models | Density | Probability density functions | Crack propagation

Journal Article

10.
Full Text
Some Aspects of the Liouville Equation in Mathematical Physics and Statistical Mechanics

International Journal of Theoretical Physics, ISSN 0020-7748, 10/2011, Volume 50, Issue 10, pp. 3251 - 3274

This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem....

String theory | Classical Liouville theorem | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Stochastic Liouville equation (SLE) | Physics | Mathematical physics | Elementary Particles, Quantum Field Theory | PROTON-TRANSFER REACTIONS | STEADY-STATES | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | CONSISTENT-FIELD APPROXIMATION | SCHRODINGER EQUATION | DISSOCIATION DYNAMICS | WAVE-PACKET DYNAMICS | NON-HAMILTONIAN SYSTEMS | NONEQUILIBRIUM MOLECULAR-DYNAMICS | SEMICLASSICAL DYNAMICS | Universities and colleges

String theory | Classical Liouville theorem | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Stochastic Liouville equation (SLE) | Physics | Mathematical physics | Elementary Particles, Quantum Field Theory | PROTON-TRANSFER REACTIONS | STEADY-STATES | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | CONSISTENT-FIELD APPROXIMATION | SCHRODINGER EQUATION | DISSOCIATION DYNAMICS | WAVE-PACKET DYNAMICS | NON-HAMILTONIAN SYSTEMS | NONEQUILIBRIUM MOLECULAR-DYNAMICS | SEMICLASSICAL DYNAMICS | Universities and colleges

Journal Article

Journal of Magnetic Resonance, ISSN 1090-7807, 2007, Volume 189, Issue 1, pp. 59 - 77

An algorithm is developed that extends the well known nitroxide slow-motional continuous wave electron paramagnetic resonance (EPR) simulation technique...

Threshold directed signature | Solution of the radical Mes ∗(CH 3)P-PMes ∗ [Mes ∗ = 2,4,6 (tBu) 3C 2H 2] in tetrahydrofuran | Simulation of EPR spectrum | Bilinear pairings | Provable security | Stochastic Liouville equation | Directed signature | Slow-motion spectrum | One electron spin coupled to two nuclear spins | Solution of the radical Mes | CH | P-PMes | in tetrahydrofuran | 2,4,6 (tBu) | Mes | FLUIDS | FOKKER-PLANCK FORMS | LANCZOS-ALGORITHM | slow-motion spectrum | BIOCHEMICAL RESEARCH METHODS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | directed signature | bilinear pairings | stochastic Lionville equation | simulation of EPR spectrum | threshold directed signature | RESONANCE | SPECTROSCOPY | ESR-SPECTRA | LOCAL-STRUCTURE MODEL | T4 LYSOZYME DYNAMICS | provable security | solution of the radical Mes(CH3)P-PMeS [Mes=2,4,6 (tBU)3C2H2] in tetrahydrofuran | one electron spin coupled to two nuclear spins | Organophosphorus Compounds - chemistry | Algorithms | Electron Spin Resonance Spectroscopy - methods | Computer Simulation | Tetrahydrofuran | Usage | Radicals (Chemistry)

Threshold directed signature | Solution of the radical Mes ∗(CH 3)P-PMes ∗ [Mes ∗ = 2,4,6 (tBu) 3C 2H 2] in tetrahydrofuran | Simulation of EPR spectrum | Bilinear pairings | Provable security | Stochastic Liouville equation | Directed signature | Slow-motion spectrum | One electron spin coupled to two nuclear spins | Solution of the radical Mes | CH | P-PMes | in tetrahydrofuran | 2,4,6 (tBu) | Mes | FLUIDS | FOKKER-PLANCK FORMS | LANCZOS-ALGORITHM | slow-motion spectrum | BIOCHEMICAL RESEARCH METHODS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | directed signature | bilinear pairings | stochastic Lionville equation | simulation of EPR spectrum | threshold directed signature | RESONANCE | SPECTROSCOPY | ESR-SPECTRA | LOCAL-STRUCTURE MODEL | T4 LYSOZYME DYNAMICS | provable security | solution of the radical Mes(CH3)P-PMeS [Mes=2,4,6 (tBU)3C2H2] in tetrahydrofuran | one electron spin coupled to two nuclear spins | Organophosphorus Compounds - chemistry | Algorithms | Electron Spin Resonance Spectroscopy - methods | Computer Simulation | Tetrahydrofuran | Usage | Radicals (Chemistry)

Journal Article

Journal of Magnetic Resonance, ISSN 1090-7807, 2008, Volume 193, Issue 1, pp. 119 - 126

A stochastic Liouville equation (SLE) was numerically solved to obtain pulsed Fourier-transform (FT) EPR spectra on a radical pair system created in a...

FT-EPR | Radical pair | Stochastic Liouville equation | CIDEP | Radicals (Chemistry)

FT-EPR | Radical pair | Stochastic Liouville equation | CIDEP | Radicals (Chemistry)

Journal Article

JOURNAL OF MAGNETIC RESONANCE, ISSN 1090-7807, 07/2008, Volume 193, Issue 1, pp. 119 - 126

A stochastic Liouville equation (SLE) was numerically solved to obtain pulsed Fourier-transform (FT) EPR spectra on a radical pair system created in a...

FT-EPR | MECHANISM | NUTATION SPECTROSCOPY | BIOCHEMICAL RESEARCH METHODS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | stochastic Liouville equation | ACETONE | Fr-EPR | ANTIPHASE STRUCTURE | MICELLAR-SOLUTION | DYNAMIC ELECTRON POLARIZATION | CIDEP SPECTRUM | PARAMAGNETIC-RESONANCE | SPECTROSCOPY | ESR-SPECTRA | radical pair | CIDEP

FT-EPR | MECHANISM | NUTATION SPECTROSCOPY | BIOCHEMICAL RESEARCH METHODS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | stochastic Liouville equation | ACETONE | Fr-EPR | ANTIPHASE STRUCTURE | MICELLAR-SOLUTION | DYNAMIC ELECTRON POLARIZATION | CIDEP SPECTRUM | PARAMAGNETIC-RESONANCE | SPECTROSCOPY | ESR-SPECTRA | radical pair | CIDEP

Journal Article

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, ISSN 0031-9015, 08/2006, Volume 75, Issue 8

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9...

3-PULSE PHOTON-ECHOES | PHYSICS, MULTIDISCIPLINARY | stochastic Liouville equation | 5TH-ORDER RAMAN RESPONSE | 2D spectroscopy | NMR | quantum Fokker-Planck equation | 2-TIME CORRELATION-FUNCTIONS | INTERMEDIATE STATE INTERACTION | 2ND-ORDER OPTICAL PROCESSES | ELECTRON-PHONON SYSTEM | 2-DIMENSIONAL VIBRATIONAL SPECTROSCOPY | PATH-INTEGRAL APPROACH | MOLECULAR-DYNAMICS SIMULATIONS | ROTATIONAL BROWNIAN MOTION

3-PULSE PHOTON-ECHOES | PHYSICS, MULTIDISCIPLINARY | stochastic Liouville equation | 5TH-ORDER RAMAN RESPONSE | 2D spectroscopy | NMR | quantum Fokker-Planck equation | 2-TIME CORRELATION-FUNCTIONS | INTERMEDIATE STATE INTERACTION | 2ND-ORDER OPTICAL PROCESSES | ELECTRON-PHONON SYSTEM | 2-DIMENSIONAL VIBRATIONAL SPECTROSCOPY | PATH-INTEGRAL APPROACH | MOLECULAR-DYNAMICS SIMULATIONS | ROTATIONAL BROWNIAN MOTION

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 05/2008, Volume 77, Issue 19

An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss...

PHYSICS, CONDENSED MATTER | TRANSPORT | PHYSICS, APPLIED | STOCHASTIC LIOUVILLE EQUATION | SPIN | MATERIALS SCIENCE, MULTIDISCIPLINARY | DRIVEN SYSTEM | RANDOM FREQUENCY MODULATIONS | ZERO-BIAS ANOMALIES

PHYSICS, CONDENSED MATTER | TRANSPORT | PHYSICS, APPLIED | STOCHASTIC LIOUVILLE EQUATION | SPIN | MATERIALS SCIENCE, MULTIDISCIPLINARY | DRIVEN SYSTEM | RANDOM FREQUENCY MODULATIONS | ZERO-BIAS ANOMALIES

Journal Article

International Journal of Modelling, Identification and Control, ISSN 1746-6172, 05/2010, Volume 9, Issue 4, pp. 392 - 399

Journal Article

Structural Safety, ISSN 0167-4730, 2008, Volume 30, Issue 1, pp. 65 - 77

The present paper aims to provide a uniform and rigorous theoretical basis for the family of newly developed probability density evolution method. Conservation...

Probability density evolution method | The principle of preservation of probability | Generalized density evolution equation | Stochastic dynamical systems | Liouville equation | ENGINEERING, CIVIL | probability density evolution method | MOTION | RELIABILITY-ANALYSIS | the principle of preservation of probability | DYNAMIC-RESPONSE ANALYSIS | SYSTEMS | UNCERTAIN PARAMETERS | stochastic dynamical systems | generalized density evolution equation | NONLINEAR STOCHASTIC STRUCTURES | Nature conservation

Probability density evolution method | The principle of preservation of probability | Generalized density evolution equation | Stochastic dynamical systems | Liouville equation | ENGINEERING, CIVIL | probability density evolution method | MOTION | RELIABILITY-ANALYSIS | the principle of preservation of probability | DYNAMIC-RESPONSE ANALYSIS | SYSTEMS | UNCERTAIN PARAMETERS | stochastic dynamical systems | generalized density evolution equation | NONLINEAR STOCHASTIC STRUCTURES | Nature conservation

Journal Article

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, ISSN 1386-1425, 2005, Volume 61, Issue 1, pp. 299 - 304

This paper discusses the process of energy migration transfer within reorientating chromophores using the stochastic master equation (SME) and the stochastic...

Förster theory | Electronic energy migration | Stochastic Liouville equation | Stochastic master equation | Memory effect | Forster theory | MOLECULAR-DYNAMICS | BROWNIAN DYNAMIC SIMULATION | MACROMOLECULES | SPECTROSCOPY | stochastic Liouville equation | electronic energy migration | FLUORESCENCE ANISOTROPY | stochastic master equation | memory effect | Probability | Motion | Energy Transfer | Models, Chemical | Stochastic Processes | Electrons

Förster theory | Electronic energy migration | Stochastic Liouville equation | Stochastic master equation | Memory effect | Forster theory | MOLECULAR-DYNAMICS | BROWNIAN DYNAMIC SIMULATION | MACROMOLECULES | SPECTROSCOPY | stochastic Liouville equation | electronic energy migration | FLUORESCENCE ANISOTROPY | stochastic master equation | memory effect | Probability | Motion | Energy Transfer | Models, Chemical | Stochastic Processes | Electrons

Journal Article

Chemical Physics, ISSN 0301-0104, 01/2015, Volume 446, pp. 134 - 141

A stochastic Liouville–von Neumann approach to solving a spin-boson model is applied to electronic energy transfer in Fenna–Matthews–Olson (FMO) complexes as a...

Energy transfer dynamics | Exciton | Long coherent dynamics | FMO complex | Stochastic Liouville–von Neumann equation | Noise generation method | Liouville-von | Stochastic | Neumann equation | LIGHT-HARVESTING COMPLEXES | QUANTUM STATE DIFFUSION | TIME EVOLUTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | DISSIPATIVE 2-STATE SYSTEM | Stochastic Liouville-von Neumann equation | SIMULATION | REDUCED DENSITY-MATRICES | TEMPERATURE | DYNAMICS | TENSOR PROPAGATOR | COHERENCE | Case studies | Population biology

Energy transfer dynamics | Exciton | Long coherent dynamics | FMO complex | Stochastic Liouville–von Neumann equation | Noise generation method | Liouville-von | Stochastic | Neumann equation | LIGHT-HARVESTING COMPLEXES | QUANTUM STATE DIFFUSION | TIME EVOLUTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | DISSIPATIVE 2-STATE SYSTEM | Stochastic Liouville-von Neumann equation | SIMULATION | REDUCED DENSITY-MATRICES | TEMPERATURE | DYNAMICS | TENSOR PROPAGATOR | COHERENCE | Case studies | Population biology

Journal Article