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Sadhasivam VG, Hunt AC, Meuser L, Litman Y, Althorpe SC. Thermal quenching of classical and semiclassical scrambling. Phys Rev E 2024; 110:L012204. [PMID: 39161010 DOI: 10.1103/physreve.110.l012204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 07/15/2024] [Indexed: 08/21/2024]
Abstract
Quantum scrambling often gives rise to short-time exponential growth in out-of-time-ordered correlators. The scrambling rate over an isolated saddle point at finite temperature is shown here to be reduced by a hierarchy of quenching processes. Two of these appear in the classical limit, where escape from the neighborhood of the saddle reduces the rate by a factor of two, and thermal fluctuations around the saddle reduce it further; a third process can be explained semiclassically as arising from quantum thermal fluctuations around the saddle, which are also responsible for imposing the Maldacena-Shenker-Stanford bound.
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Reppert M, Reppert D. Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators. J Chem Phys 2023; 158:114114. [PMID: 36948800 DOI: 10.1063/5.0135260] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023] Open
Abstract
Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.
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Affiliation(s)
- Mike Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Deborah Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
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Abstract
Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York, USA
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4
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Jansen TLC, Saito S, Jeon J, Cho M. Theory of coherent two-dimensional vibrational spectroscopy. J Chem Phys 2019; 150:100901. [DOI: 10.1063/1.5083966] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas la Cour Jansen
- University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Jonggu Jeon
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
| | - Minhaeng Cho
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
- Department of Chemistry, Korea University, Seoul 02841, South Korea
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5
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Reppert M, Brumer P. Classical coherent two-dimensional vibrational spectroscopy. J Chem Phys 2018; 148:064101. [DOI: 10.1063/1.5017985] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mike Reppert
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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Abstract
A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.
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Affiliation(s)
- Maksym Kryvohuz
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Shaul Mukamel
- Chemistry Department, University of California, Irvine, California 92697-2025, USA
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Moberg DR, Alemi M, Loring RF. Thermal weights for semiclassical vibrational response functions. J Chem Phys 2015; 143:084101. [PMID: 26328812 DOI: 10.1063/1.4929377] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Semiclassical approximations to response functions can allow the calculation of linear and nonlinear spectroscopic observables from classical dynamics. Evaluating a canonical response function requires the related tasks of determining thermal weights for initial states and computing the dynamics of these states. A class of approximations for vibrational response functions employs classical trajectories at quantized values of action variables and represents the effects of the radiation-matter interaction by discontinuous transitions. Here, we evaluate choices for a thermal weight function which are consistent with this dynamical approximation. Weight functions associated with different semiclassical approximations are compared, and two forms are constructed which yield the correct linear response function for a harmonic potential at any temperature and are also correct for anharmonic potentials in the classical mechanical limit of high temperature. Approximations to the vibrational linear response function with quantized classical trajectories and proposed thermal weight functions are assessed for ensembles of one-dimensional anharmonic oscillators. This approach is shown to perform well for an anharmonic potential that is not locally harmonic over a temperature range encompassing the quantum limit of a two-level system and the limit of classical dynamics.
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Affiliation(s)
- Daniel R Moberg
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Mallory Alemi
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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8
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Influence of the amplitude ratio between two terahertz pulses on two-dimensional spectroscopy. CHINESE SCIENCE BULLETIN-CHINESE 2014. [DOI: 10.1007/s11434-013-0042-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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9
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Hattori T. Classical theory of two-dimensional time-domain terahertz spectroscopy. J Chem Phys 2010; 133:204503. [DOI: 10.1063/1.3507256] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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10
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Gruenbaum SM, Loring RF. Semiclassical nonlinear response functions for coupled anharmonic vibrations. J Chem Phys 2009; 131:204504. [PMID: 19947691 DOI: 10.1063/1.3266566] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Observables in linear and nonlinear infrared spectroscopy may be computed from vibrational response functions describing nuclear dynamics on a single electronic surface. We demonstrate that the Herman-Kluk (HK) semiclassical approximation to the quantum propagator yields an accurate representation of quantum coherence effects in linear and nonlinear response functions for coupled anharmonic oscillators. A considerable numerical price is paid for this accuracy; the calculation requires a multidimensional integral over a highly oscillatory integrand that also grows without bound as a function of evolution times. The interference among classical trajectories in the HK approximation produces quantization of good action variables. By treating this interference analytically, we develop a mean-trajectory (MT) approximation that requires only the propagation of classical trajectories linked by transitions in action. The MT approximation accurately reproduces coherence effects in response functions of coupled anharmonic oscillators in a regime in which the observables are strongly influenced by these interactions among vibrations.
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Affiliation(s)
- Scott M Gruenbaum
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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11
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Gruenbaum SM, Loring RF. Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions. J Chem Phys 2008; 129:124510. [DOI: 10.1063/1.2978167] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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12
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Malinin SV, Chernyak VY. Classical nonlinear response of a chaotic system. I. Collective resonances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056201. [PMID: 18643136 DOI: 10.1103/physreve.77.056201] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.
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Affiliation(s)
- Sergey V Malinin
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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Malinin SV, Chernyak VY. Classical nonlinear response of a chaotic system. II. Langevin dynamics and spectral decomposition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056202. [PMID: 18643137 DOI: 10.1103/physreve.77.056202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
The spectrum of a strongly chaotic system consists of discrete complex Ruelle-Pollicott (RP) resonances. We interpret the RP resonances as eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal diffusion term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long-time asymptotic expansion in the deterministic case.
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Affiliation(s)
- Sergey V Malinin
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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14
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Gruenbaum SM, Loring RF. Interference and quantization in semiclassical response functions. J Chem Phys 2008; 128:124106. [DOI: 10.1063/1.2841943] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Malinin SV, Chernyak VY. Collective oscillations in the classical nonlinear response of a chaotic system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:025201. [PMID: 18352079 DOI: 10.1103/physreve.77.025201] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2007] [Revised: 09/26/2007] [Indexed: 05/26/2023]
Abstract
We establish a general semiquantitative phase-space picture of the classical nonlinear response in a strongly chaotic system. As opposed to the case of stable dynamics, the response functions decay exponentially at long times. Damped oscillations in response functions are attributed to collective resonances which do not correspond to any periodic classical motions. We calculate analytically the second-order response in a simple chaotic system and demonstrate the relevance of the concept for the interpretation of spectroscopic data.
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Affiliation(s)
- Sergey V Malinin
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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16
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Noid WG, Loring RF. Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations. J Chem Phys 2007; 122:174507. [PMID: 15910045 DOI: 10.1063/1.1888485] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.
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Affiliation(s)
- W G Noid
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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17
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Goj A, Loring RF. Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators. J Chem Phys 2006; 124:194101. [PMID: 16729797 DOI: 10.1063/1.2198203] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Multidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiation-matter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the third-order vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a well-defined classical mechanical limit.
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Affiliation(s)
- Anne Goj
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853, USA
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Kryvohuz M, Cao J. Classical divergence of nonlinear response functions. PHYSICAL REVIEW LETTERS 2006; 96:030403. [PMID: 16486670 DOI: 10.1103/physrevlett.96.030403] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2005] [Indexed: 05/06/2023]
Abstract
The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann distribution function. The implications of this study are discussed in the context of the conceptual development of quantum-classical correspondence in dynamic response.
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Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Kryvohuz M, Cao J. Quantum-classical correspondence in response theory. PHYSICAL REVIEW LETTERS 2005; 95:180405. [PMID: 16383881 DOI: 10.1103/physrevlett.95.180405] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2005] [Indexed: 05/05/2023]
Abstract
The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the h expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence <v + n|alpha(t)v> <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.
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Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Noid WG, Loring RF. Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams. J Chem Phys 2004; 121:7057-69. [PMID: 15473771 DOI: 10.1063/1.1792211] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
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Affiliation(s)
- W G Noid
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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Noid WG, Ezra GS, Loring RF. Vibrational Echoes: Dephasing, Rephasing, and the Stability of Classical Trajectories. J Phys Chem B 2004. [DOI: 10.1021/jp036749o] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- W. G. Noid
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853
| | - Gregory S. Ezra
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853
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Noid WG, Ezra GS, Loring RF. Semiclassical calculation of the vibrational echo. J Chem Phys 2004; 120:1491-9. [PMID: 15268274 DOI: 10.1063/1.1633550] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
The infrared echo measurement probes the time scales of the molecular motions that couple to a vibrational transition. Computation of the echo observable within rigorous quantum mechanics is problematic for systems with many degrees of freedom, motivating the development of semiclassical approximations to the nonlinear optical response. We present a semiclassical approximation to the echo observable, based on the Herman-Kluk propagator. This calculation requires averaging over a quantity generated by two pairs of classical trajectories and associated stability matrices, connected by a pair of phase-space jumps. Quantum, classical, and semiclassical echo calculations are compared for a thermal ensemble of noninteracting anharmonic oscillators. The semiclassical approach uses input from classical mechanics to reproduce the significant features of a complete, quantum mechanical calculation of the nonlinear response.
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Affiliation(s)
- W G Noid
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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Mukamel S, Maddox JB. All-forward semiclassical simulations of nonlinear response functions. J Chem Phys 2004; 121:36-43. [PMID: 15260520 DOI: 10.1063/1.1756582] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.
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Affiliation(s)
- Shaul Mukamel
- Department of Chemistry, University of California-Irvine, Irvine, California 92697-2025, USA.
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Dellago C, Mukamel S. Simulation algorithms for multidimensional nonlinear response of classical many-body systems. J Chem Phys 2003. [DOI: 10.1063/1.1616911] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
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25
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Jansen TLC, Mukamel S. Semiclassical mode-coupling factorizations of coherent nonlinear optical response. J Chem Phys 2003. [DOI: 10.1063/1.1610437] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Mukamel S. Superoperator representation of nonlinear response: unifying quantum field and mode coupling theories. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:021111. [PMID: 14524957 DOI: 10.1103/physreve.68.021111] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2003] [Indexed: 05/24/2023]
Abstract
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
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Affiliation(s)
- Shaul Mukamel
- Departments of Chemistry and Physics and Astronomy, University of Rochester, Rochester, New York 14627-0216, USA.
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