Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

S. López-López, Rocco Martinazzo, Mathias Nest

Published Mar 1, 2011• 24 citations
Publisher

Abstract

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.

DOI
10.1063/1.3556940

Related papers

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

David Gelman, Christiane P. Koch, Ronnie Kosloff

The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.

arXiv:quant-ph/0402144•The Journal of Chemical Physics•Jun 23, 2004•51 citations

Analysis of the continuous-configuration time-dependent self-consistent field method applied to system-bath dynamics

Sergio López-López, Mathias Nest

We have implemented and studied the continuous-configuration time-dependent self-consistent field scheme, a variation of the multiconfiguration time-dependent Hartree method, which aims to get around the latter's exponential scaling problem, especially with regard to system-bath dynamics. We present applications to quantum dissipative dynamics and an analysis of the computational effort. Namely, propagation times within this scheme scale linearly with the number of bath modes.

The Journal of Chemical Physics•Mar 9, 2010•7 citations

A local coherent-state approximation to system-bath quantum dynamics

Rocco Martinazzo, Mathias Nest, Peter Saalfrank +1 more

A novel quantum method to deal with typical system-bath dynamical problems is introduced. Subsystem discrete variable representation and bath coherent-state sets are used to write down a multiconfigurational expansion of the wave function of the whole system. With the help of the Dirac-Frenkel variational principle, simple equations of motion--a kind of Schrodinger-Langevin equation for the subsystem coupled to (pseudo) classical equations for the bath--are derived. True dissipative dynamics at all times is obtained by coupling the bath to a secondary, classical Ohmic bath, which is modeled by adding a friction coefficient in the derived pseudoclassical bath equations. The resulting equations are then solved for a number of model problems, ranging from tunneling to vibrational relaxation dynamics. Comparison of the results with those of exact, multiconfiguration time-dependent Hartree calculations in systems with up to 80 bath oscillators shows that the proposed method can be very accurate and might be of help in studying realistic problems with very large baths. To this end, its linear scaling behavior with respect to the number of bath degrees of freedom is shown in practice with model calculations using tens of thousands of bath oscillators.

The Journal of Chemical Physics•Nov 15, 2006•58 citations

Numerically exact quantum dynamics of bosons with time-dependent interactions of harmonic type

Axel U. J. Lode, Kaspar Sakmann, Ofir E. Alon +2 more

The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time dependency. We show that when the external trap potential and interparticle interaction have a time dependency, the numerically exact solutions of the corresponding time-dependent many-boson Schr\"odinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. 99, 030402 (2007); Phys. Rev. A 77, 033613 (2008)]. In particular, we benchmark the MCTDHB method for (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the nonequilibrium dynamic for driven scenarios where both the trap- and interparticle-interaction potentials are time-dependent. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning a Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultracold Bose-Einstein condensed systems are addressed.

arXiv:1207.5128•Physical Review A•Dec 6, 2012•117 citations

Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath

Adam Přáda, Eszter S. Pós, Stuart C. Althorpe

We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction. The resulting Matsubara TCFs are in near-perfect agreement with the exact quantum TCFs, for non-linear as well as linear operators, at a temperature at which the TCFs are dominated by quantum thermal fluctuations. These results provide compelling evidence that incoherent classical dynamics can arise in the condensed phase at temperatures at which the statistics are dominated by quantum (Boltzmann) effects, as a result of smoothing of imaginary-time Feynman paths. The techniques developed here may also lead to efficient methods for benchmarking system-bath dynamics in the overdamped regime.

arXiv:2211.02042•The Journal of Chemical Physics•Mar 15, 2023•6 citations

Decoherence and dissipation in a molecular system coupled to an environment: An application of semiclassical hybrid dynamics

Christoph-Marian Goletz, Frank Großmann

Applying the recently developed semiclassical hybrid dynamics [Grossmann, J. Chem. Phys. 125, 014111 (2006)], we study the decay of interference patterns in the reduced density as well as of the purity in a Morse oscillator test system due to the interaction with a finite harmonic bath at zero temperature. In the case that the bath mimics a continuous Ohmic spectral density, in addition to the quantum classical transition induced by the interaction with the environment, we corroborate the existence of a blueshift due to the bath coupling, predicted by Pollak [Phys. Rev. A 33, 4244 (1986)]. Furthermore, the decoherence dynamics of cat states is confirmed to be faster than that of single coherent states and we show that for a resonant bath the dissipation leads to an increase in the decoherence rate as compared to the low frequency bath.

The Journal of Chemical Physics•Jun 25, 2009•29 citations
In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.
The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.
A novel quantum method to deal with typical system-bath dynamical problems is introduced. Subsystem discrete variable representation and bath coherent-state sets are used to write down a multiconfigurational expansion of the wave function of the whole system. With the help of the Dirac-Frenkel variational principle, simple equations of motion--a kind of Schrodinger-Langevin equation for the subsystem coupled to (pseudo) classical equations for the bath--are derived. True dissipative dynamics at all times is obtained by coupling the bath to a secondary, classical Ohmic bath, which is modeled by adding a friction coefficient in the derived pseudoclassical bath equations. The resulting equations are then solved for a number of model problems, ranging from tunneling to vibrational relaxation dynamics. Comparison of the results with those of exact, multiconfiguration time-dependent Hartree calculations in systems with up to 80 bath oscillators shows that the proposed method can be very accurate and might be of help in studying realistic problems with very large baths. To this end, its linear scaling behavior with respect to the number of bath degrees of freedom is shown in practice with model calculations using tens of thousands of bath oscillators.
The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time dependency. We show that when the external trap potential and interparticle interaction have a time dependency, the numerically exact solutions of the corresponding time-dependent many-boson Schr\"odinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. 99, 030402 (2007); Phys. Rev. A 77, 033613 (2008)]. In particular, we benchmark the MCTDHB method for (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the nonequilibrium dynamic for driven scenarios where both the trap- and interparticle-interaction potentials are time-dependent. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning a Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultracold Bose-Einstein condensed systems are addressed.
We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction. The resulting Matsubara TCFs are in near-perfect agreement with the exact quantum TCFs, for non-linear as well as linear operators, at a temperature at which the TCFs are dominated by quantum thermal fluctuations. These results provide compelling evidence that incoherent classical dynamics can arise in the condensed phase at temperatures at which the statistics are dominated by quantum (Boltzmann) effects, as a result of smoothing of imaginary-time Feynman paths. The techniques developed here may also lead to efficient methods for benchmarking system-bath dynamics in the overdamped regime.
Applying the recently developed semiclassical hybrid dynamics [Grossmann, J. Chem. Phys. 125, 014111 (2006)], we study the decay of interference patterns in the reduced density as well as of the purity in a Morse oscillator test system due to the interaction with a finite harmonic bath at zero temperature. In the case that the bath mimics a continuous Ohmic spectral density, in addition to the quantum classical transition induced by the interaction with the environment, we corroborate the existence of a blueshift due to the bath coupling, predicted by Pollak [Phys. Rev. A 33, 4244 (1986)]. Furthermore, the decoherence dynamics of cat states is confirmed to be faster than that of single coherent states and we show that for a resonant bath the dissipation leads to an increase in the decoherence rate as compared to the low frequency bath.