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

New Journal of Physics

Quantum dynamics of vibrational energy flow in oscillator chains driven by anharmonic interactions

Raffaele Borrelli, Maxim F. Gelin

Published Nov 12, 2020• 14 citations
Publisher

Abstract

Abstract A new model of vibrational energy transfer in molecular systems taking into account anharmonic (third order) interactions of localized vibrations with a chain of harmonic oscillators is developed. The role of the energy spectrum of the chain and of the magnitude of the non-linear coupling is discussed in detail by an exact numerical solution of the quantum dynamical problem based on the tensor-train (matrix product state) representation of the vibrational wave function. Results show that the type of wave packet motion is determined by the eigen-spectrum of the chain and by its excitation time. It is found that when the excitation of the chain takes place on a much shorter timescale than the energy transfer along the chain the vibrational wave packet moves in a ballistic way independently of the length of the chain. On the other hand when the excitation of the chain takes place on the timescale of the energy transfer along the chain the overall motion becomes superballistic. These findings shed new light on recent observations of ballistic energy transfer along polymethylene chains.

DOI
10.1088/1367-2630/abc9ed

Related papers

Short time dynamics of harmonic oscillator coherent states in anharmonic systems. I. One-dimensional motion

Jürgen Brickmann

The dynamics of an initially excital Gaussian wave packet (harmonic oscillator coherent state, HOCS) in a general one-dimensional anharmonic system is studied analytically with the aid of a second quantization formalism for times shorter than a classical oscillation period. The initial state population probability PQ(t), its classical counterpart PC(t), and the overlap probability PQC(t) between a time evolved wave packet and a classically moving Gaussian with stationary shape are calculated in order to analyze the spreading of the wave packet. It was found that, in general, PQ(t) and PC(t) agree very well if the potential energy function has no strongly changing low order derivatives. This agreement is held even if the wave packet spreads drastically within the time scale considered as can be demonstrated by analyzing PQC(t). The analytical expressions for PQ(t), PC(t), and PQC(t) are applied to a dissociative third-order oscillator and a strongly anharmonic fourth-order oscillator. While for a harmonic system, the initial decay time of PQ(t) and PC(t) (which are identical in this case) are only dependent on the energy expectation value 〈H〉 with respect to the initial HOCS, differences up to an order of magnitude occur for HOCS with the same energy in the model systems.

The Journal of Chemical Physics•Feb 15, 1983•22 citations

Exact solution for low energy quantum anharmonic vibrations in a long polymer chain

Alexander L. Burin

We propose the algorithm for determining vibrational quantum eigenstates of periodic linear chain of atoms coupled by harmonic and third order anharmonic interactions (Fermi-Ulam-Pasta $α$ problem) in the long wavelength limit within the resonant approach. Eigenstates can be encoded by the sequence of integer numbers determining their energies and wavefunctions. Using these eigenstates we described a single phonon state time evolution showing coherent oscillations. The applications of theory to vibrational energy transport and quantum informatics are discussed.

arXiv:1508.07069•Aug 28, 2015•0 citations

Tuning energy transport using interacting vibrational modes

Chu Guo, Manas Mukherjee, Dario Poletti

We study energy transport in a chain of quantum harmonic and anharmonic oscillators where the anharmonicity is induced by interaction between local vibrational states of the chain. Using adiabatic elimination and numerical simulations with matrix product states, we show how strong interactions significantly slow down the relaxation dynamics (with the emergence of a different time scale) and can alter the properties of the steady state. We also show that steady-state properties are completely different depending on the order in which the limits of infinite time and infinite interaction are taken.

arXiv:1505.05942•Physical Review A•Aug 26, 2015•12 citations

Population transfer in quantum β -Fermi–Pasta–Ulam–Tsingou chains with fixed ends

Jinwen Cai, Xiangyu Xu, Luis Vasquez +3 more

We perform a series of numerically accurate tensor-train (TT) simulations of population dynamics and energy transfer in quantum β-Fermi-Pasta-Ulam-Tsingou (FPUT) chains comprising 10 to 30 nonlinear oscillators. The dynamics are propagated over timescales ranging from 18 to 60 fundamental vibrational periods. We demonstrate that the chain anharmonicity opens new energy-transfer channels, accelerates initial ballistic energy propagation, reduces (partial) recurrence periods relative to the harmonic limit, and regularizes oscillatory wavepacket motion. This work serves as the first proof-of-principle demonstration of the high efficiency of TT methods for simulating quantum FPUT dynamics.

The Journal of Chemical Physics•Jun 8, 2026•0 citations

Quantum dynamics and control of vibrational dephasing

Martin Gruebele

This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.

Journal of Physics Condensed Matter•Jul 17, 2004•22 citations

Propagation of excitation in long 1D chains: Transition from regular quantum dynamics to stochastic dynamics

Viktor A. Benderskii, Efim I Kats

The quantum dynamics problem for a 1D chain consisting of 2 N + 1 sites ( N ≫ 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N . The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = ±1 (0 < C ≤ 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2 N , with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH 2 fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.

Journal of Experimental and Theoretical Physics•Jan 1, 2013•10 citations
Abstract A new model of vibrational energy transfer in molecular systems taking into account anharmonic (third order) interactions of localized vibrations with a chain of harmonic oscillators is developed. The role of the energy spectrum of the chain and of the magnitude of the non-linear coupling is discussed in detail by an exact numerical solution of the quantum dynamical problem based on the tensor-train (matrix product state) representation of the vibrational wave function. Results show that the type of wave packet motion is determined by the eigen-spectrum of the chain and by its excitation time. It is found that when the excitation of the chain takes place on a much shorter timescale than the energy transfer along the chain the vibrational wave packet moves in a ballistic way independently of the length of the chain. On the other hand when the excitation of the chain takes place on the timescale of the energy transfer along the chain the overall motion becomes superballistic. These findings shed new light on recent observations of ballistic energy transfer along polymethylene chains.
The dynamics of an initially excital Gaussian wave packet (harmonic oscillator coherent state, HOCS) in a general one-dimensional anharmonic system is studied analytically with the aid of a second quantization formalism for times shorter than a classical oscillation period. The initial state population probability PQ(t), its classical counterpart PC(t), and the overlap probability PQC(t) between a time evolved wave packet and a classically moving Gaussian with stationary shape are calculated in order to analyze the spreading of the wave packet. It was found that, in general, PQ(t) and PC(t) agree very well if the potential energy function has no strongly changing low order derivatives. This agreement is held even if the wave packet spreads drastically within the time scale considered as can be demonstrated by analyzing PQC(t). The analytical expressions for PQ(t), PC(t), and PQC(t) are applied to a dissociative third-order oscillator and a strongly anharmonic fourth-order oscillator. While for a harmonic system, the initial decay time of PQ(t) and PC(t) (which are identical in this case) are only dependent on the energy expectation value 〈H〉 with respect to the initial HOCS, differences up to an order of magnitude occur for HOCS with the same energy in the model systems.
We propose the algorithm for determining vibrational quantum eigenstates of periodic linear chain of atoms coupled by harmonic and third order anharmonic interactions (Fermi-Ulam-Pasta ααα problem) in the long wavelength limit within the resonant approach. Eigenstates can be encoded by the sequence of integer numbers determining their energies and wavefunctions. Using these eigenstates we described a single phonon state time evolution showing coherent oscillations. The applications of theory to vibrational energy transport and quantum informatics are discussed.
We study energy transport in a chain of quantum harmonic and anharmonic oscillators where the anharmonicity is induced by interaction between local vibrational states of the chain. Using adiabatic elimination and numerical simulations with matrix product states, we show how strong interactions significantly slow down the relaxation dynamics (with the emergence of a different time scale) and can alter the properties of the steady state. We also show that steady-state properties are completely different depending on the order in which the limits of infinite time and infinite interaction are taken.
We perform a series of numerically accurate tensor-train (TT) simulations of population dynamics and energy transfer in quantum β-Fermi-Pasta-Ulam-Tsingou (FPUT) chains comprising 10 to 30 nonlinear oscillators. The dynamics are propagated over timescales ranging from 18 to 60 fundamental vibrational periods. We demonstrate that the chain anharmonicity opens new energy-transfer channels, accelerates initial ballistic energy propagation, reduces (partial) recurrence periods relative to the harmonic limit, and regularizes oscillatory wavepacket motion. This work serves as the first proof-of-principle demonstration of the high efficiency of TT methods for simulating quantum FPUT dynamics.
This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
The quantum dynamics problem for a 1D chain consisting of 2 N + 1 sites ( N ≫ 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N . The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = ±1 (0 < C ≤ 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2 N , with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH 2 fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.