Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

Kocia, Lucas; Heller, Eric J.

doi:10.1063/1.4901301

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…Certain directions lead to maximal exploration, whereas others lead to none. Identifying the relevant directions allows one to reduce greatly the dimensionality of the search space, in fact to just a few dimensions [50][51][52].…”

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confidence: 99%

Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

et al. 2018

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Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generate interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e. scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences. We develop a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, it is shown that this theory captures post-Ehrenfest quantum interference phenomena very accurately, and contains relevant phase information to perform many-body spectroscopy with high precision.

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confidence: 99%

Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

et al. 2018

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“…applying a Metropolis algorithm for the mean variable integral [3]). Most recent success in improving the convergence of SC calculations has been reported in a study that employs a sampling along the fastest growing manifold of a defining trajectory [31]. For the first account of the new methodology presented here we have not tried to optimize the numerical details, however.…”

Section: Numerical Resultsmentioning

confidence: 99%

A semiclassical hybrid approach to linear response functions for infrared spectroscopy

Großmann

2016

Phys. Scr.

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Based on the integral representation of the semiclassical propagator of Herman and Kluk (HK), and in the limit of high temperatures, we formulate a hybrid expression for the correlation function of infrared spectroscopy. This is achieved by performing a partial linearization inside the integral over the difference of phase space variables that occurs after a twofold application of the HK propagator. A numerical case study for a coupled anharmonic oscillator shows that already for a total number of only two degrees of freedom, one of which is treated in the simplified manner, a substantial reduction of the numerical effort is achieved.

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“…Semiclassical methods based on classical mechanics are a natural choice as they can capture quantum behavior while providing an intuitive picture of the system. Moreover, incrementally adding additional quantum features (for instance, different orders of expansions of the semiclassical propagator [33]) to these approximations can provide insight into which effects are indeed quantum mechanical and which are artifacts of classical mechanics.…”

Section: A Semiclassical Modelsmentioning

confidence: 99%

Approach to coherent interference fringes in helium-surface scattering

Schram

Heller

2018

Phys. Rev. A

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The conventional notion of elastic, coherent atom-surface scattering originates from the scattering particles acting as a quantum-mechanical matter wave, which coherently interfere to produce distinct Bragg peaks which persist at finite temperature. If we introduce inelastic scattering to this scenario, the result is that the surface particles become displaced by the scattering atoms, resulting in emission or absorption of phonons that shift the final energy and momentum of the scatterer. As the lowest-lying phonons are gapless excitations, the ability to measure these phonons is very difficult and this difficulty is exacerbated by the roughly 1-eV resolution found in high-energy helium scattering experiments. Even though the surface has in effect measured the presence of the scatterer which decoheres the particle, we retain the diffraction spots which are referred to as coherent scattering. How do we reconcile these disparate viewpoints? We propose an experiment to more precisely examine the question of coherence in atom-surface scattering. We begin with an initially coherent superposition of helium particles with equal probabilities of interacting with the surface or not interacting with the surface. The beams are directed so that after the scattering event, the atoms are recombined so that we can observe the resulting interference pattern. The degree to which phonons are excited in the lattice by the scattering process dictates the fringe contrast of the interference pattern of the resulting beams. We use semiclassical techniques to simulate and test the viability of this experiment and show that for a wide range of conditions, despite the massive change in the momentum perpendicular to the surface, we can still expect to have coherent (in the superposition sense) scattering.

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Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

Cited by 7 publications

References 13 publications

Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

A semiclassical hybrid approach to linear response functions for infrared spectroscopy

Approach to coherent interference fringes in helium-surface scattering

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