Andrej Junginger

Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.

Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.

Transition state geometry of driven chemical reactions on time-dependent double-well potentials

Reaction rates across time-dependent barriers are difficult to define and difficult to obtain using standard transition state theory approaches because of the complexity of the geometry of the dividing surface separating reactants and products. Using perturbation theory (PT) or Lagrangian descriptors (LDs), we can obtain the transition state trajectory and the associated recrossing-free dividing surface. With the latter, we are able to determine the exact reactant population decay and the corresponding rates to benchmark the PT and LD approaches. Specifically, accurate rates are obtained from a local description regarding only direct barrier crossings and to those obtained from a stability analysis of the transition state trajectory. We find that these benchmarks agree with the PT and LD approaches for obtaining recrossing-free dividing surfaces. This result holds not only for the local dynamics in the vicinity of the barrier top, but also for the global dynamics of particles that are quenched at the reactant or product wells after their sojourn over the barrier region. The double-well structure of the potential allows for long-time dynamics related to collisions with the outside walls that lead to long-time returns in the low-friction regime. This additional global dynamics introduces slow-decay pathways that do not result from the local transition across the recrossing-free dividing surface associated with the transition state trajectory, but can be addressed if that structure is augmented by the population transfer of the long-time returns.

Quantum-classical lifetimes of Rydberg molecules

A remarkable property of Rydberg atoms is the possibility of creating molecules formed by one highly excited atom and another atom in the ground state. The first realization of such a Rydberg molecule has opened an active field of physical investigations, and showed that its basic properties can be described within a simple model regarding the ground state atom as a small perturber that is bound by a low-energy scattering process with the Rydberg electron (Greene et al 2000 Phys. Rev. Lett. 85 2458). Besides the good agreement between theory and the experiment concerning the vibrational states of the molecule, the experimental observations yield the astonishing feature that the lifetime of the molecule is clearly reduced as compared to the bare Rydberg atom (Butscher et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 184004). With focus on this yet unexplained observation, we investigate in this paper the vibrational ground state of the molecule in a quantum-classical framework. We show that the Rydberg wavefunction is continuously detuned by the presence of the moving ground state atom and that the timescale on which the detuning significantly exceeds the natural linewidth is in good agreement with the observed reduced lifetimes of the Rydberg molecule. (Some figures may appear in colour only in the online journal)

Transition state theory for wave packet dynamics: II. Thermal decay of Bose–Einstein condensates with long-range interaction

We apply transition state theory to coupled Gaussian wave packets and calculate thermal decay rates of Bose-Einstein condensates with additional long-range interaction. The ground state of such a condensate is metastable if the contact interaction is attractive and a sufficient thermal excitation may lead to its collapse. The use of transition state theory is made possible by describing the condensate within a variational framework and locally mapping the variational parameters to classical phase space as has been demonstrated in the preceding paper [A. Junginger, J. Main, and G. Wunner, submitted to J. Phys. A]. We apply this procedure to Gaussian wave packets and present results for condensates with monopolar 1/r-interaction comparing decay rates obtained by using different numbers of coupled Gaussian trial wave functions as well as different normal form orders.

Lagrangian descriptors in dissipative systems

The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

Transition states and thermal collapse of dipolar Bose-Einstein condensates

We investigate thermally excited, dipolar Bose-Einstein condensates. Quasi-particle excitations of the atomic cloud cause density fluctuations which can induce the collapse of the condensate if the inter-particle interaction is attractive. Within a variational approach, we identify the collectively excited stationary states of the gas which form transition states on the way to the BECs collapse. We analyze transition states with different

Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schrodinger systems

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Lagrangian descriptors of driven chemical reaction manifolds

-fold rotational symmetry and identify the one which mediates the collapse. The latters symmetry depends on the trap aspect ratio of the external trapping potential which determines the shape of the BEC. Moreover, we present the collapse dynamics of the BEC and calculate the corresponding decay rate using transition state theory. We observe that the thermally induced collapse mechanism is important near the critical scattering length, where the lifetime of the condensate can be significantly reduced. Our results are valid for an arbitrary strength of the dipole-dipole interaction. Specific applications are discussed for the elements

Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins

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Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

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