Academic Year 2017

The semiclassical Heller-Herman-Kluk-Kay (HHKK) propagator [1-3] is a well-established approximation to the quantum evolution operator. By associating semiclassical phases to an ensemble of classical trajectories, the HHKK propagator incorporates quantum effects, such as coherence and zero-point energy, into the dynamics. However, the direct application of the HHKK approach to large scale systems is computationally unfeasible due to the oscillatory nature of the integrand involved. A common way of dealing with this problem is based on application of the cellularization (Filinov filtering) [4, 5] technique to smooth out the oscillatory behavior of the integrand. Here we present a refined cellularization scheme for the HHKK propagator [6], which employs the inverse Weierstrass transform and optimal scaling of the cell size with the number of cells, and was previously only used in the context of the dephasing representation [7]. In the new methodology the size of the sampling weight for the cell centers correlates with the size of cells, allowing for effective sampling of the phase space covered by the initial state of the system. The main advantage of the presented approach is that, unlike the standard cellularization scheme, it converges to the original HHKK result in the limit of an infinite number of trajectories. We illustrate the performance of the refined cellularization scheme by calculating autocorrelation functions and spectra of both integrable and chaotic model systems.

[1] E. J. Heller, J. Chem. Phys. 75, 2923 (1981).
[2] M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984).
[3] K. G. Kay, J. Chem. Phys. 100, 4377 (1994).
[4] N. Makri and W. H. Miller, J. Chem. Phys. 89, 2170 (1988).
[5] E. J. Heller, J. Chem. Phys. 94, 2723 (1991).
[6] S. V. Antipov and J. Vanicek, In preparation.
[7] E. Zambrano, M.SŠulc, and J. Vanicek, J. Chem. Phys. 139, 054109 (2013).

We present a method to efficiently compute the eigenfunctions of classically chaotic systems and vibrational molecular states. The key point is the definition of a Gram-Schmidt procedure which selects the most suitable elements from a basis set of localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical properties of such functions.

Resonance Raman scattering (RRS) is a powerful technique for the materials, which electronic band structure depend on the thickness and the defect present in the materials. We have observed RRS in molybdenum disulfide (MoS2) nanosheets by using different excitation laser source in the Raman measurement. The Raman spectra of MoS2 are recorded by four excitation lasers-- 405 nm, 532, 632 and 785 nm. The MoS2 nanosheets show two distinct Raman peaks-- one at 385 cm-1 and other at 408 cm-1 , these peaks are known as E 1 2g and A1g peaks, respectively. In case of 405, 632 and 785 nm laser sources, the intensity of E 1 2g peak is higher than the intensity of A1g peak, while for 532 nm laser source the intensity profile is reversed. We observed resonance phenomenon happening for 532 nm laser in the Raman measurement. We performed density functional theory (DFT) based calculation and simulation, and obtained the electron energy loss spectra (EELS) of MoS2 nanosheets. In EELS, a peak around 2.48 eV is observed when there is Mo vacancy in the system, while no such peak is observed for pristine MoS2 and MoS2 with S vacancy. The DFT study shows that due to vacancy of Mo atom in the MoS2 nanosheets, the resonance in the Raman study for 532 nm laser source is observed. Further, we have studied the resonance energy transfer (RET) in two dimensional (2D) nanosheets of graphene, MoS2 and tungsten disulfide (WS2). The RET is a photo-physical phenomenon where non-radiative energy transfers from donor to acceptor nanomaterials. We used protein molecules (bovine serum albumin; BSA) as donor and 2D nanosheets of graphene, MoS2 and WS2 as acceptors. The fluorescence emission from BSA arises at 350 nm, in presence of 2D nanosheets, the fluorescence intensity of BSA decreases. The time resolved fluorescence study shows that there is decrease in the fluorescence lifetime of BSA molecules in presence of 2D nanosheets. The decrease in fluorescence lifetime of BSA confirms the energy transfer phenomenon in bio-nano interactions.

1- ''Resonance Raman iscattering and ab initio calculation of electron energy loss spectra of MoS2 nanosheets'' Anirban Chakraborti, Arun SinghPatel, Pawan K. Kanaujia, Palash Nath, G.Vijaya Prakash, and Dirtha Sanyal, Phys. Lett. A, 380 (2016) 4057.
2- ''Investigating resonance energy transfer from protein molecules to van der Waals nanosheets'' Arun Singh Patel, Praveen Mishra, Pawan K. Kanaujia, Syed Shariq Husain, G. Vijaya Prakash, and Anirban Chakraborti, RSC Adv., 7 (2017) 26250.

We [1] introduce a semiclassical theory for strong localization that may arise in the context of many body thermalization. It echos the work of Heller regarding quantum localization and the rate of exploration of phase space [2]. The minimal example is a few site Bose Hubbard model that consists of two weakly interacting subsystems that can exchange particles [3]. The occupation $x$ satisfies in the classical treatment a Fokker-Planck equation [4] with diffusion coefficient $D(x)$. We demonstrate that it is possible to deduce from the classical description a quantum breaktime, and hence the manifestations of a strong localization effect [5]. For this purpose it is essential to take the geometry of the energy shell into account, and to make a distinction between different notions of phase-space exploration. We also make a clear distinction between Anderson-type localization and semiclassical localization. The latter is related to KAM structures in phase space. A notable application is the the metastability criteria for the flow states in ring-shaped Bose Hubbard superfluid circuits [6,7]

[1] C. Khripkov, A. Vardi, D. Cohen, in preparation.
[2] E.J. Heller, Phys. Rev. A 35, 1360 (1987).
[3] C. Khripkov, A. Vardi, D. Cohen, New J. Phys. 17, 023071 (2015).
[4] I. Tikhonenkov, A. Vardi, J.R. Anglin, D. Cohen, Phys. Rev. Lett. 110, 050401 (2013).
[5] D. Cohen, V.I. Yukalov, K. Ziegler, Phys. Rev. A 93, 042101 (2016).
[6] G. Arwas, A. Vardi, D. Cohen, Scientific Reports 5, 13433 (2015).
[7] G. Arwas, D. Cohen, Phys. Rev. B 95, 054505 (2017).

Even very small fluctuations in the ocean depth can randomly focus tsunami waves leading to an order of magnitude variation in their energy flux density in random directions, with severe implications for the predictability of tsuna- mis [1]. This is an example of a branched flow: When waves propagate through weakly scattering but correlated, disordered environments they are randomly focused into pronounced branch-like structures. This phenomenon has been studied in a range of systems including the sound propagation in the ocean, electron transport in two-dimensional electron gases, microwave transmission through random arrangements of scatterers and the dynamics of wind-driven ocean waves. In contrast to these systems, which are well characterized as iso- tropic random media, the structures in the ocean floor topography that scatter tsunami waves show a pronounced anisotropy. This motivated us to study the influence of anisotropy on the natural focusing events in branched flows. We found a strong and non-intuitive dependence on the propagation angle in the fluctuations and even the mean intensity of the flow [2].

[1] H. Degueldre, J. J. Metzger, T. Geisel, and R. Fleischmann, Random focusing of tsunami waves, Nature Phys. 12, 259262 (2016).
[2] H. Degueldre, J. J. Metzger, E. Schultheis, and R. Fleischmann, Channeling of Branched Flow in Weakly Scattering Anisotropic Media, Phys. Rev. Lett. 118, 024301 (2017).

The semiclassical initial value formalism to solve the time-dependent Schroedinger equation will be reviewed. Special focus will be laid on Heller's thawed and frozen Gaussians [1], as well as on the Herman-Kluk propagator [2]. A combination of the frozen and thawed Gaussian methods for many degree of freedom systems, the semiclassical hybrid dynamics [3], will then be introduced.
After a brief digression to the semiclassical description of the scattering of two identical particles [4], we present results for the quantum-classical transition of a nonlinear oscillator coupled to an Ohmic heat bath [5], as well as for the thermalization of the expectation values of such an oscillator [6]. We contrast two different approaches to open system dynamics: the explicit treatment of the bath degrees of freedom and the reduced density matrix method, respectively.

[1] E. J. Heller, J. Chem. Phys. 62, 1544 (1975), J. Chem. Phys. 75, 2923 (1981)
[2] M. Herman and E. Kluk, Chem. Phys. 91, 27 (1984)
[3] F. Grossmann, J. Chem. Phys. 125, 014111 (2006)
[4] F. Grossmann, M. Buchholz, E. Pollak and M. Nest, Phys. Rev. A 89, 032104 (2014)
[5] C.-M. Goletz and F. Grossmann, J. Chem. Phys. 130, 244107 (2009)
[6] W. Koch, F. Grossmann, J. T. Stockburger and J. Ankerhold, Phys. Rev. Lett.100, 230402 (2008)

The phenomenon of branched, directed flow, i.e. weak random deflection accumulated one many correlation lengths, is found in very many disparate physical situations. Its properties and ubiquity are late being recognized, and some fields may still not know they live in the random flow regime. We give now challenges focusing this field.

Three topics in semiclassical tunneling are discussed. The first involves semiclassical time dependent tunneling through a barrier. Most semiclassical time dependent tunneling methods require the use of trajectories in the complex plane. A simple approximate semiclasscial method for this problem is presented, and it is shown to give very good results for model problems. The second topic discusses the solution of the semiclassical equations for the amplitude and phase of the wavefunction that satisfy the time independent Schrodinger equation through order first in Planck’s constant. The third topic shows how trajectories with forbidden hops can be incorportated into the surface hopping calculations.

In the early 1970's significant progress was made in the understanding of the geometry underlying the theory of chemical reactions. Central to this work was variational transition state theory. The basic idea was to examine the set of all possible transition states and to identify the one with the minimum flux across it. Phil Pechukas observed that for systems with two degrees of freedom the solution is provided by periodic orbits which touch both equipotentials dividing coordinate space into product and reactant regions.
The extension of these ideas to systems with three or more degrees of freedom has been very problematical. In retrospect, the difficulty encountered was the focus on partitioning coordinate space into reactant and product regions, when in reality the question of interest was the partitioning of phase space (the space of all states). Jaffé et al [1] addressed this issue in their study of the chaotic ionization of hydrogen in crossed electromagnetic field. They demonstrated, for the first time, how to construct a transition state in phase space. In a subsequent study [2] they demonstrated the existence of phase space transition states in celestial mechanics where they control the rate of transport of small masses. Since the theory was reformulated in the phase space, progress has been rapid.
This reformulation was placed on a firm mathematical foundation by Uzer et al [3]. The central geometrical object is a stationary point in phase space. It must be stable in all but one degrees of freedom and consequently it has the topology of a saddle. Associated with this saddle are a number of invariant manifolds which are central to the theory of reaction dynamics. An exposition of these objects and the role they play in determining the rate of chemical reactions (and the rate of transport of small bodies in the solar system) is the central theme of this talk. Today a sizable number of groups are working on this and related problems. The central theme of these efforts is to understand the geometry of phase space various different situations and the consequences for transport in phase space.

1. Transition States in Atomic Physics, Charles Jaffe, David Farrelly, and T. Uzer, Phys. Rev. A 60, 3833 (1999).
2. Statistical Theory of Asteroid Escape Rates, Charles Jaffe, Shane D. Ross, Martin W. Lo, Jerrold Marsden, David Farrelly and T. Uzer, Phys. Rev. Lett. 89, 011101 (2002).
3. The Geometry of Reaction Dynamics, T. Uzer, Charles Jaffe, Jesus Palacian, Patricia Yanguas and Stephen Wiggins, Nonlinearity 15, 957 (2002), Impenetrable Barriers in Phase Space, S. Wiggins, L. Wiesenfeld, C. Jaffe and T. Uzer, Phys. Rev. Lett. 86, 5478 (2001), A New Look at the Transition State: Wigner's Dynamical Perspective Revisited, Charles Jaffe, Shinnosuke Kawai, Jesus Palacian, Patricia Yanguas and T. Uzer, Adv. Chem. Phys. 130A, 171 - 216 (2005).
4. Transitionstatetheorynearhigher-ranksaddlesinphasespace,GeorgeHaller,T.Uzer,Jesus Palacian, Patricia Yanguas and Charles Jaffe, Nonlinearity 24 527-561 (2011).

We study, under very general conditions and in a variety of geometries, quantum enhancement of transport in open systems. Both static disorder and dephasing associated with dynamical disorder (or finite temperature) are fully included in the analysis. We show that quantum coherence effects may significantly enhance transport in open quantum systems even in the semiclassical regime (where the decoherence rate is greater than the inter-site hopping amplitude), as long as the static disorder is sufficiently strong. When the strengths of static and dynamical disorder are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected, for example in the FMO photosynthetic complex, which may be viewed as intermediate between these paradigmatic models. We furthermore show that a nonzero dephasingrate assists transport in an open linear chain when the disorder strength exceeds a critical value, and obtain this critical disorder strength as a function of the degree of opening.

Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. Despite their promise, these methods have until now been limited to short time propagation, due to the numerical and conceptual difficulties introduced by the complexification. A detailed investigation of the caustic structure of the complex classical phase space combined with an analysis of the branch cut topology of complex time contour propagation allows for divergences to be avoided and Stokes phenomena to be eliminated. Using a new Final Value Representation of the Coherent State Propagator (FINCO) we demonstrate accurate wavepacket propagation, all the way to the revival time of a strongly anharmonic system.

The origin of ''jets'' in the dust tails surrounding comets has been a much debated topic in astrophysics, with some theories proposing geyser type outbreak. The Rosetta space mission following comet 67P/Churyumov-Gersamineko has brought back a long-time study of the dust collimination and points to a different type of jets: the jets are caused by the random initial conditions of dust particles along topographical concave areas, resulting in focal points above the comet. I show our analysis of this phenomenon and how it is connect to (semi-) classical trajectory fields.
[1] Homogeneous dust emission and jet structure near active cometary nuclei: the case of 67P/Churyumov-Gerasimenko T. Kramer, M. Noack, D. Baum, H.-C. Hege, E. J. Heller (2015), https://arxiv.org/abs/1505.08041
[2] Seasonal changes of the volatile density in the coma and on the surface of comet 67P/Churyumov-Gerasimenko T. Kramer, M. Läuter, M. Rubin, K. Altwegg Monthly Notices of the Royal Astronomical Society (2017)
[3] On the origin of inner coma structures observed by Rosetta during a diurnal rotation of comet 67P/Churyumov-Gerasimenko T. Kramer, M. Noack, The Astrophysical Journal Letters, 823, L11 (2016)

The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some remarkable specific cases have been solved in one dimension. Here we show that the guiding center approximation---valid for charges moving in two dimensions in the limit of large constant magnetic fields---simplifies the three-body problem for an arbitrary interparticle interaction invariant under rotations and translations, making it solvable by quadratures.
A spinorial representation for the system is introduced, which allows a visualization of its phase space as the corresponding Bloch sphere. Finally, a discussion of the quantization of the problem is presented.

A generic distinct mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either π phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension. Derivation and analysis of three Hopf-Turing amplitude equations in two space dimensions reveals a local dynamics pinning mechanism for Hopf fronts, which in turn allows the emergence of perpendicular (to the Hopf front) Turing states. The results are shown to agree well with the comb-like core size that forms inside spiral waves. In the context of 2:1 resonance, these localized states form outside the 2:1 resonance region and thus extend the frequency locking domain for spatially extended media, such as periodically driven Belousov-Zhabotinsky chemical reactions. Implications to chlorite-iodide-malonic-acid and shaken granular media are also addressed.

We present the transport properties in small interacting many-body fermionic networks. To model the system, we use embedded Gaussian Ensembles (EGE). With this model we can manipulate k-body interactions among n-spinless fermions distributed over l-single particle states. We analyze two types of ensembles: the EGE and this same ensemble with centrosymmetry (csEGE). In the context of quantum transport, the question we address is which of the two ensembles (EGE vs csEGE) is more efficient, either in state transfer, or in coherent transport of fermions over a network. To compare these two ensembles, we study first the transport efficiency in a closed system. For both ensembles we obtain their respective efficiency distributions over the ensemble. We notice that centrosymmetry enhances significantly the transport efficiency when compared to the EGE. Next, we open the system and study the transport properties in the EGE versus the csEGE. The conductance bandwidth as well as the ensemble-averaged total current attain their maximal values if the system is highly filled n ∼ l − 1 and k ∼ n/2. For the cases k = 1 and k = n the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever the centrosymmetric ensembles (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and causes backscattering-free transmission resonances, which enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak or n = l − 1, close to the highest observed currents.

We study effects of different configurations of adsorbates on the vibrational modes as well as symmetries of polyacenes and poly- p-phenylenes focusing on lithium atom adsorption. We found that the spectra of the vibrational modes distinguish the different configurations. For more regular adsorption schemes the lowest states are bending and torsion modes of the skeleton, which are essentially followed by the adsorbate. On poly-p-phenylenes we found that lithium adsorption reduces and often eliminates the torsion between rings thus increasing symmetry. There are spontaneous symmetry breaking in poly-p-phenylenes due to double adsorption of lithium atoms on alternating rings.

Quantum scars are enhancements of quantum probability density along unstable periodic orbits. This unexpected feature that brings order through chaos was first reported over 30 years ago by Eric J. Heller [1]. Here, we suggest a scheme to exploit quantum scars in a controlled way [2]. Our idea builds on the recently reported finding that unexpectedly strong quantum scarring can be achieved by local perturbations in an otherwise regular (symmetric) system [3]. We focus on a prototype of such a system: a two-dimensional harmonic oscillator in a magnetic field, which is realistic model for quantum dots (QDs) fabricated in semiconductor heterostructures [4].
We show that a locally perturbed QD exhibits strong scarring [2]. Moreoever, even a a single bump in the potential is sufficient to attach with the scar (pinning effect). In a QD, this bump could be represented by a voltage of a nanotip. Now, the combination of the magnetic field and a nanotip provides us with a scheme to coherently manipulate preferred electron paths (and thus the local conductance) in the QD. This could lead to a new subfield of “scartronics”, where the local conductance of a nanoscale system is modulated by inducing and manipulating scarred states.
[1] E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
[2] J. Keski-Rahkonen, P. J. J. Luukko, L. Kaplan, E. J. Heller, and E. Räsänen, submitted (2017).
[3] P. J. J. Luukko, B. Drury, A. Klales, L. Kaplan, E. J. Heller, and E. Räsänen, Sci. Rep. 6, 37656 (2016).
[4] S. M. Reimann and M. Manninen, Rev. Mod. Phys. 74, 1283 (2002).

Quantum scars are enhancements of quantum probability density along unstable periodic orbits. This unexpected feature that brings order through chaos was first reported over 30 years ago by Eric J. Heller [1]. Here, we suggest a scheme to exploit quantum scars in a controlled way [2]. Our idea builds on the recently reported finding that unexpectedly strong quantum scarring can be achieved by local perturbations in an otherwise regular (symmetric) system [3]. We focus on a prototype of such a system: a two-dimensional harmonic oscillator in a magnetic field, which is realistic model for quantum dots (QDs) fabricated in semiconductor heterostructures [4].
We show that a locally perturbed QD exhibits strong scarring [2]. Moreoever, even a a single bump in the potential is sufficient to attach with the scar (pinning effect). In a QD, this bump could be represented by a voltage of a nanotip. Now, the combination of the magnetic field and a nanotip provides us with a scheme to coherently manipulate preferred electron paths (and thus the local conductance) in the QD. This could lead to a new subfield of “scartronics”, where the local conductance of a nanoscale system is modulated by inducing and manipulating scarred states.

[1] E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
[2] J. Keski-Rahkonen, P. J. J. Luukko, L. Kaplan, E. J. Heller, and E. Räsänen, submitted (2017).
[3] P. J. J. Luukko, B. Drury, A. Klales, L. Kaplan, E. J. Heller, and E. Räsänen, Sci. Rep. 6, 37656 (2016).
[4] S. M. Reimann and M. Manninen, Rev. Mod. Phys. 74, 1283 (2002).

Photosynthetic complexes are molecular aggregates in charge of the energy transfer within the light-harvesting apparatus of bacteria and higher plants. The interaction and functioning of the complexes are modelled using quantum mechanical methods. The conversion of light captured within the antenna part to the reaction center is strongly affected by the surrounding proteins, which can disturb or enhance the efficiency of the process. Recent progress in ultrafast laser technology has made it possible to track the time-dependent dynamics between the involved molecules. We use the Hierarchical Equations of Motion to model the time dependent laser matter interactions [1] and provide a correct description of recent experimental results. Furthermore, we describe how environment assisted transport is responsible for the energy transfer within the large molecular complexes [2].

[1] High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes, C Kreisbeck, T Kramer, M Rodriguez, B Hein, J. Chem. Theory Comput., 2011, 7 (7), pp 2166-2174.
[2] Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria, T Kramer, M Rodriguez, Scientific Reports 7, Article number 45245, (2017).

We study two setups of a one-dimensional tight-binding model with balanced gain/loss diagonal terms. In the first model with perfect leads attached to the scattering region, the attention is payed to the unidirectional reflectivity that is due to exceptional points emerging in the energy spectra. Our main findings are the new effects that appear when couplings between neighboring sites are non-symmetric. In the second model with closed boundaries we study the dynamics of wave packets when it is strongly influenced by exceptional points. Our predictions can be be used in experiments with the wave propagation along one-mode waveguides with asymmetric next-neighbor couplings.

Exciton transport plays a key role in the operation of all natural and artificial photosynthetic systems, a process that becomes complex when the absorption and emission of second excited state overlaps that of the first. The S2-S1 gap for Chlorophyll-a (Chl-a) is small and its precise value had been debated for over 50 years. We demonstrate that no previous proposed spectral assignment for Chl-a was correct, introducing a new Born-Oppenheimer-breakdown model that is shown to account for a wide selection of data for over 30 chlorophyllides in many solvents and in situ in photosystems. In Chl-a in photosystems, mixing of the first two excited states (Qy and Qx) is maximal, explaining the observation that decoherence of the Qx state occurs more rapidly for Chl-a than for any other chlorophyllide. We introduce 3 new methods for the interpretation of magnetic-circular dichroism (MCD) spectroscopy and for high-resolution polarized fluorescence-excitation spectroscopy that allow previously hidden critical experimental information to be revealed. One of these, a real-time graphics-based MCD spectral simulation program, is inspired by Heller's time dependent approach to quantum mechanics. We also demonstrate a priori computational methods that are able to discriminate between assignments and to detect anomalies in experimental data sets. These methods should be widely applicable to the characterization of artificial devices. Compounds synthesized to test these ideas led to the discovery of a new fundamental form of isomerization called ''akamptisomerism'' involving bond-angle inversion of singly bonded centres. This process offers a new chemical dimension in device applications, and is shown by geometrical analysis to be the last-possible simple form of isomerization, paralleling the 1914 discovery of atropisomerism.

The electronic transport in deformed graphene is studied theoretically. We show that deformations are not necessarily disadvantageous but can be used to tailor certain transport properties. In this way, deformations can be used to focus the current flow or to filter electrons from a certain valley. Moreover, effects of general relativity can be emulated in deformed graphene. We compare the current flow paths obtained from two fundamentally different approaches: (a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function (NEGF) method to a tight-binding model with local strain, (b) the general relativistic approach in which classical trajectories of relativistic massless point particles moving in a curved surface with a pseudo-magnetic field are calculated. We obtain very good numerical agreement between the quantum and the classical approaches for a fairly wide set of parameters. The presented method offers an enormous reduction of complexity from irregular tight-binding Hamiltonians defined on large lattices to geometric language for curved continuous surfaces.
T. Stegmann, N. Szpak: Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space, New Journal of Physics 18:053016 (2016)

Following an idea by Joyner et al. [1] a microwave graph with an antiunitary symmetry $T$ obeying $T^2=-1$ has been realized [2]. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. After 50 year of random matrix theory this has been the first experimental realization of the GSE. In addition recent results on the two-point correlation function, the spectral form factor, the number variance and the spectral rigidity will be presented, as well as the transition from GSE to GOE statistics by continuously changing $T$ from $T^2=-1$ to $T^2=1$.

[1] C. H. Joyner, S. Müller, and M. Sieber. Europhys. Lett. 107, 50004 (2014).
[2] A. Rehemanjiang, M. Allgaier, C. H. Joyner, S. Müller, M. Sieber, U. Kuhl, and H.-J. Stöckmann. Phys. Rev. Lett. 117, 064101 (2001).

Heller's thawed Gaussian approximation (TGA) [1] is combined with an on-the-fly ab initio (OTF-AI) scheme in order to calculate vibrationally resolved electronic spectra of polyatomic systems. First, we present, within the Franck-Condon approximation, emission spectra of oligothiophenes with up to five rings [2] as well as absorption and photoelectron spectra of ammonia [3]. On one hand, the efficiency of the OTF-AI-TGA permits treating all 105 vibrational degrees of freedom of pentathiophene explicitly and on an equal footing. On the other hand, the accuracy of the OTF-AI-TGA succeeds in describing accurately the electronic spectra of ammonia, which was chosen as a prototypical example of a floppy molecule exhibiting large amplitude motion. In all these cases the thawed Gaussian approximation performs significantly better than the standard global harmonic approximations, popular for large systems. Second, the OTF-AI-TGA is extended [4, 5, 6] in order to capture coordinate dependence of the transition dipole and this is demonstrated on the Herzberg-Teller absorption spectra of the phenyl radical and of benzene, a paradigm of an electronically forbidden, but vibronically allowed transition. Third, the OTF-AI thawed Gaussian approximation is used to evaluate vibrationally resolved resonance Raman spectra and excitation profiles of ammonia [7, 8]. Finally, to provide a deeper insight into the associated physical and chemical processes, we also develop a novel systematic approach [2] to assess the importance and coupling between individual vibrational degrees of freedom during the dynamics. This allows us to explain how the vibrational line shapes of the oligothiophenes change with an increasing number of rings.

[1] E. J. Heller, J. Chem. Phys. 62, 1544 (1975).
[2] M. Wehrle, M. Sulc, and J. Vanicek, J. Chem. Phys. 140, 244114 (2014).
[3] M. Wehrle, S. Oberli, and J. Vanicek, J. Phys. Chem. A 119, 5685 (2015).
[4] S. Lee and E. J. Heller, J. Chem. Phys. 76, 3035 (1982).
[5] A. Patoz, T. Begusic, and J. Vanicek, in preparation.
[6] T. Begusic, A. Patoz, and J. Vanicek, in preparation.
[7] D. J. Tannor and E. J. Heller, J. Chem. Phys. 77, 202 (1982).
[8] S. Reynaud, S. V. Antipov, and J. Vaníček, in preparation.