Ionization Pathway Interference in Photoionization Time Delays in Molecules.

The photoionization time-delay in linear conjugated molecules is computed using the Wigner scattering approach. We find that, in general, there are two additive contributions to the ionization time-delays. One originates from interferences between various ionization pathways that belong to different cationic eigenstates, while the other is due to time delays associated with each pathway and originates due to electron-electron correlations in the molecule. The former contribution scales up rapidly with the conjugation length, leading to larger time delays, as observed in recent experiments, while the latter is much less sensitive to the molecular conjugation.

Structure of quantum supercooled liquids.

Supercooled liquids show a drastic slowdown in the dynamics with decreasing temperature, while their structure remains similar to that of normal liquids. In this paper, the structural features in a quantum supercooled liquid are explored in terms of cages defined using the Voronoi polyhedra and characterized in terms of their volumes and geometries. The cage volume fluctuations are sensitive to the quantum effects, and decrease as the glass transition is approached by varying the quantumness. This is in contrast to the classical case where the volumes are insensitive to temperature variations as one approaches the transition. The cage geometry becomes more spherical upon increasing quantumness from zero, pushing the system closer to the glass transition. The cage geometry is found to be significantly correlated with asymmetry in the position uncertainty of the caged particle in the strongly quantum regime.

Stochastic walker with variable long jumps.

Motivated by recent interest in the stochastic resetting of a random walker, we propose a generalized model where the random walker takes stochastic jumps of lengths proportional to its present position with certain probability, otherwise it makes forward and backward jumps of fixed (unit) length with given rates. The model exhibits a rich stochastic dynamic behavior. We obtain exact analytic results for the first two moments of the walker's displacement and show that a phase transition from a diffusive to superdiffusive regime occurs if the stochastic jumps of lengths that are twice (or more) of its present positions are allowed. This phase transition is accompanied by a reentrant diffusive behavior.

Ionization Induced Time Delay in Hole Dynamics in Molecules.

Ionization time delay is a measure of the time of arrival of an electron from a bound molecular state to a free state. A similar time scale is associated with the hole dynamics in response to the ionization. We show that the ionization time delay and the time delay in hole dynamics are interdependent. Both time delays originate due to complex amplitudes of multiple ionization pathways, which lead to different cationic states. For sudden ionization (zero ionization time delay), the time delay for hole dynamics vanishes. We compute the ionization and hole dynamics time delays in glycine molecule and show how the photoionization process influences the hole dynamics and leads to nonzero hole-density flux as soon as the ionization takes place.

Tagged particle dynamics in supercooled quantum liquids.

We analyze the dynamics of quantum supercooled liquids in terms of tagged particle dynamics. Unlike the classical case, uncertainty in the position of a particle in quantum liquid leads to qualitative changes. We demonstrate these effects in the dynamics of the first two moments of displacements, namely, the mean-squared displacement, 〈Δr^{2}(t)〉, and 〈Δr^{4}(t)〉. Results are presented for a hard-sphere liquid using mode-coupling theory formulation and simulation on a binary Lennard-Jones liquid. As the quantumness (controlled by the de Broglie thermal wavelength) is increased, a nonzero value of the moments at zero time leads to significant deviations from the classical behavior in the initial dynamics. Initial displacement shows ballistic behavior 〈Δr^{2}(t)〉∼t^{2}, but, as a result of large uncertainty in the position, the dynamical effects become weaker with increasing quantumness over this timescale.

Quantum uncertainty effects in the dynamics of supercooled liquids: A molecular dynamics study.

Dynamics of density fluctuations in quantum supercooled liquids is analyzed using molecular dynamics simulations. In contrast to the classical case, the uncertainty in the particle position (delocalization of quantum particle in space) leads to significant differences in the dynamics of quantum liquids, both in the short- and long-time limits. The effect of uncertainty is found to be significant for length scales smaller than the uncertainty itself, and diminishes as the length scale grows. The dynamic heterogeneity of the system at short times is enhanced due to uncertainty. In the intermediate (ß-relaxation) time regime, the heterogeneity tends to get suppressed due to quantum uncertainty. The probability distribution of particle displacements shows highly nonclassical behavior with double-peak structure at short timescales.

Photo-Ionization Time Delay in Linearly Extended π-Conjugated Molecular Systems.

We calculate the photo-ionization time delay for extended, linear, π-conjugated molecules. Ionization can be realized as scattering of an electron from bound to continuum states due to interaction with an ionizing radiation field. This allows us to use the Wigner method, whereby the rate of change in phase of the scattered electron wave packet with respect to the electron energy gives a measure of the ionization time delay. An analytical expression for ionization time delay is obtained using a model system that shows how interference between different ionization pathways leads to a finite time delay, even if there is a zero time delay corresponding to individual pathways. It is observed that the ionization time delay increases linearly as the size of the chain increases. We compute the ionization time delay also using computational chemistry and compare the results with those obtained from the model system. In qualitative agreement with the model calculation, we find that the ionization time delay increases linearly with increasing conjugation.

Frequency-dependent specific heat in quantum supercooled liquids: A mode-coupling study.

Frequency-dependence of specific heat in supercooled hard sphere liquid is computed using quantum mode-coupling theory (QMCT). Mode-coupling equations are solved using a recently proposed perturbative method that allows us to study relaxation in the moderate quantum regime where quantum effects assist liquid to glass transition. Zwanzig's formulation is used to compute the frequency-dependent specific heat in the supercooled state using dynamical information from QMCT. Specific heat shows strong variation as the quantumness of the liquid is changed, which becomes more significant as density is increased. It is found that, near the transition point, different dynamical modes contribute to specific heat in classical and quantum liquids.

Structural relaxation in quantum supercooled liquids: A mode-coupling approach.

We study supercooled dynamics in a quantum hard-sphere liquid using quantum mode-coupling formulation. In the moderate quantum regime, classical cage effects lead to slower dynamics compared to the strongly quantum regime, where tunneling overcomes classical caging, leading to faster relaxation. As a result, the glass transition critical density can become significantly higher than for the classical liquids. A perturbative approach is used to solve time dependent quantum mode-coupling equations to study in detail the dynamics of the supercooled liquid in the moderate quantum regime. Similar to the classical case, the relaxation time shows the power-law increase with the increase in the density in the supercooled regime. However, the power-law exponent is found to be dependent on the quantumness; it increases linearly as the quantumness is increased in the moderate quantum regime.

The Photoionization Time in π-Conjugated Molecular Systems.

The photoionization time of C2H4 is calculated as a model for π-conjugated molecular systems. Analytical results are obtained using the Wigner phase delay, which is compared with energy-streaking measurements. We find that, although the ionization time averaged over nuclear configurations compares well in the two measures, the dependence on the nuclear configuration is different. Interference between different ionization pathways depends significantly on the molecular geometry and the ionizing electron energy and may lead to qualitative changes in the ionization time.

Energy, Particle, and Photon Fluxes in Molecular Junctions.

Electroluminescence from a current-carrying molecular junction at steady state is simulated. (Charge) particle conservation and energy conservation are satisfied by a perturbative expansion in the radiation/matter coupling. Our approach makes it possible to adopt standard tools of traditional (equilibrium) spectroscopy to study signals from open systems such as molecular junctions. The nonperturbative analysis of spontaneous light emission signals coincides with the perturbative approach for weak molecule-field coupling.

Spontaneous Light Emission from Molecular Junctions: Theoretical Analysis of Upconversion Signal.

Spontaneous light emission from a current-carrying molecular junction is analyzed. There are two leading processes, fluorescence and electroluminescence, as defined using Liouville space diagrams within the perturbative method, that contribute to the light emission from junctions. This allows us to identify a general mechanism that explains the origin of the so-called upconversion electroluminescence (UCEL) signal, which has been observed in a variety of molecular junctions [Umera et al. Chem. Phys. Lett. 2007, 448, 232; Dong et al. Nat. Photonics 2010, 4, 50]. Here, we show that a double-peak signal, one at energy less than the applied bias and the other at higher energy (UCEL), is generated due to overlap between two processes: one is electron transfer to create the required excited state, and the other is radiative relaxation of the excited state. The lifetimes induced by the lead interactions play a crucial role in determining the required overlap between these processes. Our analysis shows that, unlike the higher-energy signal, the lower-energy peak is sensitive to the applied bias and does not correspond to any optical resonance in the junction. The signal at higher energy is enhanced as the temperature is increased. We demonstrate our findings using nonperturbative analytic results for a model system.

Electroluminescence in Molecular Junctions: A Diagrammatic Approach.

We compute electroluminescent signal in a current carrying single molecule junction using a superoperator formalism. Liouville space loop diagrams are used to identify all density matrix pathways that emit photons via the electroluminescence process. A frequency resolved spectrum is expressed in terms of the various Fock space states of the isolated molecule that participate in the creation and subsequent recombination of exciton. Application is made to a multilevel Coulomb blockade model system and to a gold-benzene-1,4-dithiol-gold molecular junction.

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions.

The nonlinear optical response of a current-carrying single molecule coupled to two metal leads and driven by a sequence of impulsive optical pulses with controllable phases and time delays is calculated. Coherent (stimulated, heterodyne) detection of photons and incoherent detection of the optically induced current are compared. Using a diagrammatic Liouville space superoperator formalism, the signals are recast in terms of molecular correlation functions which are then expanded in the many-body molecular states. Two dimensional signals in benzene-1,4-dithiol molecule show cross peaks involving charged states. The correlation between optical and charge current signal is also observed.

Electron transfer statistics and thermal fluctuations in molecular junctions.

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects.

Descending from infinity: convergence of tailed distributions.

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not eliminated. Relaxation stronger than linear suppresses long tails immediately, but may lead to strong transient peaks in the probability distribution. We also find that a δ-function initial distribution under stronger than linear decay displays not one but two different regimes of diffusive spreading.

Globally coupled stochastic two-state oscillators: fluctuations due to finite numbers.

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N → ∞ and t → ∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.