Quantum Decay Rates Research Articles

Modeling pH-Dependent Biomolecular Photochemistry.

The tuning mechanism of pH can be extremely challenging to model computationally in complex biological systems, especially with respect to the photochemical properties. This article reports a protocol aimed at modeling pH-dependent photodynamics using a combination of constant-pH molecular dynamics and semiclassical nonadiabatic molecular dynamics simulations. With retinal photoisomerization in Anabaena sensory rhodopsin (ASR) as a testbed, we show that our protocol produces pH-dependent photochemical properties, such as the isomerization quantum yield or decay rates. We decompose our results into single-titrated residue contributions, identifying some key tuning amino acids. Additionally, we assess the validity of the single protonation state picture to represent the system at a given pH and propose the most populated protein charge state as a compromise between cost and accuracy.

Multiplexing-oriented plasmon-MoS2 hybrid metasurfaces driven by nonlinear quasi bound states in the continuum

Rapid progress in nonlinear plasmonic metasurfaces enabled many novel optical characteristics for metasurfaces, with potential applications in frequency metrology [Zimmermann et al. Opt. Lett. 29:310 (2004)], timing characterization [Singh et al. Laser Photonics Rev. 14:1 (2020)] and quantum information [Kues et al. Nature. 546:622 (2017)]. However, the spectrum of nonlinear optical response was typically determined from the linear optical resonance. In this work, a wavelength-multiplexed nonlinear plasmon-MoS2 hybrid metasurface with suppression phenomenon was proposed, where multiple nonlinear signals could to be simultaneously processed and optionally tuned. A clear physical picture to depict the nonlinear plasmonic bound states in the continuum (BICs) was presented, from the perspective of both classical and quantum approaches. Particularly, beyond the ordinary plasmon-polariton effect, we numerically demonstrated a giant BIC-inspired second-order nonlinear susceptibility 10-5m/V of MoS2 in the infrared band. The novelty in our study lies in the presence of a quantum oscillator that can be adopted to both suppress and enhance the nonlinear quasi BICs. This selectable nonlinear BIC-based suppression and enhancement effect can optionally block undesired modes, resulting in narrower linewidth as well as smaller quantum decay rates, which is also promising in slow-light-associated technologies.

Spectral problems in open quantum chaos

We present an overview of mathematical results and methods relevant for the spectral study of semiclassical Schrödinger (or wave) operators of scattering systems, in cases where the corresponding classical dynamics is chaotic; more precisely, we assume that in some energy range, the classical Hamiltonian flow admits a fractal set of trapped trajectories, which hosts chaotic (hyperbolic) dynamics. The aim is then to connect the information on this trapped set with the distribution of quantum resonances in the semiclassical limit.Our study encompasses several models sharing these dynamical characteristics: free motion outside a union of convex hard obstacles, scattering by certain families of compactly supported potentials, geometric scattering on manifolds with (constant or variable) negative curvature. We also consider the toy model of open quantum maps, and sketch the construction of quantum monodromy operators associated with a Poincaré section for a scattering flow.The semiclassical density of long-living resonances exhibits a fractal Weyl law, related to the fact that the corresponding metastable states are ‘supported’ by the fractal trapped set (and its outgoing tail). We also describe a classical condition for the presence of a gap in the resonance spectrum, equivalently a uniform lower bound on the quantum decay rates, and present a proof of this gap in a rather general situation, using quantum monodromy operators.

Distribution of resonances in the quantum open baker map

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum p direction of the 2-torus phase space, modeling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.

Quantum decay rates in chaotic scattering

We study quantum scattering on manifolds equivalent to the Euclidean space near infinity, in the semiclassical regime. We assume that the corresponding classical flow admits a non-trivial trapped set, and that the dynamics on this set is of Axiom A type (uniformly hyperbolic). We are interested in the distribution of quantum resonances near the real axis. In two dimensions, we prove that, if the trapped set is sufficiently “thin”, then there exists a gap between the resonances and the real axis (that is, quantum decay rates are bounded from below). In higher dimension, the condition for this gap is given in terms of a certain topological pressure associated with the classical flow. Under the same assumption, we also prove a resolvent estimate with a logarithmic loss compared to non-trapping situations.

Resonance distribution in open quantum chaotic systems

In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the distribution of (quantum) decay rates is shown to cluster near a "typical" value, which is larger than the classical decay rate of the corresponding damped ray dynamics. The speed of this clustering may be quite slow, which could explain why it has not been detected in previous numerical data.

Experimental and theoretical study of temperature dependent exciton delocalization and relaxation in anthracene thin films

The spectroscopy of solid anthracene is examined both experimentally and theoretically. To avoid experimental complications such as self-absorption and polariton effects, ultrathin polycrystalline films deposited on transparent substrates are studied. To separate the contributions from different emitting species, the emission is resolved in both time and wavelength. The spectroscopic data are interpreted in terms of a three-state kinetic model, where two excited states, a high energy state 1 and a low energy state 2, both contribute to the luminescence and are kinetically coupled. Using this model, we analyze the spectral lineshape, relative quantum yield, and relaxation rates as a function of temperature. For state 1, we find that the ratio of the 0-0 vibronic peak to the 0-1 peak is enhanced by roughly a factor of 3.5 at low temperature, while the quantum yield and decay rates also increase by a similar factor. These observations are explained using a theoretical model previously developed for herringbone polyacene crystals. The early-time emission lineshape is consistent with that expected for a linear aggregate corresponding to an edge-dislocation defect. The results of experiment and theory are quantitatively compared at different temperatures in order to estimate that the singlet exciton in our polycrystalline films is delocalized over about ten molecules. Within these domains, the exciton's coherence length steadily increases as the temperature drops, until it reaches the limits of the domain, whereupon it saturates and remains constant as the temperature is lowered further. While the theoretical modeling correctly reproduces the temperature dependence of the fluorescence spectral lineshape, the decay of the singlet exciton appears to be determined by a trapping process that becomes more rapid as the temperature is lowered. This more rapid decay is consistent with accelerated trapping due to increased delocalization of the exciton at lower temperatures. These observations suggest that exciton coherence can play an important role in both radiative and nonradiative decay channels in these materials. Our results show that the spectroscopy of polyacene solids can be analyzed in a self-consistent fashion to obtain information about electronic delocalization and domain sizes.

Direct Measurement of the Triplet Quantum Yield of Poly(3-dodecylthiophene) in Solution

The photophysics, including radiative and nonradiative quantum yields and decay rates, of regioregular poly(3-dodecylthiophene) (P3DT) in benzene were studied by means of UV−visible spectroscopy, photoluminescence spectroscopy, photothermal beam deflection (PBD), photoacoustic calorimetry (PAC), and time-resolved photoluminescence spectroscopy. We observe the fluorescence quantum efficiency to be 0.30 ± 0.01 and the internal conversion (from S1 to S0) quantum yield of 0.59 ± 0.02 as well as the intersystem crossing (from S1 to T1) quantum yield of 0.11 ± 0.01. By measuring the fluorescence lifetime of ca. 490 ps, we estimate a radiative lifetime of 1.64 ns for the singlet excitons and nonradiative decay rate constants of kic = 1.21 ns-1 and kisc = 0.22 ns-1 for internal conversion and intersystem crossing, respectively. The nature and photophysics of triplet states in poly(3-dodecylthiophene) are well characterized using PBD and PAC, and the result suggests that internal conversion plays a major role in energy depletion.

Quantum decay rates for driven barrier potentials in the strong friction limit

Quantum decay rates for barrier potentials driven by external stochastic and periodic forces in the strong damping regime are studied. Based on the quantum Smoluchowski equation derived recently by Ankerhold, Pechukas, and Grabert [Phys. Rev. Lett. 87, 086802 (2001)] explicit analytical and numerical results are presented for the case of the resonant activation phenomenon in a bistable potential and the escape from a metastable well with oscillating barrier, respectively. The significant impact of quantum fluctuations is revealed.

Scar and antiscar quantum effects in open chaotic systems.

We predict and numerically observe strong periodic orbit effects in the properties of weakly open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow isolated resonances when the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at long times is thus exponentially enhanced over the random matrix theory prediction. The distribution of resonance widths and the probability to remain are quantitatively given in terms of only the stability matrix of the orbit on which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhanced or suppressed near orbits other than the one on which the lead is located, depending on the periods and classical actions of these other orbits. These effects of the short periodic orbits on quantum decay rates have no classical counterpart, and first appear on times scales much larger than the Heisenberg time of the system. All the predictions are quantitatively compared with numerical data.

Microwave ionization of hydrogen atoms: quantum decay rates and classical phase-space structures

We examine the ionization of highly excited hydrogen atoms by a linearly polarized microwave field quantum mechanically and classically. We investigate the role of classical phase-space resonances on the process of ionization and quantum mechanical ionization rates.

Quantum decay rate of a nonlinear dissipative system with fission-like potential nearT c

We use a thermodynamic scheme (imaginary free energy method) in terms of the path integral technique to study the quantum decay rates of a metastable state system coupled to a heat bath in the crossover temperature (Tc) region. In this region the transition between thermally activated decay and tunneling occurs. A nonlinear coupling form factor is used to overcome the divergent integral in the partition function nearTc. The decay rate formula based on the steepest descent approximation has been improved. A method is developed to calculate the real and imaginary parts of the partition function which combines a random walk method with fast-Fourier transform Monte-Carlo evaluation. For a nonlinear dissipative system with a damping correlation kernel of exponential form, the accurate numerical calculations are presented. The effects of nonlinear and frequency-dependent damping on the rate are shown.

Damping mechanisms in the path-integral approach to special effects in superconductivity

Previous work on semiclassical approximations in SQUIDs (which involved Feynman's path-integral technique) is here extended to damped Josephson systems. Quantum decay rates of unstable energy levels near the bottom of the quartic potential well are examined. Rates diagram is compared with that obtained for the undamped case. Agreement with Caldeira-Leggett results is discussed. A description of continuous flux measurements is developed. The spreading of the wave function leads to the treatment of flux and charge as canonically conjugate variables.

Quantum decay rates in dense media

A quantum theory of decay processes in condensed phases is presented. It is based on a general dynamic rate theory applied to a model in which a particle is bilinearly coupled to a system of harmonic oscillators. Both adiabatic and nonadiabatic processes are considered. The many-dimensional problem is reduced to a one-dimensional case making use of a separable (normal mode) coordinate correlated to the particle coordinate. The rate constant is calculated throughout the temperature range. The results of earlier work using stochastic theory are obtained in the limit of weak particle-medium coupling.

Quantum decay rates for dissipative systems at finite temperatures.

The decay of a metastable state of a system coupled to a heat-bath environment is studied. A functional-integral method is presented allowing for the calculation of decay rates at finite temperatures and in the presence of dissipation. The theory is utilized to determine the rate for a wide range of parameters. The temperature extends from the region where the decay is thermally activated down to very low temperatures where the system decays by tunneling from its ground state in the metastable well. The range of damping parameters covers the region from weakly damped to heavily overdamped motions. It is found that the transition between thermally activated decay and tunneling occurs near a crossover temperature ${T}_{0}$ which decreases with increasing damping strength. Well above ${T}_{0}$ the rate follows the classical Arrhenius law where the preexponential factor is affected by the frequency-dependent damping. As ${T}_{0}$ is approached, quantum corrections to the classical rate formula become increasingly important. In the vicinity of ${T}_{0}$ the rate follows a scaling law describing the crossover between thermally activated and quantum-mechanical decay. In the region below ${T}_{0}$ the decay rate can be determined analytically only in limiting cases. For a system with Ohmic dissipation and a cubic potential, accurate numerical calculations are presented exhausting the range of parameters not covered by analytical results.

Transition state theory for quantum decay rates in dissipative systems: the high-temperature limit

The quantum theory of activated events in condensed phases, developed by Wolynes using path integral techniques, is derived via harmonic quantum state theory.

Temperature dependence of quantum decay rates in dissipative systems.

The exponent and the prefactor of the decay rate of a metastable system coupled to an environment at temperature T are determined. Analytical methods for high and intermediate temperatures are combined with an accurate numerical method for low temperatures where tunneling transitions prevail. The calculations cover the entire range of parameters of interest in the problem of macroscopic quantum tunneling in systems involving the Josephson effect.

The determination of translational diffusion constants in liquid crystals from pulsed field gradient double quantum spin echo decays

Proton double quantum decay rates in presence of pulsed magnetic field gradients have been used to measure translational diffusion coefficients. The method is superior to analogous techniques based on single quantum echoes because double quantum coherence experiences effectively twice the applied field gradient. In cases where the natural double quantum decay rate is less than that of single quantum coherence, further increases in precision can be realized. The method is illustrated by measurements of solute diffusion parallel and perpendicular to the director axis in nematic and smectic liquids crystalline media.

Remarks on a normalization of the curves of angular distributions of e − e + pairs annihilation quanta

A normalization procedure is proposed for the measurement of the two and three positron annihilation quantum decay rates. An apparatus coefficient α has been introduced which expresses the measured to total triple decay rates and a method of measuring this was indicated.