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Shaul Mukamel

Publications and source records attributed to Shaul Mukamel.

45 records · Page 3Linked to original sources
PubMed2003

Superoperator representation of nonlinear response: unifying quantum field and mode coupling theories.

Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.

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PubMed2003

One-dimensional transport with dynamic disorder.

We study the mean quenching time distribution and its moments in a one-dimensional N-site donor-bridge-acceptor system where all sites are coupled to a two-state jump bath for arbitrary disorder and an arbitrary ratio kappa identical with /R of the bath jump rate R and the average hopping rate . When kappaN approximately 1, the quenching time distribution has long power-law tails even when the waiting times are exponentially distributed. These disappear for kappaN<<1 where the hopping rate self-averages on the bath relaxation time scale. In the absence of disorder or for small kappa, the mean quenching time scales linearly with N. Otherwise, we observe a power law, approximately N1+gamma, with a crossover to linear scaling (gamma=0) for large N. Distributions of particle position, its second moment, velocity and diffusion coefficient are computed in the infinite N limit. For times longer than R-1, the dynamic disorder self-averages and the average position, velocity, and diffusion coefficient scale linearly in time.

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PubMed2003

Quantum extension of the Jarzynski relation: analogy with stochastic dephasing.

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary time scale and the corresponding equilibrium free energy difference is generalized to quantum systems. Using the adiabatic representation, we show that this relation holds for isolated systems as well as for systems coupled to a bath described by a master equation. A close formal analogy is established between the present "classical trajectory" picture over populations of adiabatic states and phase fluctuations (dephasing) of a quantum coherence in spectral line shapes, described by the stochastic Liouville equation.

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PubMed2003

Simulation strategies and signatures of chaos in classical nonlinear response.

Algorithms are presented for overcoming the computational challenge of nonlinear response functions which describe the response of a classical system to a sequence of n pulses and depend on nth order multipoint stability matrices containing signatures of chaos. Simulations for the Lorentz gas demonstrate that finite field algorithms can be effectively used for the robust, long time calculation of nonlinear response functions. These offer the possibility to characterize chaos beyond the commonly used Lyapunov exponents and suggest new experimentally accessible measures of chaos.

Models, Statistical↗
PubMed2002

Three-dimensional nonlinear optical chromophores based on through-space delocalization.

Six permutations of 4-fold donor and/or acceptor substitution of paracyclophane at the 4, 7, 12, and 15 positions were synthesized to probe the phenomenon of three-dimensional delocalization on the nonlinear optical properties of organic materials. The interplay between through-bond intramolecular charge transfer (ICT) as well as three-dimensional, or through-space, ICT processes gives rise to large quadratic hyperpolarizability values. The determination of dipolar (beta(J)(=1)) and octupolar (beta(J)(=3)) irreducible tensor contributions to the overall beta tensor value is made possible by the polarized harmonic light scattering technique at 1.32 microm. The electric field-induced second-harmonic generation technique was also used at 1.91 microm for comparison. Significant experimental beta values for members of the series made of two centrosymmetric benzene-like units are a clear signature of a purely through-space ICT between two aryl subunits. The two configurational isomers that pair two dipolar donor-acceptor chromophores also exhibit octupolar character. Analysis of these two with an additive model for beta(J)(=1) and beta(J)(=3) reveals a strong three-dimensional inter-ring charge transfer.

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PubMed2002

Coherent x-ray Raman spectroscopy: a nonlinear local probe for electronic excitations.

Nonlinear x-ray four-wave mixing experiments are becoming feasible due to rapid advances in high harmonic generation and synchrotron radiation coherent x-ray sources. By tuning the difference of two x-ray frequencies across the valence excitations, it is possible to probe the entire manifold of molecular electronic excitations. We show that the wave vector and frequency profiles of this x-ray analogue of coherent Raman spectroscopy provide an excellent real-space probe that carries most valuable structural and dynamical information, not available from spontaneous Raman techniques.

Journal Article↗
PubMed2002

Disorder and funneling effects on exciton migration in treelike dendrimers.

The center-bound excitonic diffusion on dendrimers subjected to several types of nonhomogeneous funneling potentials is considered. We first study the mean first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations g to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature T is lowered. This is a transition from a high-T regime in which all paths contribute to the MFPT to a low-T regime in which only a few of them do. We further explore the funneling within a realistic nonlinear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the time-dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with g but crosses over, beyond a molecular-specific and T-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the small world model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power law or to a logarithmic scaling with g, depending on the strength of the funneling force.

Journal Article↗
PubMed2001

Influence of Structural and Rotational Isomerism on the Triplet Blinking of Individual Dendrimer Molecules J.H. thanks the FWO for a post-doctoral fellowship. T.V. wishes to thank the I.W.T. for a doctoral fellowship. Financial support by the FWO, the DWTC (through IUAP-4-11), and the Flemish Ministry of Education (through GOA/1/2001) is gratefully acknowledged. The EC (through TMR Sisitomas), ESF (through Smarton), and the Volkswagen-Stiftung are also thanked for financial support. Dr. L. Latterini is thanked for the triplet absorption measurements.

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