Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by Mikami and Okazaki invoking the path-integral influence functional method [J. Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode of a small amino-acide like molecule, N-methylacetamide, in heavy water.Comment: 16 pages, 5 figures, 5 tables, submitted to J. Chem. Phy

Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.Comment: 20 pages, 5 figures, submitted to J. Chem. Phy

Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J.E. Straub, J. Chem. Phys. {\bf 124}, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along an MD trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times ($\lesssim$ 200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide.Comment: 24 pages, 7 figures, submitted to J. Chem. Phy

Bosonic D-branes at finite temperature with an external field

Bosonic boundary states at finite temperature are constructed as solutions of boundary conditions at $T\neq 0$ for bosonic open strings with a constant gauge field $F_{ab}$ coupled to the boundary. The construction is done in the framework of thermo field dynamics where a thermal Bogoliubov transformation maps states and operators to finite temperature. Boundary states are given in terms of states from the direct product space between the Fock space of the closed string and another identical copy of it. By analogy with zero temperature, the boundary states heve the interpretation of $Dp$-brane at finite temperature. The boundary conditions admit two different solutions. The entropy of the closed string in a $Dp$-brane state is computed and analysed. It is interpreted as the entropy of the $Dp$-brane at finite temperature.Comment: 21 pages, Latex, revised version with minor corrections and references added, to be published in Phys. Rev.

Hidden variable interpretation of spontaneous localization theory

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM-GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.Comment: 13 page

Boneh-Franklin Identity Based Encryption Revisited

Contains fulltext : 33216.pdf (preprint version ) (Open Access

Particle Production and Gravitino Abundance after Inflation

Thermal history after inflation is studied in a chaotic inflation model with supersymmetric couplings of the inflaton to matter fields. Time evolution equation is solved in a formalism that incorporates both the back reaction of particle production and the cosmological expansion. The effect of the parametric resonance gives rise to a rapid initial phase of the inflaton decay followed by a slow stage of the Born term decay. Thermalization takes place immediately after the first explosive stage for a medium strength of the coupling among created particles. As an application we calculate time evolution of the gravitino abundance that is produced by ordinary particles directly created from the inflaton decay, which typically results in much more enhanced yield than what a naive estimate based on the Born term would suggest.Comment: 23 pages + 13 figure

The CWKB Method of Particle Production in Periodic Potential

In this work we study the particle production in time dependent periodic potential using the method of complex time WKB (CWKB) approximation. In the inflationary cosmology at the end of inflationary stage, the potential becomes time dependent as well as periodic. Reheating occurs due to particle production by the oscillating inflaton field. Using CWKB we obtain almost identical results on catastrophic particle production as obtained by others.Comment: 17 pages, latex, 2 figure

Random Oracles in a Quantum World

The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore post-quantum secure. We conclude with a rich set of open problems in this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a related paper by Boneh and Zhandr