Relationship between quantum decoherence times and solvation dynamics in condensed phase chemical systems

A relationship between the time scales of quantum coherence loss and short-time solvent response for a solute/bath system is derived for a Gaussian wave packet approximation for the bath. Decoherence and solvent response times are shown to be directly proportional to each other, with the proportionality coefficient given by the ratio of the thermal energy fluctuations to the fluctuations in the system-bath coupling. The relationship allows the prediction of decoherence times for condensed phase chemical systems from well developed experimental methods.Comment: 10 pages, no figures, late

Ab initio Study of Exciton Transfer Dynamics from a Core-Shell Semiconductor Quantum-Dot to a Porphyrin-Sensitizer

The observed resonance energy transfer in nanoassemblies of CdSe/ZnS quantum dots and pyridyl-substituted free-base porphyrin molecules [Zenkevich et al., J. Phys. Chem. B 109 (2005) 8679] is studied computationally by ab initio electronic structure and quantum dynamics approaches. The system harvests light in a broad energy range and can transfer the excitation from the dot through the porphyrin to oxygen, generating singlet oxygen for medical applications. The geometric structure, electronic energies, and transition dipole moments are derived by density functional theory and are utilized for calculating the Förster coupling between the excitons residing on the quantum dot and the porphyrin. The direction and rate of the irreversible exciton transfer is determined by the initial photoexcitation of the dot, the dot–porphyrin coupling and the interaction to the electronic subsystem with the vibrational environment. The simulated electronic structure and dynamics are in good agreement with the experimental data and provide real-time atomistic details of the energy transfer mechanism. © 2007 Elsevier B.V. All rights reserved

Impediments to mixing classical and quantum dynamics

The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very basic requirements related to the time evolution of the two sectors when they are decoupled. (ii) The classical sector cannot inherit quantum fluctuations from the quantum sector. And, (iii) a coupling among the two sectors is incompatible with the requirement of physical positivity of the theory, i.e., there would be positive observables with a non positive expectation value.Comment: RevTex, 21 pages. Title slightly modified and summary section adde

Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter

Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.Comment: 10 page

Quantum and classical descriptions of a measuring apparatus

A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality. Alternatively, the apparatus may always be treated by quantum mechanics, and be measured by a second apparatus which has such a dual description. This article examines whether these two different descriptions are mutually consistent. It is shown that if the dynamical variable used in the first apparatus is represented by an operator of the Weyl-Wigner type (for example, if it is a linear coordinate), then the conversion from quantum to classical terminology does not affect the final result. However, if the first apparatus encodes the measurement in a different type of operator (e.g., the phase operator), the two methods of calculation may give different results.Comment: 18 pages LaTeX (including one encapsulated PostScript figure

Mixing quantum and classical mechanics and uniqueness of Planck's constant

Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf 8} 545\cite{sahoo}). We show that the tensor-product of two quantum Hamilton algebras, each characterized by a different Planck's constant is an algebra of the same type characterized by yet another Planck's constant. The algebraic structure of mixed quantum and classical systems is then analyzed by taking the limit of vanishing Planck's constant in one of the component algebras. This approach provides new insight into failures of various formalisms dealing with mixed quantum-classical systems. It shows that in the interacting mixed quantum-classical description, there can be no back-reaction of the quantum system on the classical. A natural algebraic requirement involving restriction of the tensor product of two quantum Hamilton algebras to their components proves that Planck's constant is unique.Comment: revised version accepted for publication in J.Phys.A:Math.Phy

Universal dynamical control of quantum mechanical decay: Modulation of the coupling to the continuum

We derive and investigate an expression for the dynamically modified decay of states coupled to an arbitrary continuum. This expression is universally valid for weak temporal perturbations. The resulting insights can serve as useful recipes for optimized control of decay and decoherence.Comment: 4 pages, 2 figures. Rewritten, changed figures, added reference