Applicability of the method of kinetic equations for describing nuclear quadrupole resonance in molecular crystals

The applicability of the method of kinetic equations for describing nuclear quadrupole resonance (NQR) in molecular crystals is demonstrated for the case in which the relaxation processes are produced by torsional vibrations of the molecules. The Bloch system of equations for NQR spins I=3/2 situated in an axisymmetric electrical field and expressions for spin-lattice relaxation times were obtained.     

Simultaneous stochastic effects of a thermal reservoir and an electromagnetic field on the optical susceptibility of a two-level system

In this paper we derive analytical expressions for the optical susceptibility of a two-level system immersed in a thermal bath and interacting with an external electromagnetic field, where both of them are considered as noise sources. The dynamics of the system is described by a set of optical stochastic Bloch equations. The noise sources are modeled as Ornstein-Uhlenbeck processes. The optical stochastic Bloch equations are perturbatively solved up to second order in the external field. We found that each noise affects the dynamics in a different manner. Thus, at first order, the bath modifies the transverse relaxation time, whereas the effect of a random field can only be appreciated if the expansion is calculated up to second order, where correlations begin to be important.     

The validity of the “few-level” approximation in gaseous relaxation phenomena

The Bloch equations including damping are formulated for a molecular system excited by incident radiation. In contrast with a previous treatment the present formalism gives an intuitively satisfactory form of relaxation terms. A three-level system irradiated by a single oscillating field is specifically considered, and using this manifold as a model for a two-level system immersed in a heat bath, the problem of “embedding” a pair of levels connected by radiation within a multi-level manifold is treated. A brief discussion of transient solutions to the Bloch equations is included.     

Generalized non-Markovian optical Bloch equations

By considering single chromophore systems whose radiative decay can be written in terms of a nonlocal Lindblad-type evolution, the authors extend the formalism of generalized optical Bloch equations [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] to non-Markovian dynamics. They demonstrate that photon statistical properties such as bunching and antibunching, as well as sub- and super-Poissonian photon statistics can be fitted in the context of non-Markovian dynamics. The nonlocal effects may arise due to the interaction with a complex structured environment. In this case, the photon statistics can be related with the parameters that define the microscopic system-environment interaction. Alternatively, the authors demonstrate that effective dynamics such as triplet blinking, where the system is coupled via incoherent transitions to an extra dark state, can also be worked out in terms of generalized non-Markovian optical Bloch equations. The corresponding memory contributions are mapped with those that arise from the microscopic approach.     

Transformation of Bloch representation into atomic orbital representation and combined matrix element calculation technique for spatially bounded basis functions in crystals

A method is proposed for transforming the Hamiltonian from Bloch to atomic function representation. For spatially bounded functions, this is a rigorous method based on solution of a certain algebraic system of equations. Unlike the conventional procedure based on integration over the Brillouin zone, the new method requires knowledge of the matrix elements of the Bloch representation only at several points of the Brillouin zone. The number of these points is determined by the trimming radius for the spatially bounded functions and by the lattice constant. The method can be used for calculating matrix elements in a basis of atomic functions and for reducing computations in matrix element calculations of the Bloch representation for procedures using numerical integration.     

Collisional relaxation times in a three-level maser

We derive the Bloch equations for a three-level system, introducing phenomenological relaxation rates. Microscopic expressions are developed for these rates in the case of a gas of molecular absorbes for which relaxation is due to collisions with other molecules. Assuming that the colliding species move on classical paths and interact through long-range dipole terms, we can derive simple formulae for all the rates. A notable prediction is that certain off-diagonal rates are non-zero, though smaller than the diagonal terms. The physical significance of the results is briefly discussed.     

A BASIC program for least-squares estimation of the parameters influencing line shapes in multi-site chemical exchange in nuclear magnetic resonance spectrometry

The OPTAO program in BASIC solves modified Bloch equations and calculates the line shape for a given set of parameters, which are then optimized by a Gauss-Newton non-linear least-squares method to provide the best fit to experimental data. Up to five sites can be handled. The program is suitable for personal computers.     

Derivation and pilot application of a scheme for intermediate Hamiltonians in Fock space

A Fock space formulation of the intermediate Hamiltonian approach is derived by introducing shift operators in the equations determining effective Hamiltonians in Fock space. A non-hermitian intermediate Hamiltonian is constructed from the Fock space Bloch equation. An alternative derivation, based on a similarity transformation expression, is presented providing access to hermitian intermediate Hamiltonians. In a pilot application, the potential curves of the two lowest¹ _g ⁺ states of the H₂ molecule are calculated demonstrating the applicability of the scheme.     

Theory and calculations of second-order anharmonic corrections to the radial distribution function of polyatomic molecules

A theory of the thermal averages of normal coordinates was suggested for polyatomic molecules. Second-order approximation equations were obtained on the basis of iterations of the Bloch integral equation. These equations can be used to calculate anharmonic corrections to the radial distribution function and the parameters that determine the intensity of fast electron scattering by molecules in gas-phase electron diffraction.     

Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation

We consider the time-optimal control of an ensemble of uncoupled spin 1/2 particles in the presence of relaxation and radiation damping effects, whose dynamics is governed by nonlinear equations generalizing the standard linear Bloch equations. For a single spin, the optimal control strategy can be fully characterized analytically. However, in order to take into account the inhomogeneity of the static magnetic field, an ensemble of isochromats at different frequencies must be considered. For this case, numerically optimized pulse sequences are computed and the dynamics under the corresponding optimal field is experimentally demonstrated using nuclear magnetic resonance techniques.     

Emulsion polymerization: Theory of particle size distribution in copolymerization system

A mathematical model for describing the particle size distribution (PSD) in emulsion copolymerization system is developed by analogy to that in emulsion homopolymerization system as proposed by Lichti and co-workers. By use of the appropriate combinations of the kinetic parameters of the comonomers, the complicated equations for copolymerization systems can be reduced to simpler equations identical to those of homopolymerization systems. The two calculation examples, styrene–methyl methacrylate and styrene-butadiene systems, are given to demonstrate the applicability of the proposed theory. The conditions for producing bimodal PSD from a seeded emulsion polymerization are discussed.     

Excitation of two-level atoms in mode-locked laser fields

The excitation of two-level atoms in a laser field comprising many equally spaced coupled laser modes corresponding to a coherent pulse train is examined. The atom-field interaction is analysed via the optical Bloch equations for a rotating wave. In the limit of weak excitation they can be solved analytically and the time-averaged atomic excitation turns out to be a linear superposition of the contributions from the individual laser modes. Thus excitation spectra simply reflect the mode structure of the laser spectrum. Excitation spectra for strong fields are obtained by numerical integration of the optical Bloch equations. They exhibit a saturation behaviour differing significantly from the well known single-mode case. The temporal evolution towards the steady state is calculated for several numerical examples to clarify the origin of this behavior. For achieving maximum excitation, the laser pulse area, as in the single-pulse case, should be an odd multiple of π, and the mode spacing (pulse repetition rate) should exceed the natural linewidth of the atomic transition considerably. Under these conditions the time-averaged excited-state population approaches 1/2 while saturation broadening ensures nearly frequency-independent excitation within an extended fraction of the laser bandwidth.     

Langevin-Bloch equations for a spin bath

We derive the Bloch equations for a two-level system coupled to a spin bath of infinitely many two-level atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of "motional narrowing" of spectral line. The theoretical results are discussed in the light of absorption-emission experiments on single quantum dots.     

Aspects of quantum coherence in the optical Bloch equations

Aspects of coherence and decoherence are analyzed within the optical Bloch equations. By rewriting the analytic solution in an alternate form, we are able to emphasize a number of unusual features: (a) despite the Markovian nature of the bath, coherence at long times can be retained; (b) the long-time asymptotic degree of coherence in the system is intertwined with the asymptotic difference in level populations; (c) the traditional population-relaxation and decoherence times, T1 and T2, lose their meaning when the system is in the presence of an external field, and are replaced by more general overall time scales; (d) increasing the field strength, quantified by the Rabi frequency Omega, increases the rate of decoherence rather than reducing it, as one might expect; and (e) maximum asymptotic coherence is reached when the system parameters satisfy Omega2=1(T1T2).     

Optical bloch equations: disagreement between experiment and theory explained by quantum dynamical semigroups

Very recent optical as well as former magnetic resonance experiments at strong strength of the alternating field have suggested a phenomenological generalization of ordinary Bloch equations which is shown to be consistent with the basic laws of quantum mechanics and. in particular, can be derived from the theory of completely positive quantum dynamical semigroups for irreversible processes under Markovian conditions.     

Time-resolved electron spin resonance with electron spin polarization (CIDEP) as a sensitive probe of degenerate electron exchange reactions

It is shown that the occurrence of electron-exchange processes produces a distinctive effect in the time-resolved electron spin resonance spectra of spin-polarized radicals observed in the continuous presence of a microwave field. The effects observed are consistent with a theory based upon the Bloch equations.     

The AsO radical detected by infrared laser magnetic resonance

The Pauli master equation for intramolecular vibrational relaxation and the heat bath feedback Bloch equations for radiative pumping of polyatomic molecules can be derived by replacing the standard assumption of random matrix element coupling between zero-order vibrational states by an assumption that relaxation is governed by restricted quantum exchange.     

The interference in the decay of two ½ spins in a molecular medium,studied by the Nakajima–Zwanzig technique

This paper studies the decay, due to the spin-lattice coupling, of two ½ spins with slightly different Zeeman energies when the lattice is thermally excited. The analysis is based on obtaining, by means of the Nakajima–Zwanzig projection operator technique, an equation for the evolution of the reduced density operator of the spin system which manifests the influence of one spin on the relaxation process of the other. The zero-order solutions obtained for the evolution of the expectation values of the spin dynamics operators are essentially equivalent to the Bloch equations; higher order solutions are also obtained.     

The effects of electroosmosis on the structure of isotachophoresis boundaries

The influence of convection on the structure of an isotachophoretic boundary is investigated using an asymptotic method to simplify the conservation equations. To illustrate the methodology it is applied to a simple strong electrolyte system consisting of three ions and the relevant equations solved numerically. The technique, however, is of general applicability and can be useful in exploring the influence of various flow processes on analytical and preparative electrophoretic separation techniques in addition to isotachophoresis.