Time-dependent Perturbation Series Research Articles

Transient MHD free convective chemically reacting flow over a moving hot vertical porous plate with heat generation/absorption, thermal radiation, viscous dissipation, and oscillating suction and free stream velocity effects

In this paper, the transient MHD free convective chemically reacting flow over a moving hot vertical porous plate with heat generation/absorption, thermal radiation, viscous dissipation, oscillating suction and free stream effects is investigated. The governing non-linear and coupled partial differential equations are solved using the oscillating time-dependent perturbation series solutions. Expressions for the dependent flow variables are obtained and presented graphically. The results show, amidst others, that increase in the heat generation/absorption parameter increases the temperature, velocity, Nusselt number and skin friction; increase in the chemical reaction rate parameter increases the temperature, velocity, Nusselt, Sherwood numbers and skin friction but decreases the concentration; increase in the frequency of oscillation parameter increases the temperature and velocity but decreases the Nusselt, Sherwood numbers and skin friction. Furthermore, it is seen that Hartmann number increases the temperature, velocity, Nusselt number and skin friction; Schmidt number decreases the temperature, concentration, velocity, Nusselt number and skin friction but increases the Sherwood number; Raleigh number increases the temperature, velocity, Nusselt number and skin friction.

Time-dependent quantum transport: Causal superfermions, exact fermion-parity protected decay modes, and Pauli exclusion principle for mixed quantum states

We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and/or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing ``causal'' field superoperators using the fundamental physical principles of causality/probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time evolution is renormalized by explicitly performing the wideband limit on the superoperator level. As a result, the occurrence of destruction and creation superoperators are shown to be tightly linked to the physical short- and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time. (ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading-order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization. (iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli-principle also simplifies problems with nonzero Coulomb interaction.

In-depth analysis of Coulomb–Volkov approaches to ionization and excitation by laser pulses

In perturbation conditions, above-threshold ionization spectra produced in the interaction of atoms with femtosecond short-wavelength laser pulses are well predicted by a theoretical approach called CV2−, which is based on Coulomb–Volkov-type states. However, when resonant intermediate states play a significant role in a multiphoton transition, the CV2− transition amplitude does not take their influence into account. In a previous paper, this influence has been introduced separately as a series of additional sequential processes interfering with the direct process. To give more credit to this procedure, called modified CV2− (MCV2−), a perturbation expansion of the standard CV2− transition amplitude is compared here to the standard time-dependent perturbation series and the strong field approximation. It is shown that the CV2− transition amplitude consists merely in a simultaneous absorption of all photons involved in the transition, thus avoiding all intermediate resonant state influence. The present analysis supports the MCV2− procedure that consists in introducing explicitly the other quantum paths, which contribute significantly to ionization, such as passing through intermediate resonances. Further, this analysis permits to show that multiphoton excitation may be addressed by a Coulomb-Volkov approach akin to MCV2−.

Multiple-scale technique and the frequency operator for anharmonic oscillators

We investigate the connection between a multiple-scale approach recently applied to anharmonic oscillators to avoid secular terms in the time-dependent perturbation series, and a frequency-operator method developed earlier for the same purpose.

Using relaxation theory to compute the electronic absorption spectrum of a chromophore coupled to a condensed phase environment

A time-dependent method for computing the electronic absorption spectrum of a chromophore in a condensed phase environment is presented. The cumulant expansion-based relaxation theory of Nitzan and Silbey [J. Chem. Phys. 60, 4070 (1974)] is adapted to enable approximate calculation of the absorption spectrum of a general system coupled to an arbitrary bath. The system–bath interaction potential operator is expanded to second order in a time-dependent perturbation series and then exponentiated in an attempt to capture the long-time dynamics. The dynamics of the bath is contained in Heisenberg correlation functions of the bath operators which are related to their classical counterparts. The formalism is applied to a harmonic and an anharmonic (Morse) system oscillator coupled to a harmonic bath. The exactly solvable harmonic model, a two-dimensional model of a Morse oscillator coupled to a single bath oscillator and a comparison to the time-dependent Hartree approximation are used to illustrate the accuracy of the formalism.

An adiabatic and near-adiabatic model of multiphoton ionisation

A model of multiphoton ionisation is presented which can be used when the turn-on of the atom-field interaction is adiabatic or near adiabatic. It is shown that in the adiabatic limit, the probability of the atom not being ionised is given by a single exponential decaying in time. A time-independent perturbation series is developed which can be used to calculate the adiabatic limit ionisation rate to any desired order. A time-dependent perturbation series is used to calculate the ionisation probability in the near-adiabatic limit. Comparison is made between results obtained with this model and those obtained using the more common sudden approximation to the turn-on.

Classical limit of the probability density for a perturbed change in the Hamiltonian

The stationary perturbation series is derived from the time-dependent perturbation series up to any order by using a formula derived from the theory of divergent series. The probability density of the perturbed state turns out as the evolution of the density operator of the pure unperturbed initial state as h -+ 0. This result, for h -+ 0, indicates that the particle moves in the classical trajectory with the Hamiltonian H = Ho + V immediately after V is turned on, if it is in the trajectory of H0 initially. This confirms the classical dynamics. Further, the adiabatic theorem is introduced in order to get the same conclusion for arbitrary finite potential V.

Perturbation theory of a many-fermion system

Methods are developed in the time-dependent perturbation theory of a ground state, many-fermion system for the study of the self-energy and factorization problems. The diagrammatic, time-dependent perturbation series is rearranged so that all the self-energy structures are contained in a single function which has the role of a line-weighting factor. These line-weighting factors are related to the single-particle occupation probabilities and are determined by the choice of the model single-particle potential. A systematic procedure is developed for choosing a model single-particle potential which satisfies the principle of maximal cancellation of perturbation diagrams. The model single-particle energies resulting from this choice of the model single-particle potential are shown to satisfy Landau's theory of a normal fermi liquid. This choice is compared with, and is found to differ from, the usual choice based on the “generalizedtime-ordering procedure” in the time-independent Goldstone series.

Convergence properties of the time-dependent perturbation series of a N fermion system

The convergence of the time-dependent perturbation series of a system of N fermions is shown under certain conditions of boundedness imposed on the potential representing the interaction. Furthermore, this proof gives the justification of the procedure of adiabatic switching.

Evolution of the Density Matrix of Large Systems

The time dependent perturbation series for the density matrix is shown to be equivalent to an integral equation. This integral equation is given in the form of a series in the coupling parameter λ, which is allways convergent when t →∞. The terms of this series can be represented by time retarded operators.

The evolution equation for the homogeneous crystal

A method for the exact summation of the diagrams in the time-dependent perturbation series is applied to the derivation of the evolution equation for the homogeneous crystal. This equation is given as a sum over connected diagrams only.