Decoherence function

This factor 77 may be called the decoherence function since it describes the effective loss of coherence in the fullerene state. For elastic scattering with an isotropic potential and the gas initially in a thermal state it reads [Homberger 2003 (b)]... 

Schematic representation of the quantum-to-classical transition and the accumulation over time of classical populations N1 and N2, respectively, in electronic states 1 and 2. We have arbitrarily considered a Gaussian function for the decoherence function D in this figure.

Figure 5.7 Decoherence within the [Cu(Mim X 2] + complex. Evolution of the average decoherence function (taking the real part) and the phase and overlap terms (computed with eqn 5.33 and 5.34).

Then, if the coupling term (TP) between the position and momentum is neglected, one obtains an approximate expression for the overlap part of the decoherence function given by eqn (5.39) ... 

Figure 5.8 Analysis of the overlap contribution to the decoherence function within the [Cu(Mim )02] (left) and [Cu(Mim )02] (right) copper-dioxygen adducts. The full lines are the (real part) of the overlap term and the dotted...

If one is interested solely in the estimation of a characteristic decoherence time, an alternative to the generation and the analysis of a large set of diverging trajectories has been proposed by Schwartz et al Based on a second-order Taylor expansion of the positions and momentums of the nuclei at / = 0, the real part of the decoherence function can be approximated as ... 

Figure 7.9 (a) Echo-detected X-band EPR spectrum of a powder sample of Gd001 Y099W30 at T = 6 K. (b) Decoherence times 7, (solid symbols) and T2 (open symbols) measured at fi0H = 0.347 T, as a function of the atomic concentration of Gd ions. 

Section 4 is entitled Ideas (for mechanisms and models). It deals with how we can interpret/calculate the behavior of molecular transport junctions utilizing particular model approaches and chemical mechanisms. It also discusses time parameters, and coherence/decoherence as well as pathways and structure/function relationships. 

These interference patterns are wonderful manifestations of wave function behavior, and are not found in classical electronics or electrodynamics. Since the correspondence principle tells us that quantum and classical systems should behave similarly in the limit of Planck s constant vanishing, we suspect that adequate decoherence effects will change the quantum equation into classical kinetics equations, and so issues of crosstalk and interference would vanish. This has been... 

A quantum state loses quantum coherence (decoheres) when Sqd wave functions are peaked along classical trajectories. And it decoheres when each trajectory loses quantum coherence with its neighbors. Quantum decoherence is realized when the diagonal term density matrix dominates over the off-diagonal term (fts-... 

Finally, we discuss the effect of nonlinear coupling on domain growth, decoherence, and thermalization. As the wave functionals l/o of Ho are easily found, Eq. (16) leads to the wave functional beyond the Hartree approximation. Putting the perturbation terms (19) into Eq. (16), we first find the wave functional of the form... 

In Section 8.4.2, we considered the problem of the reduced dynamics from a standard DFT approach, i.e., in terms of single-particle wave functions from which the (single-particle) probability density is obtained. However, one could also use an alternative description which arises from the field of decoherence. Here, in order to extract useful information about the system of interest, one usually computes its associated reduced density matrix by tracing the total density matrix p, (the subscript t here indicates time-dependence), over the environment degrees of freedom. In the configuration representation and for an environment constituted by N particles, the system reduced density matrix is obtained after integrating pt = T) (( over the 3N environment degrees of freedom, rk Nk, ... 

For the weak coupling case with Eq. (32), our master equation reduces to the well-known quantum master equation, obtained through the approximation, widely used in quantum optics. This equation describes, among other things, quantum decoherence due to Brownian motion. Hence, we have derived an exact quantum master equation for the transformed density operator p that describes exact decoherence. Furthermore, our master equation cannot keep the purity of the transformed density matrix. Indeed, one can show that if p(t) is factorized into a product of transformed wave functions at t = 0, it will not be factorized into their product for t > 0. This is consistent the nondistributivity of the nonunitary transformation (18). 

It is the spread of oscillation frequencies a>j that causes the environment response to decohere after a (typically short) correlation time t (Figure 4.3b). Hence, the Markovian assumption that the correlation function decays to 0 instantaneously, d>(t) 8 t), is widely used it is, in particular, the basis for the... 

It is advantageous to consider the frequency domain as it gives more insight into the mechanisms of decoherence. For this purpose, we define the finite-time Fourier transform of the modulation function ... 

While the formalism of DD is quite different from the formalism presented here, it can be easily incorporated into the general framework of universal dynamical decoherence control by introducing impulsive PM. Let the phase of the modulation function periodically jump by an amount 4> at times r, 2t,. .. Such modulation can be achieved by a train of identical, equidistant, narrow pulses of nonres-onant radiation, which produce pulsed AC-Stark shifts of co. When (/> = tt, this modulation corresponds to DD pulses. 

Figure 4.7 Average modified final decoherence rate R(T), normalized with respect to the unmodulated rate as a function of energy constraint. DD-dash, cyan. Optimal modulation-solid, dark green. Insets optimal modulation Q(t) for different energy constraints, (a) Single-peak resonant dephasing spectrum (inset E = 20). (b) Single-peak off-resonant spectrum (inset E = 50). (c) 1 // spectrum (inset E = 30). (d) Multipeaked spectrum (inset E = 30). (See color plate section for the color representation of this figure.)...

Finally, cross-decoherence can be understood from the spectral-domain analysis as the coupling of two systems via common bath modes, that is, Eq. (4.203) is the overlap of three functions, namely, cross-coupling spectrum and the individual modulation spectra of the two systems. For example, if two systems couple to different modes, then in the absence of modulations, they will not experience any cross-decoherence. Hence, in order to impose cross-decoherence, one should modulate the systems in such a way that they effectively couple to the same modes with the same strength. On the other hand, if one wishes to eliminate cross-decoherence, one should apply local modulations, such that the modulation spectra have different peaks, which would result in the two systems coupling to different modes and thus experiencing no cross-decoherence. 

Assume that a noninteracting nanosystem is coupled weakly to a thermal bath (in addition to the leads). The effect of the thermal bath is to break phase coherence of the electron inside the system during some time Tph, called decoherence or phase-breaking time. rph is an important time-scale in the theory, it should be compared with the so-called tunneling time - the characteristic time for the electron to go from the nanosystem to the lead, which can be estimated as an inverse level-width function / 1. So that the criteria of sequential tunneling is... 

The finite decoherence time is due to some inelastic scattering mechanism inside the system, but typically this time is shorter than the energy relaxation time re, and the distribution function of electrons inside the system can be nonequilibrium (if the finite voltage is applied), this transport regime is well known in semiconductor superlattices and quantum-cascade structures. 

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