Adiabatic transport

S. Masuda. Acceleration of adiabatic transport of interacting particles and rapid manipulations of a dilute Bose gas in the ground state. Phys. Rev. A, 86(6) 063624-063630(2012). 

B. A. Hess The notion of a geometric phase generally requires an adiabatic situation, where an adiabatic connection and adiabatic transport can be defined. In the presence of many nearby avoided crossings, in a highly nonadiabatic situation (as in the case of the inverse Bom-Oppenheimer regime), the notion of a geometric phase is ill defined. 

We distinguish the adiabatic evolution for nonresonant processes, for resonant processes at zero held, and for processes with a dynamical resonance. For nonresonant processes the adiabatic transport of the dressed states is simple The dynamics follows, up to a phase, the instantaneous dressed state whose eigenenergy is continuously connected to the one associated to the initial dressed state. This adiabatic transport will be generalized if more than one dressed state is involved in the dynamics. 

One can see in this example the necessity to consider an adiabatic transport along more than one dressed state. 

More than one Floquet state can be involved in the dynamics—for example, if the initial condition is a linear combination of the instantaneous eigenvectors. These Floquet states span a subspace ff, and the adiabatic transport can be formulated in terms of eigenvectors ... 

Thus in this case the dynamics is at all times adiabatic in the sense that it mainly follows the dressed eigenstate whose eigenvalue is continuously connected to the one associated to the initial dressed state. This adiabatic transport results at the end of the pulse in an (almost) complete return in the initially populated state. It is important to point out that the dynamics is affected by the resonance in the sense that the excited bare state 2) is highly populated during the pulse if ft is of the same order as A or larger at the peak laser amplitude. For two-level systems, the nonadiabatic small corrections lost to the other eigenstate have been extensively studied (see, for example, Ref. 59 and references therein). 

For the pump-Stark sequence, we start with the lifting of degeneracy (r (r j) = cos( /2) /+) — sin((/2) v / ). Using the adiabatic transport for each branch, the state solution reads at the end... 

Figure 3.7. Zonally averaged distribution of the potential temperature unbroken lines, in K) from the surface to approximately 30 km altitude 10 hPa). The isolines for the absolute temperature (dashed lines, in K) are also shown. The tropopause is represented by the dotted line. Note that isentropes corresponding to potential temperatures larger than 380 K are located exclusively in the stratosphere (an area called the overworld ). Air parcels located in the lowermost stratosphere between the tropopause and the 380 K isentrope (an area called the middle world) are susceptible to crossing the tropopause when adiabatically transported, and entering the troposphere also called the underworld). From Holton et al. (1995), based on Appenzeller 1994).

The sum is taken over all the discrete vibrational levels if of state g>. Vr (f) is the component of the wavepacket on the g channel evolved up to time t from the field-free vibrational state v > prepared at time f = 0. Note that Pbound(y if) actually represents the total bound state population at any time after tj, since no further decay is then possible, the laser being turned off at such a time. It is clear that Eq. (71) gives a useful approximation for the result of a full time-dependent wavepacket evolution, [Eq. (73)], only if the assumption of an adiabatic transport of Floquet states is valid. 

At the frontier of non-adiabaticity (i.e., of the breakdown of the single resonance adiabatic transport approximation) lies the EPs that can be... 

For the fuel-rich stoichiometry = 6.9, the predictions in Fig. 3.4 refer to adiabatic, transport-limited conditions (Case 4, T 4) and to finite-rate chemistry with detailed hetero-Zhomogeneous reaction mechanisms and the frill model of Section 3.3 (Case 5, T s). As in matter of fact, the results of Case 5 were the same in the absence of gaseous chemistry (the surface temperatures in the q> = 6.9 simulations were too low for homogeneous... 

For the Berry phase, we shall quote a definition given in [164] ""The phase that can be acquired by a state moving adiabatically (slowly) around a closed path in the parameter space of the system. There is a further, somewhat more general phase, that appears in any cyclic motion, not necessarily slow in the Hilbert space, which is the Aharonov-Anandan phase [10]. Other developments and applications are abundant. An interim summai was published in 1990 [78]. A further, more up-to-date summary, especially on progress in experimental developments, is much needed. (In Section IV we list some publications that report on the experimental determinations of the Berry phase.) Regarding theoretical advances, we note (in a somewhat subjective and selective mode) some clarifications regarding parallel transport, e.g., [165], This paper discusses the projective Hilbert space and its metric (the Fubini-Study metric). The projective Hilbert space arises from the Hilbert space of the electronic manifold by the removal of the overall phase and is therefore a central geometrical concept in any treatment of the component phases, such as this chapter. 

Let S be any simply connected surface in nuclear configuration space, bounded by a closed-loop L. Then, if 4>(r,R) changes sign when transported adiabatically round L, there must be at least one point on S at which (r, R) is discontinuous, implying that its potential energy surface intersects that of another electronic state. 

Nitromethane [75-52-5] is produced in China. Presumably a modified Victor Meyer method is being employed. Nitromethane is transported in dmms or smaller containers. Two tank cars of nitromethane exploded in separate incidents in the 1950s. Both explosions occurred in the switching yard of a railroad station. In both cases, essentially adiabatic vapor compression of the nitromethane—air mixture in the gas space of the tank car resulted in the detonation of the Hquid nitromethane. Other nitroparaffins do not, however, detonate in this manner. 

Measurement of Performance The amount of useful work that any fluid-transport device performs is the product of (1) the mass rate of fluid flowthrough it ana (2) the total pressure differential measured immediately before and after the device, usually expressed in the height of column of fluid equivalent under adiabatic conditions. The first of these quantities is normally referred to as capacity, and the second is known as head. 

Leakage losses when the gas is transported from pressure side to suction side. Since the phenomenon is equalizing pressure in an adiabatic system, this will increase the entropy in the system. 

All the other linear terms vanish because they have opposite parity to the flux, (x(r)x(r))0 = 0. (This last statement is only true if the vector has pure even or pure odd parity, x(T) = x(T j. The following results are restricted to this case.) The static average is the same as an equilibrium average to leading order. That is, it is supposed that the exponential may be linearized with respect to all the reservoir forces except the zeroth one, which is the temperature, X()r = 1 /T, and hence xofT) = Tffl j, the Hamiltonian. From the definition of the adiabatic change, the linear transport coefficient may be written... 

This is equal and opposite to the adiabatic change in the odd exponent. (More detailed analysis shows that the two differ at order Af, provided that the asymmetric part of the transport matrix may be neglected.) It follows that the steady-state probability distribution is unchanged during adiabatic evolution over intermediate time scales ... 

In many respects, the solutions to equations 12.7.38 and 12.7.47 do not provide sufficient additional information to warrant their use in design calculations. It has been clearly demonstrated that for the fluid velocities used in industrial practice, the influence of axial dispersion of both heat and mass on the conversion achieved is negligible provided that the packing depth is in excess of 100 pellet diameters (109). Such shallow beds are only employed as the first stage of multibed adiabatic reactors. There is some question as to whether or not such short beds can be adequately described by an effective transport model. Thus for most preliminary design calculations, the simplified one-dimensional model discussed earlier is preferred. The discrepancies between model simulations and actual reactor behavior are not resolved by the inclusion of longitudinal dispersion terms. Their effects are small compared to the influence of radial gradients in temperature and composition. Consequently, for more accurate simulations, we employ a two-dimensional model (Section 12.7.2.2). 

Natural gas (CH4) is transported through a 6 in. ID pipeline at a rate of 10,000 scfm. The compressor stations are 150 mi apart, and the compressor suction pressure is to be maintained at lOpsig above that at which choked flow would occur in the pipeline. The compressors are each two stage, operate adiabatically with interstage cooling to 70°F, and have an efficiency of 60%. If the pipeline temperature is 70°F, calculate ... 

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