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where V == J K,/27r, with K, being the cavity decay rate introduced in the rate equations earlier in the chapter. The zeroth-order approximation with this correction, (8.92) is the Gardiner-Collett Hamiltonian [109, 225], which is widely used in quantum optics to model damping in high-Q cavities. In 9 we discuss it in more detail and even derive it from first principles. Using the Gardiner-Collett Hamiltonian to describe the cavity damping, the Hamiltonian of our ideal laser can be written as (8.93) where we have made the rotating-wave approximation. The classical dipole is resonant with the cavity mode and X is Rabi frequency obtained from the product of its dipole moment, the vacuum strength in the cavity, and the cavity mode function at the position of the dipole. Using the technique of Fano diagonalization introduced in 7, we can rewrite the Gardiner-Collett Hamiltonian as (Problem 8.6) (8.94) where the global annihilation operator ..4.(w) is given in terms of the cavity and external annihilation operators by

9. Indicate in the checkbox at the bottom of the window whether the discount should be applied before or after sales tax. 10. Click Next to enter another Item or OK to exit the window.

Note Best in Africa, but only fair in comparison to other countries Weak regulatory infrastructure Severely lacking Living conditions impede recruitment of scientists Widespread poverty and racial tension limit educational opportunities Research is tolerated or unknown to the public Signi cant source of nancing Backs biotech incubators Economic constraints of most universities limit investment Modest funding available About a third of biotech companies are publicly traded Most companies are early stage Limited collaborative research with other countries Early stage therapeutics Signi cant local market Reported signi cant history with biological weapons production Limited access to supercomputer power Primarily services local market No biomaterial production facilities

d1] f3(w, 1])b(1]),

(8.95)

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17This is a reasonable approximation as long as We is much larger than V2 in (8.91). See, for example, the discussion in Sec. II.A of [225].

Your undeposited funds wait in a special account by that name in QuickBooks for you to take them to the bank. Follow these steps to make the transfer from your QuickBooks Undeposited Funds account to your checking account (or other bank account where you deposit funds). 1. Choose Bankings Make Deposits. If you have any payments to deposit, the Payments to Deposit window appears (see Figure 16-13).

a(w) f3(w,7])

Israel Israel and South Africa are not only on different ends of the African continent, but their relative abilities to contribute to the biotech sector are mirror images of each other as well. Israel is home to a population of ap proximately 6 million in an area of only 2 million hectares. With military and economic aid from the United States amounting to half of its debt, the government has been able to invest in developing local industry, including biotech. The population is highly literate, and about a third is online.

(8.96)

Figure 16-13: All undeposited payment money appears in the Payments to Deposit window. If you do not have any undeposited funds, the Make Deposits window appears instead. You can click the Previous button from that screen to view a list of the payments that were deposited in the last deposit you made.

8(w -

a(w).

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In contrast with South Africa, the information technology, legal-regulatory, intellectual property, labor, education, and public attitude infra structures are in place and rated good Israel has the highest number of engineers and scientists in the world, and over half of the scienti c publica tions are in the life sciences Furthermore, life sciences represent over a third of civilian research activities In addition, research centers, such as the Weizman Institute and Technion, provide support for the governmentorchestrated industrial sector As of 2002, there are over 160 biotech companies in Israel, with an emphasis on agricultural and medical biotech In addition, there are about 25 pharmaceutical plants, including Teva, Agis, Dexxon, Taro, and Rakah Teva, which has global sales in excess of $22 billion, is the largest manu facturer of generic drugs sold in the United States Local production of drugs from all sources amounted to about $1.

(8.97)

(8.99) In the interaction picture, the time evolution operator (h derived from this Hamiltonian is given by

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