By Benjamin Fain (auth.)
The challenge of irreversibility is ubiquitous in physics and chemistry. the current ebook makes an attempt to give a unified theoretical and conceptual framework for the outline of varied irreversible phenomena in quantum mechanics. In a feeling, this publication vitamins traditional textbooks on quantum mechanics by means of together with the idea of irreversibilities. although, the content material and elegance of this e-book are extra acceptable for a monograph than a textbook. we now have attempted to rearrange the cloth in order that, so far as attainable, the reader needn't constantly refer somewhere else. The references to the literature make no pretense of completeness. The e-book is in no way a survey of current theoretical paintings. we've got attempted to spotlight the elemental rules and their effects, whereas the eye has been typically paid to the issues within which the writer himself has been concerned. The ebook as an entire is designed for the reader with wisdom of theoretical physics (especially quantum mechanics) at college point. This publication relies at the classes of lectures given on the Chemistry division of Tel-Aviv University.
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Extra info for Irreversibilities in Quantum Mechanics
3). The projection operator D in our case transforms density matrix into its diagonal part. e. 3) provided certain approximations are performed. 8) According to Eqs. 9) while operator L, according to Eq. 10) Taking into account Eqs. 14) It is easy to show that L0P = PL0 and therefore the kernel K in Eq. 2 Relaxation of the dissipative system. 15) is still exact, provided = 0. 3) we have to perform two approximations: the Born approximation and the Markovian approximation. In the Born approximation we assume the smallness of the perturbation G and calculate the matrix K up to the terms G².
18)). , by imposing an ultrashort (femtosecond) laser pulse on the system. We assume that before the pulse is imposed, the whole system is in the equilibrium state. 22). In the conclusion of this section an important comment has to be made. 23) which is Thus the deviation from the factorized density matrix is of the order not a small quantity. 14) are satisfied. 1) contains the memory. The derivative of depends on the density matrix at all the previous moments oftime, starting from t0 till t. This equation may be essentially simplified in the Markovian approximation.
17). 14) has been derived in the Markovian approximation. There is another approach to the irreversible processes which have been developed during the last decades [39-42]. This approach is based on a number of properties of time development of the density matrix of the dynamic system, such as the Markovian property, and positive definiteness of the density matrix Employment of these properties leads to the certain form of the equation for the density matrix Interestingly enough this equation is quite general and does not depend explicitly on the concrete form of the Hamiltonian of the total system (interacting dynamic and dissipative system).