Nonperturbative theory

Nesbet, R.K. (1986). Nonperturbative theory of exchange and correlation in one-electron quasiparticle states, Phys. Rev. B 34, 1526-1538. 

The nonperturbative theory for the haliwidth and shift of ZPL is discussed in [8, 30] in more detail. 

Seidner L, Stock G and Domcke W 1995 Nonperturbative approach to femtosecond spectroscopy - general theory and application to multidimensional nonadiabatic photoisomerization processes J. Chem. Phys. 103 4002... 

Our analysis is based on solution of the quantum Liouville equation in occupation space. We use a combination of time-dependent and time-independent analytical approaches to gain qualitative insight into the effect of a dissipative environment on the information content of 8(E), complemented by numerical solution to go beyond the range of validity of the analytical theory. Most of the results of Section VC1 are based on a perturbative analytical approach formulated in the energy domain. Section VC2 utilizes a combination of analytical perturbative and numerical nonperturbative time-domain methods, based on propagation of the system density matrix. Details of our formalism are provided in Refs. 47 and 48 and are not reproduced here. 

At zero temperature and quark chemical potential the simplest effective Lagrangian describing a relevant part of the nonperturbative physics of the Yang-Mills (YM) theory is the glueball Lagrangian whose potential is [1-4] ... 

If we understand FM or magnetic properties of quark matter more deeply, we must proceeds to a self-consistent approach, like Hartree-Fock theory, beyond the previous perturbative argument. In ref. [11] we have described how the axial-vector mean field (AV) and the tensor one appear as a consequence of the Fierz transformation within the relativistic mean-field theory for nuclear matter, which is one of the nonperturbative frameworks in many-body theories and corresponds to the Hatree-Fock approximation. We also demonstrated... 

M = (Mx,My,M ) is the dipole moment of the system. Moreover, the indices i, j designate the Cartesian components x, y, z of these vectors, ()q realizes an averaging over all possible realizations of the optical field E, and () realizes an averaging over the states of the nonperturbed liquid sample. Two three-time correlation functions are present in Eq. (4) the correlation function of E(t) and the correlation function of the variables/(q, t), M(t). Such objects are typical for statistical mechanisms of systems out of equilibrium, and they are well known in time-resolved optical spectroscopy [4]. The above expression for A5 (q, t) is an exact second-order perturbation theory result. 

This question can be answered by means of scattering experiments for molecules in fields [1-3] or accurate calculations of the scattering matrices for collisions of molecules in nonperturbative external fields. The purpose of this chapter is to describe the theory for such calculations and present selected results illustrating the effects of external electromagnetic fields on molecular collisions at low temperatures. 

V-clcctron state T, correlation energy can be defined for any stationary state by Ec = E — / o, where Eo = ( //1) and E = ( // 4 ). Conventional normalization ) = ( ) = 1 is assumed. A formally exact functional Fc[4>] exists for stationary states, for which a mapping — F is established by the Schrodinger equation [292], Because both and p are defined by the occupied orbital functions occupation numbers nt, /i 4>, E[p and E[ (p, ] are equivalent functionals. Since E0 is an explicit orbital functional, any approximation to Ec as an orbital functional defines a TOFT theory. Because a formally exact functional Ec exists for stationary states, linear response of such a state can also be described by a formally exact TOFT theory. In nonperturbative time-dependent theory, total energy is defined only as a mean value E(t), which lies outside the range of definition of the exact orbital functional Ec [ ] for stationary states. Although this may preclude a formally exact TOFT theory, the formalism remains valid for any model based on an approximate functional Ec. 

This statement should be qualified The heatment that leads to the golden-rule result for the exponential decay rate of a state interacting with a continuum is not a short-time theory and in this sense nonperturbative, however we do require that the continuum will be broad. In relaxation involving two-level systems tliis implies 21 T = In p. that is, a relatively weak coupling. 

Whether or not perturbation theory with respect to the interaction described by the interaction Hamiltonian is meaningful depends on the problem under consideration. Otherwise, we have to search for appropriate, nonperturbative approximations for the time-evolution operator U. 

Effective Hamiltonians play a key role in quasidegenerate perturbation theory. If an eigenvalue is degenerate or near-degenerate, the standard perturbation cannot be applied, because zero or small energy denominators would arise. However the first block diagonalization can often be done by perturbation theory, the final diagonalization of Hg/f must be done nonperturbatively. 

For example, this form is in harmony with the superposition of energy states in Eq. (2), whose coefficients have been obtained formally by Fano [29]. Although, for the solution of particular problems involving unstable states, we have implemented, in conjunction with the methods of the SSA, the real-energy, Hermitian, Cl in the continuum formalism that characterizes Fano s theory, e.g.. Refs. [78, 82-87] and Chapter 6, in this chapter I focused on the theory and the nonperturbative method of solution of the complex eigenvalue Schrodinger equation (CESE), Eq. (27). 

The continuous spectrum is also present, both in physical processes and in the quantum mechanical formalism, when an atomic (molecular) state is made to interact with an external electromagnetic field of appropriate frequency and strength. In conjunction with energy shifts, the normal processes involve ionization, or electron detachment, or molecular dissociation by absorption of one or more photons, or electron tunneling. Treated as stationary systems with time-independent atom - - field Hamiltonians, these problems are equivalent to the CESE scheme of a decaying state with a complex eigenvalue. For the treatment of the related MEPs, the implementation of the CESE approach has led to the state-specific, nonperturbative many-electron, many-photon (MEMP) theory [179-190] which was presented in Section 11. Its various applications include the ab initio calculation of properties from the interaction with electric and magnetic fields, of multiphoton above threshold ionization and detachment, of analysis of path interference in the ionization by di- and tri-chromatic ac-fields, of cross-sections for double electron photoionization and photodetachment, etc. 

By the end of the 1980s and early 1990s, the literature on the various aspects and directions of fhe general theme of atoms (molecules) interacting with strong EMFs was already extensive. (We recall that the atomic unit of radiation intensity is = 3.5 x 10 W / cm ). Since the scope of the present article is concerned mainly with computation-oriented theory (rather than with phenomenology), that is capable of handling nonperturbatively fhe TDMEP in real sysfems, we cite three books published around 1990, rather... 

X. Tang, H. Rudolph, P. Lambropoulos, Nonperturbative time-dependent theory of helium in a strong laser field, Phys. Rev. A 44 (1991) R6994. 

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