Quantum many-body system

Pollock, E.L. Ceperley, D.M., Simulation of quantum many-body systems by path-integral methods, Phys. Rev. B 1984, 30, 2555-2568... 

Andricioaei, I. Straub, J.E., Computational methods for the simulation of classical and quantum many body systems sprung from the nonextensive thermostatistics. In Nonextensive Statistical Mechanics and Its Application, Abe, S. Okamoto, Y., Eds., Lecture Notes in Physics. Springer Berlin, Heidelberg, New York, 2001, ch. IV, pp. 195-235... 

We have examined two assisted adiabatic transfer schemes designed to control the dynamical evolution of a quantum many-body system. That control is achieved by active manipulation with external fields that work cooperatively with coherence and interference effects embedded in the system quantum dynamics. The schemes we have discussed are a small subset of the many that have been proposed to induce complete transfer of population from an arbitrary initial state to a selected target state of a system, yet they illuminate the generic character of the... 

Thus our closed, isolated, quantum many-body system is described macroscopi-cally by a master equation of the form discussed extensively in this book. 

The formulation of the calculation of the optimal control field that guides the evolution of a quantum many-body system relies, basically, on the solution of the time-dependent Schrodinger equation. Messina et al. [25] have proposed an implementation of the calculation of the optimal control field for an n-degree-of-freedom system in which the Hartree approximation is used to solve the time-dependent Schrodinger equation. In this approximation, the n-degree-of-freedom wave function is written as a product of n single-degree-of-freedom wave functions, and the factorization is assumed to be valid for all time. 

The topic of this chapter is the description of a quantum-classical approach to compute transport coefficients. Transport coefficients are most often expressed in terms of time correlation functions whose evaluation involves two aspects sampling initial conditions from suitable equilibrium distributions and evolution of dynamical variables or operators representing observables of the system. The schemes we describe for the computation of transport properties pertain to quantum many-body systems that can usefully be partitioned into two subsystems, a quantum subsystem S and its environment . We shall be interested in the limiting situation where the dynamics of the environmental degrees of freedom, in isolation from the quantum subsystem [Pg.521]

G. Ciccotti, C. Pierleoni, F. Capuani, and V. S. Filinov (1999) Wigner approach to the semiclassical dynamics of a quantum many-body system the dynamic scattering function of He. Comp. Phys. Commun. 121, p. 452... 

It is not easy to find a quantum many-body system for which the Schrodinger equation may be solved analytically. However, a useful example is provided by the problem of two electrons in an external harmonic-oscillator potential, called Hooke s atom. The Hamiltonian for this system is... 

Ze /I fj — U represents potential energy of interaction of all electrons with all nuclei. The last term describes the Coulomb electron-electron interactions. Calculation of this term presents great difficulties. We must consider the Coulomb interactions between each electron and aU other electrons in the atom. The determination of the ground-state eigenfunction and the ground-state energy of a quantum many-body system appears to be a formidable problem. 

Quantum Many-Body Systems in Two and Higher Dimensions. 

The primitive approximation contains all the physics involved in the treatment of quantum many-body systems at nonzero temperature. It is simple, intuitive, and highly flexible. Moreover, it reveals clearly the so-called classical isomorphism, Eqs. (25)-(27), a correspondence that has important consequences on a range of different issues (e.g., formal study of structures and computational techniques). Nevertheless, the computational efficiency of the primitive scheme is generally poor as pointed out in earlier applications. A couple of examples will help to understand these drawbacks. First, the kinetic energy, given by the first two terms on the right-hand side of Eq. (31), which shows increasing variances with P, a fact associated with the stiffness of the harmonic links in [63]. Second, the P con-... 

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