Quantum systems

Consider a quantum system with two levels, a and b, with energy levels and Furthemiore, let the perturbation... 

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

Gillan M J 1990 Path integral simulations of quantum systems Computer Modeling of Fluids and Polymers ed C R A Catlow et al (Dordrecht Kluwer)... 

Berne B J and Thirumalai D 1986 On the simulation of quantum systems path integral methods Ann. Rev. Rhys. Chem. 37 401... 

Wahnstrom G and Metiu H 1988 Numerical study of the correlation function expressions for the thermal rate coefficients in quantum systems J. Phys. Chem. JPhCh 92 3240-52... 

In this section we look briefly at the problem of including quantum mechanical effects in computer simulations. We shall only examine tire simplest technique, which exploits an isomorphism between a quantum system of atoms and a classical system of ring polymers, each of which represents a path integral of the kind discussed in [193]. For more details on work in this area, see [22, 194] and particularly [195, 196, 197]. 

Plakhotnik T, Walser D, Pirotta M, Renn A and Wild U P 1996 Nonlinear spectroscopy on a single quantum system two-photon absorption of a single molecule Science 271 1703-5... 

The most accurate information about quantum systems is obtained via spectroscopic measurements. Such measurements have, until quite recently. 

Let us consider the time evolution of a quantum system, which satisfies the time-dependent Schiodinger equation [55]... 

One of the discussion points is how the quantum system reacts back on the classical d.o.f., i.e., how the forces on the classical system should be derived from the quantum system. One can use the gradient of the effective energy, i.e., of the expectation value of the total energy... 

Berendsen, H.J.C., Mavri, J. Quantum dynamics simulation of a small quantum system embedded in a classical environment. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 157-179. 

QCMD describes a coupling of the fast motions of a quantum particle to the slow motions of a classical particle. In order to classify the types of coupled motion we eventually have to deal with, we first analyze the case of an extremely heavy classical particle, i.e., the limit M —> oo or, better, m/M 0. In this adiabatic limit , the classical motion is so slow in comparison with the quantal motion that it cannot induce an excitation of the quantum system. That means, that the populations 6k t) = of the... 

In the mixed quantum-classical molecular dynamics (QCMD) model (see [11, 9, 2, 3, 5] and references therein), most atoms are described by classical mechanics, but an important small portion of the system by quantum mechanics. The full quantum system is first separated via a tensor product ansatz. The evolution of each part is then modeled either classically or quan-tally. This leads to a coupled system of Newtonian and Schrbdinger equations. 

The computer simulation of models for condensed matter systems has become an important investigative tool in both fundamental and engineering research [149-153] for reviews on MC studies of surface phenomena see Refs. 154, 155. For the reahstic modeling of real materials at low temperatures it is essential to take quantum degrees of freedom into account. Although much progress has been achieved on this topic [156-166], computer simulation of quantum systems still lags behind the development in the field of classical systems. This holds particularly for the determination of dynamical information, which was not possible until recently [167-176]. 

A successful method to obtain dynamical information from computer simulations of quantum systems has recently been proposed by Gubernatis and coworkers [167-169]. It uses concepts from probability theory and Bayesian logic to solve the analytic continuation problem in order to obtain real-time dynamical information from imaginary-time computer simulation data. The method has become known under the name maximum entropy (MaxEnt), and has a wide range of applications in other fields apart from physics. Here we review some of the main ideas of this method and an application [175] to the model fluid described in the previous section. 

Furthermore, one can infer quantitatively from the data in Fig. 13 that the quantum system cannot reach the maximum herringbone ordering even at extremely low temperatures the quantum hbrations depress the saturation value by 10%. In Fig. 13, the order parameter and total energy as obtained from the full quantum simulation are compared with standard approximate theories valid for low and high temperatures. One can clearly see how the quasi classical Feynman-Hibbs curve matches the exact quantum data above 30 K. However, just below the phase transition, this second-order approximation in the quantum fluctuations fails and yields uncontrolled estimates just below the point of failure it gives classical values for the order parameter and the herringbone ordering even vanishes below... 

Suppose a quantum system consists of a pair of spin- particles, and that the system is prepared in such a way that (1) the total spin angular momentum is zero (i.e. the... 

As emphasized by Sadovskii and Zhilinskii [2], this latter point is important for quantum systems for which the lattice is too small to allow the constmction in Fig. 16a, because there is still a systematic reorganization of the spectra, involving transfer of individual levels or groups of levels from lower to upper bands, as y increases from 0 to 1. Figure 17 shows examples for n = A and i = j, 1, and, which illustrate the influence of quantum monodromy far from the classical limit. 

Electronic Charge Density of Quantum Systems in the Presence of an Electric Field a Search for Alternative Approaches... 

For a quantum system with a single degree of freedom (dimensionality D=l), a procedure parallel to that sketched above leads to the following result... 

ELECTRONIC CHARGE DENSITY OF QUANTUM SYSTEMS 3. An elementary application of the formalism... 

ELECTRONIC CHARGE DENSITY OF QUANTUM SYSTEMS Acknowledgments... 

Electronic charge density of quantum systems in the presence of an electric field a search for alternative approaches... 

Angular momentum plays an important role in both classical and quantum mechanics. In isolated classical systems the total angular momentum is a constant of motion. In quantum systems the angular momentum is important in studies of atomic, molecular, and nuclear structure and spectra and in studies of spin in elementary particles and in magnetism. 

In Sections IVA, VA, and VI the nonequilibrium probability distribution is given in phase space for steady-state thermodynamic flows, mechanical work, and quantum systems, respectively. (The second entropy derived in Section II gives the probability of fluctuations in macrostates, and as such it represents the nonequilibrium analogue of thermodynamic fluctuation theory.) The present phase space distribution differs from the Yamada-Kawasaki distribution in that... 

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