Individual quantum system

The loss of coherence for an individual quantum system is always due to an entanglement with some other system and this holds even for a thermal reservoir. This can be seen from the following consideration assume that the quantum system studied is coupled to the reservoir with a coupling strength a and the reservoir relaxation rate is given by k. Standard adiabatic elimination of the reservoir then yields an atomic decay rate 7 = a2/k which tends to zero for an arbitrarily fast reservoir. This is due to the fact that for such a reservoir the combined system would truly remain in a product state and no entanglement would ever be built up. This may also be taken as a variant of quantum Zeno effect, in which the decay into an infinitely fast reservoir corresponds to very rapidly repeated measurements that prevent the spontaneous decay. 

The last argument is based on an essential of the quantum description In a measurement, an ensemble reveals an expectation value that allows the observer to learn about an average value of the observable, that characterises the "macrostate" of the system. Any measurement on an individual system, however, yields an eigenvalue, and repeated observations provide a string of information on this system that defines a "micro-state" of the ensemble of the repeated measurements. The particular features of measurements on individual quantum systems have been... 

TABLE 2.1 Preparation and addressing of an individual quantum system... 

System Ensemble Individual quantum system Application... 

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. 

Data on individual atomic systems provided most of the clues physicists used for constructing quantum mechanics. The high spherical S5munetry in these cases allows significant simplifications that were of considerable usefulness during times when procedural uncertainties were explored and debated. When the time came... 

Next we must verify that the Ust is long enough. If we measure the z-spins of both particles, we must find one of the six listed states. Also, none of these states have multiplicities because the spin states of the two individual particles have no multiplicities. Hence the set of six ordered pairs above is a basis for the quantum system consisting of one spin-1/2 and one spin-1 particle. 

N. C. Petroni, C. Dewdney, P. Holland, A. Kyprianidis, and J. P. Vigier, Causal space-time paths of individual distinguishable particle motions in V-body quantum systems Elimination of negative probabilities, Lett. Nuovo Cimento 42(6) (Ser. 2), 285-294 (1985). 

The fascination of this and similar systems [ NeHF (Clary, Lovejoy, ONeil, and Nesbitt 1988 Nesbitt et al. 1989 ONeil et al. 1989), NeDF (Lovejoy and Nesbitt 1991), and ArHF (Nesbitt, Child, and Clary 1989)] arises from the possibility of studying molecular breakup on the level of individual quantum states (Nesbitt 1988a,b). 

The Exclusion Principle can be expressed in severed ways in Pauli s early statement that no two electrons can have all their quantum numbers the same or, more satisfactorily (since individual quantum numbers are, strictly speaking, physically meaningless in systems of strongly interacting particles) in Heisenberg s later statement that the wave function for a system of fermions must be antisymmetric. 

We have examined the nature of LIFS in some detail. The response of an atomic or molecular system is described in terms of appropriate rate (or balance) equations whose individual terms represent the rate at which individual quantum states are populated and depopulated by radiative and collisional processes. Given the response of a system to laser excitation, one may use the rate equations to recover information about total number density, temperature and collision parameters. 

Here, two sources of uncertainty become apparent in preparation and measurement of a quantum system they originate precisely from the way the system is prepared (first aspect) and thereafter the interactions leading to the change of quantum state allows for detection (second aspect). These two aspects have not always been well acknowledged (cf. de Muynck [8]). Furthermore, the standard theory requires that each individual material system, once it is measured, be left only in one eigenstate so that the amplitude squared is assigned a statistical interpretation. This sort of transition is named as the collapse of the wavefunction [9]. 

Quantum mechanics predicts the quantum state (all possibilities at once) but not individual events. Independent collections of such events do reflect quantum states as extensively discussed in this paper. The quantum state does not represent the material system that as a matter of theoretical fact only sustains it. This result may be difficult to swallow within a probabilistic approach. But this is the way it is in a quantum physics where quantum states for quantum measurements occupy center stage. Individual quantum events elicit targeted quantum states we have to design the measuring device to determine just the quantum state that has been prepared. Statistical predictions are not compulsorily required statistics gather a sufficiently large set of events to display the quantum state pattern (e.g., Tonomura s experiment). 

Averaging over all different possible stochastic behaviors in SMS yields the master equation used in ensemble spectroscopy, but the averaged master equation does not determine the dynamics of the (pure) states of individual molecules. Certain attempts have been made to derive a proper theory of individual behavior of single quantum systems, but a rigorous interpretation is still lacking. 

Some interesting behavior in single-molecule spectroscopy involves the stochastic migration of lines. Usual statistical quantum theory describes only mean values or dispersions of observables, but not the actual fluctuations in the dynamics of single quantum systems. In an individual formalism of quantum mechanics, such fluctuations are of great importance. 

Recall again, that it is quite tricky to use two-level systems (instead of, say, an ammonia molecule) in individual quantum theory. Nevertheless, two-level systems can be quite instructive, precisely because simple visualization is possible by means of the Bloch sphere. 

Abstract Interaction between a quantum system and its surroundings - be it another similar quantum system, a thermal reservoir, or a measurement device - breaks down the standard unitary evolution of the system alone and introduces open quantum system behaviour. Coupling to a fast-relaxing thermal reservoir is known to lead to an exponential decay of the quantum state, a process described by a Lindblad-type master equation. In modern quantum physics, however, near isolation of individual quantum objects, such as qubits, atoms, or ions, sometimes allow them only to interact with a slowly-relaxing near-environment, and the consequent decay of the atomic quantum state may become nonexponential and possibly even nonmonotonic. Here we consider different descriptions of non-Markovian evolutions and also hazards associated with them, as well as some physical situations in which the environment of a quantum system induces non-Markovian phenomena. 

We have considered repeated projective measurements on an ancilla as a tool for manipulating the evolution of a dynamic quantum system of interest. Due to an interaction between the dynamic system and the ancilla, the nonunitary evolution of the ancilla extends equally to the dynamic system, but close to the Zeno-limit the coherence of the dynamic system may still be preserved. Of particular interest here are systems coupled with a nondemolition interaction, since they can be described in an essentially simplified manner. Depending on the dimension Na of the ancilla, individual elements of the reduced state of the dynamic part obey master equations that are iV order differential equations in time. Equivalently, the master equations can be written in the Nakajima-Zwanzig or time convolutionless form. 

The one-dimensional variations of the INADEQUATE experiment suppress the intense C- C main signal, so that both AX and AB systems appear for all C— C bonds in one spectrum. The two-dimensional variations segregate these AB systems on the basis of their individual double quantum frequencies (the sum of the C shifts of A and B) as a second dimension. Using the simple example of 1-butanol (12), Fig. 2.12a demonstrates the use of the two-dimensional INADEQUATE technique for the purpose of structure elucidation. For every C—C bond the contour diagram gives an AB system parallel to the abscissa with double quantum frequency as ordinate. By following the arrows in Fig. 2.12a, the carbon connectivities of butanol can be derived immediately. The individual AB systems may also be shown one-dimension-ally (Fig. 2.12b) the C- C coupling constants often provide useful additional information. 

In refuting this argument, one should keep in mind the guiding principles in the development of the topological method. First, all analysis must be completely consistent with quantum mechanics. The atomic basins defined by the zero-flux surfaces are valid quantum systems. These separable spaces individually obey the laws of quantum mechanics. The collection of orbitals used in the Mulliken analysis or the natural analysis are not quantum mechanically meaningful. These orbitals are either completely arbitrary (MPA) or the set that best... 

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