[en] We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the probe in a dynamical way. We first discuss single measurements, where the system proper is coupled to one probe with arbitrary coupling strength. The goal is to obtain information on the system detecting the probe position. We find the reduced density operator of the system, and show how Lüders rule emerges as the limiting case of strong coupling. The von Neumann model is then generalized to two probes that interact successively with the system proper. Now we find information on the system by detecting the position-position and momentum-position correlations of the two probes. The so-called 'Wigner's formula' emerges in the strong-coupling limit, while 'Kirkwood's quasi-probability distribution' is found as the weak-coupling limit of the above formalism. We show that successive measurements can be used to develop a state-reconstruction scheme. Finally, we find a generalized transform of the state and the observables based on the notion of successive measurements

[en] The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in quantum mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of the von Neumann model of measurement, coupling the system to N ‘probes’, with a strength that is at our disposal, and detecting the latter. The model parallels the procedure followed in experiments on quantum electrodynamic cavities. The modification of the probability of the observable eigenvalues due to the coupling to the probes can be computed analytically and the results compare qualitatively well with those obtained numerically by the experimental groups. We find that the problem is not ergodic, except in the case of an eigenstate of the observable being studied. (paper)

[en] A common formulation of the law of increase of entropy, found in textbooks on thermodynamics, states that in a process taking place in a completely isolated system the entropy of the final equilibrium state cannot be smaller than that of the initial equilibrium state. This statement does not specify that thermal isolation is all that is needed for its validity, with no need for mechanical isolation. For the purpose of illustrating this situation, we exhibit examples of thermodynamic processes carried out with thermally isolated—although not mechanically isolated—systems, which we know to be allowed by the second law because the entropy of the system increases. We believe that the analysis presented in this paper may be useful in a first undergraduate course on thermodynamics. (paper)

[en] We find the invariant measure for two new types of S matrices relevant for chaotic scattering from a cavity in a waveguide. The S matrices considered can be written as a 2x2 matrix of blocks, each of rank N, in which the two diagonal blocks are identical and the two off-diagonal blocks are identical. The S matrices are unitary; in addition, they may be symmetric because of time-reversal symmetry. The invariant measure, with and without the condition of symmetry, is given explicitly in terms of the invariant measures for the well known circular unitary and orthogonal ensembles. Some implications are drawn for the resulting statistical distribution of the transmission coefficient through a chaotic cavity. (author)

[en] We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the various pairs of projectors onto two bases—which have no mutually orthogonal vectors. The two members of each pair are measured in succession. We show that this scheme implies measuring the joint quasi-probability of any pair of non-degenerate observables having the two bases as their respective eigenbases. The model Hamiltonian underlying the scheme makes use of two meters initially prepared in an arbitrary given quantum state, following the ideas that were introduced by von Neumann in his theory of measurement. (paper)

[en] We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Lueders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength