Showing papers on "Quantum state published in 1972"

Approach to equilibrium of free quantum systems

Abstract: It is proved for fermi systems that each translationally invariant state ω with square integrable correlation functions approaches a limit under the free time evolution. The limit state is the gauge invariant quasi-free state with the same two-point function as ω and it is characterized by a maximum entropy principle. Various properties of the limit are discussed, and the extension of the results to bose systems is also given.

Renormalization of the hilbert space in the mass shift model.

Abstract: The (φ2)s+1 quantum field theory model can be solved exactly, where the number of space dimensions is s ≤ 3. Thus this model explicitly illustrates many properties of nontrivial models such as (φ2n)2 and Yukawa2. In particular we study hyperbolicity, the energy spectrum, local Fockness, and the change of Hilbert space as the spatial cut off is removed.

Dissipative properties of quantum systems.

Abstract: We consider the dissipative properties of large quantum systems from the point of view of kinetic theory. The existence of a nontrivial collision operator imposes restrictions on the possible collisional invariants of the system. We consider a model in which a discrete level is coupled to a set of quantum states and which, in the limit of a large “volume,” becomes the Friedrichs model. Because of its simplicity this model allows a direct calculation of the collision operator as well as of related operators and the constants of the motion. For a degenerate spectrum the calculations become more involved but the conclusions remain simple. The special role played by the invariants that are functions of the Hamiltonion is shown to be a direct consequence of the existence of a nonvanishing collision operator. For a class of observables we obtain ergodic behavior, and this reformulation of the ergodic problem may be used in statistical mechanics to study the ergodicity of large quantum systems containing a small physical parameter such as the coupling constant or the concentration.

Garding domains and analytic vectors for quantum fields.

Abstract: If one studies the canonical commutation relations (CCR's) of quantum field theory in the unitary Weyl form, one does not know if one can find a common dense domain for the field operators since their domain of definition depends on the test function. We consider here a general class of test function spaces including the spaces S and D of Schwartz and the space U0≃R(∞) of all finite linear combinations of a countable basis. It is shown that there exists an invariant Garding domain D on which all fields are defined and strongly continuous. D consists of analytic vectors for the fields. It turns out that the test function space can be enlarged by continuity. For irreducible or factor representations it becomes even a Hilbert space. The basic idea of the proof is the same as in the Schrodinger representation for one degree of freedom and very transparent. We simply use rapidly decreasing functions in ``Q‐space'' and ``P‐space'' as smoothing factors. That this can be done in the infinite case also is due to a...

Quantum Space-Time

Abstract: Space-time is quantized so as to obtain a four-dimensional simple cubic lattice. The covariance under Poincare transformation is guaranteed. The particles interact non-locally. The interaction region is spread so as to form a closed (Euclidean) area in the lattice of space-time.

Theorem on the Reality of the Electromagnetic Potentials

Abstract: The Bohm-Aharanov effect reminds us that the EM potentials have a certain physical reality even in a fieldfree region if that (multiply connected) region encloses nonzero flux. We prove a theorem which isolates for any such vector field the physically significant, gauge-independent component. Application to “hydrodynamical” quantum mechanics and to the macroscopic quantum states exemplified in superconductivity shows that such curl-less potentials are responsible for nonzero angular momentum, which is another aspect of their physical reality.

Quantum Mechanical State Preparation: A Simple Model

Abstract: Quantum dynamics is normally used to describe the causal evolution of the quantum state of a physical system between initial acts of preparation and final measurement operations. But logical consistency and completeness require that the same dynamical principles be applicable to the physical description of the preparation and measurement processes themselves. There is an extensive literature of contributions to the quantum theory of measurement, but very little theoretical scrutiny has been given to the process of state preparation. This paper begins with a philosophical analysis of the concept of preparation in quantum physics, then develops a classification of preparation schemes into selective and coercive types. An exact mathematical model illustrating coercive preparation is presented in detail.