Showing papers on "Open quantum system published in 1977"

Quantum Meaning of Classical Field Theory

Abstract: Recent researches have shown that it is possible to obtain information about the physical content of nontrivial quantum field theories by semiclassical methods. This article reviews some of these investigations. We discuss how solutions to field equations, treated as classical, c-number nonlinear differential equations, expose unexpected states in the quantal Hilbert space with novel quantum numbers which arise from topological properties of the classical field configuration or from the mixing of internal and space-time symmetries. Also imaginary-time, c-number solutions are reviewed. It is shown that they provide nonperturbative information about the vacuum sector of the quantum theory.

Classical and quantum statistical mechanics in a common Liouville space

Abstract: It is shown that the extremal phase-space representations of quantum mechanics can be expressed in terms of wave-functions on L2-spaces which are embedded in L2(Γ). In L2(Γ) all these representations are restrictions of a globally defined representation of the canonical commutation relations. The master Liouville space B 2(Γ) over L2(Γ) can accommodate representations of both classical and quantum statistical mechanics, and serves as a medium for their comparison. As a specific example, a Boltzmann-type equation on B 2(Γ) is considered in the classical as well as quantum context.

A time-dependent approach to the completeness of multiparticle quantum systems

Abstract: 1. Introduction The basic questions of single channel scattering systems depend on the existence of the generalized wave operators where Pa,(.) is the projection onto the absolutely continuous space for a selfadjoint operator, (see [19], Chap. VII for the necessary spectral theory background) and their completeness In this context, the following elementary proposition is well-known and fundamental: PROPOSITION. Suppose that n*(A, B) exist. Then O*(A, B) are complete if and only if R*(B, A) exist. The importance of this proposition is that it reduces the completeness question to the proof of the existence of a limit. This timedependent approach to scattering has been raised to a high art by Kato, Kuroda, and Birman (see Kato [14] or Reed-Simon [20] for textbook presentations, or Pearson [18] for a recent and significant simplification). Our goal in this note is to prove an analogue of this basic proposition for rnultiparticle quantum

The non-relativistic limit ofP(ϕ)2 quantum field theories: Two-particle phenomena

Abstract: It is proved that for two-particle phenomena theP(ϕ)2 quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a δ function potential in the limitc→∞.

On state transformations induced by yes-no experiments, in the context of quantum logic

Abstract: The standard formulation of quantum mechanics think, e.g., to the Hilbert space formulation, which has historically been the most influential and the best shaped for an analysis of its foundations is intimately related with the changes undergone by the state of the physical system as effect of the measurement of observables on the system. The probabilistic interpretation of the inner product in the Hilbert space is itself related to these state transformations: if the system is in a state represented by the unit vector 0 then the probability that the measurement of the observable represented by the self adjoint operator A gives a numerical value in the (Borel) set E C R is given by (0, PE ) where PE is the projection operator associated to the set E by the spectral decomposition of A, and PE is, up to a normalizing factor, a vector representing the state in which the system is left by the action of the measurement of A with numerical result in E. Quantum logic has taught us that a great deal of the Hilbert space structure of quantum mechanics can be traced back and, so to speak, condensed in typical properties of the sets 2 and S formed, respectively, by the nonequivalent yes-no experiments on the system, and by the states (or nonequivalent preparations) of the system. It is then natural to ask where and how the notion of state transformations caused by yes-no experiments is related and intertwined with the (2, S) structure. A review of this point is our present purpose and a great deal of what follows refers to existing literature. We shall mention results without reproducing proofs. Three aspects of the role of state transformations will be considered: first, the connection with the orthomodular lattice structure of 2; second, the connection with a structure of transition probability space which can be attached to S; third, the connection with a notion of logical implication which can be established in a language associated to 2.

Quantum communication systems (Corresp.)

Abstract: A mathematical formulation of the notion of an idealized continuous time quantum-mechanical communication system is given, using ideas from stochastic processes and from quantum field theory. The formalism is developed at an abstract level and illustrated by constructing a model of a coherent quantum communication system.

The cluster expansion for potentials with exponential fall-off

Abstract: Continuing the work of a previous paper, the Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by potentials that fall off exponentially at large distance. The HamiltonianH0+V need be stable in the extended sense thatH0+4V+BN≧0 for someB. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infinite volume limit of the correlation functions exists, at low enough density. These infinite volume correlation functions cluster exponentially. A natural system included in the present treatment is that of matter with ther−1 potential replaced bye−ar/r. The Hamiltonian is stable, but the system would collapse in the absence of the exclusion principle—the potential is unstable. Therefore this system cannot be handled by the classic work of Ginibre, which requires stable potentials.

Renarks on the classical limit of quantum field theories

Abstract: Recently, there has been an increasing interest in computing quantum mechanical corrections to solutions of classical field equations. In this note, we want to proceed in the opposite way and we summarize theorems about the classical limit of relativistic quantum field models. These results are a byproduct of the so called ‘constructive’ approach to quantum field theory. After a section on generalities, we discuss in Section 2 the situation where no phase transitions occur in the limith→0 and in Section 3 we reformulate one result in the case where such a transition occurs (Glimmet al. [7]). We discuss the validity of the loop expansion. It seems however that the tools to show the rigorous validity of soliton calculations are not yet prepared.

Quantum uncertainty in the final state of gravitational collapse

Abstract: THE ratio of the action S to ħ (Planck's constant/2π) determines whether the physical system in question is to be treated classically or quantum mechanically. In the area of classical physics the ratio S/ħ is large compared with unity, and the governing equations are given by δS = 0. Quantum mechanics begins to be important when S ≲ ħ, and the definitive approach of classical physics is replaced by quantum uncertainty. We discuss here the behaviour of a physical system which is initially in the classical domain (S ≫ ħ) but whose later development may well take it into the region of quantum uncertainty. We consider a specific example of this—the gravitational collapse of a spherical dust ball. While classically such a dust ball ends up in a space–time singularity, the corresponding quantum mechanical result suggests a range of final states some of which are non-singular.

Functional Integral Methods in Quantum Field Theory

Abstract: We give a special form of the Osterwalder-Schrader axioms in terms of conditions on a functional integral S{f} = ∫eiϕ(f)dμ. This yields a simple, self-contained construction of a Hamiltonian H, a relativistic, local boson quantum field Φ, and a Feynman-Kac formula to study perturbations H + Φ of H.

On fermi quantum fields constructed from bose quantum fields and their applications

Abstract: In former papers a representation of the quantum Fermi and para-Fermi fields was proposed. This representation is such that the only basic quantum entities are Bose quantum fields. In this paper we show several possibilities of application: (i) to lower the number of “elementary” particles; (ii) to describe as separate states of a fundamental particle other particles that presently are considered as different, and to induce an ordering among them; (iii) to obtain relations among the quantum numbers of those particles; (iv) to obtain a physical picture of some unstable particles. This article is concerned with the physical interpretation of the formalism, and some of the statements that are contained here have a conjectural character.

From the origin of quantum concepts to the establishment of quantum mechanics

Abstract: The article deals with the origins and development, in the first quarter of the 20th century, of the fundamental ideas advanced by Planck and Einstein and by Bohr and de Broglie concerning the quantum of action, the quanta of energy and the quanta of light, the stationary states of atomic systems and jumplike transitions between them, the correspondence principle, and the particle-wave dualism. It is shown how the development of the quantum concepts have led to two approaches to the creation of quantum mechanics by Heisenberg, Born, and Dirac in algebraic form and by Schrodinger in analytic form. The main stages in the evolution of nonrelativistic quantum mechanics are described, namely the development of wave mechanics and matrix mechanics, the proofs of their equivalence, the physical interpretation of the wave function, the generalized formulation of quantum mechanics as a unified theory, and the discovery of the uncertainty relations. The most important trends in the development of quantum mechanics in the course of its evolution are considered. A complete bibliography of the main period of evolution of quantum mechanics (July 1925?March 1928), classified by topics and by time of publication, is included.

Continuous measurements in quantum theory

Abstract: I t has been questioned recently by various authors (1-4) the meaningfulness of cont inuous (in time) measurements in quantum mechanics; problems arise because of the, eventually apparent, paradoxical results obtained. The decay of an unstable system is a peculiar case (1,3)-* if we hypothize that the system is observed to be uudecayed at time t o and that after t o it is continuously observed, then it will never decay. Similarly (i.3) a system which is confined in a finite space region at time to, will remain confined there if we suppose it to be subjected to a continuous observation which establishes whether the system is in the region or not at each instant. The enunciation of such results, sketched above, seems effectively rather surprising and defying our intuition. Surely when one deals, as in this case, with problems involving in an essential way the concept of measurement, one faces the most controversial aspects of quantum theory but, at the same time, the most revealing about its structure. So it may be very interesting to consider such limit situations as continuous measurements which exasperate the constrast with the classical intuition. In what follows we shall t ry to give an interpretational contribution, finally suggesting that the mentioned paradoxical aspects are qualitatively understandable and hence, perhaps, not so antiintuit ive from the quantum mechanical point of view. We shall limit to consider the ease of an unstable system. One is dealing with a quantum system which can be observed in two states, undecayed or decayed, with relative probabilities Pu(t) and P~(t). By starting from an initial measurement at to, where the system is observed to be undecayed, P~(t) and P~(t) evolve with time so that finally Pu(c~) = 0 and P~(c~) = 1. The quant i ty of interest is the rate of decrease of P,(t) . The decrease with time of Pu(t) is reasonably hyphotized from the fact that in examining a lot of similar systems, initially in the undecayed state, the number of them which are found to be decayed after some interval At increases with At.

A causal explanation for quantum phenomena in macroscopic physics

Abstract: The dynamics underlying quantum theory for macroscopic physics is based on the topology of flows on a cusp catastrophe obtained by the minimization of a potential function. By this relation at a known potential energy, a causal explanation of the quantum effect is provided.