1,721,006 research outputs found
Time scales in quantum mechanics by a scattering map
No full textIn quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics
Subdynamics of relevant observables : a field theoretical approach
No full textAn approach to the description of subdynamics inside the nonrelativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given, leading to a master equation expressed in terms of the operator-valued dynamic structure factor, a two-point correlation function which compactly takes the statistical mechanics properties of the macrosystem into account. For the case of a free quantum gas the dynamic structure factor can be exactly calculated and in the long wavelength limit a Fokker–Planck equation for the description of quantum dissipation and in particular quantum Brownian motion is obtained, where peculiar corrections due to quantum statistics can be put into evidence
Incoherent dynamics in neutron-matter interaction
Full text linkCoherent and incoherent neutron-matter interaction is studied inside a recently introduced approach to subdynamics of a macrosystem. The equation describing the interaction is of the Lindblad type and, using the Fermi pseudopotential, we show that the commutator term is an optical potential leading to well-known relations in neutron optics. The other terms, usually ignored in optical descriptions and linked to the dynamic structure function of the medium, give an incoherent contribution to the dynamics, which keeps diffuse scattering and attenuation of the coherent beam into account, thus warranting fulfillment of the optical theorem. The relevance of this analysis to experiments in neutron interferometry is briefly discussed
Dynamical semigroup description of coherent and incoherent particle-matter interaction
Full text linkThe meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of nonrelativistic quantum field theory is proposed to describe both coherent and incoherent interaction of a single microsystem with matter. Compactly developing the calculations with superoperators, it is shown that the introduction of a time scale linked to irreversibility of the reduced dynamics directly leads to a dynamical semigroup expressed in terms of quantities typical of scattering theory. Its generator consists of two terms, the first linked to a coherent wavelike behavior, the second related to an interaction having a measuring character, possibly connected to events the microsystem produces propagating inside matter. In case these events breed a measurement, an explicit realization of some concepts of modern quantum mechanics (“effects” and “operations”) arises. The relevance of this description to a recent debate questioning the validity of ordinary quantum mechanics to account for such experimental situations as, e.g., neutron interferometry is briefly discussed
Subdynamics as a mechanism for objective description
No full textThe relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics which is briefly presented
Description of isolated macroscopic systems inside quantum mechanics
Full text linkFor an isolated macrosystem classical state parameters zeta (t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [T,t(0)] a statistical operator is constructed as a solution of the Liouville-von Neumann equation, exhibiting at time t the state parameters zeta (t'), t(0) less than or equal to t' less than or equal to t, and preparation parameters related to times T less than or equal to t' less than or equal to t(0). Relation with Zubarev's nonequilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale
Quantum theory : the role of microsystems and macrosystems
No full textWe stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence for particles. In this approach particles appear as interaction carriers between preparation and registration apparatuses. We further briefly point out the more modern and versatile formalism of quantum theory, stressing the relevance of probabilistic concepts in its formulation. At last we discuss the role of macrosystems, focusing on quantum field theory for their description and introducing objective state parameters for them
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