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Register a new userA new estimate on the indirect Coulomb Energy
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We prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller constant, 1.45 < 1.68) but involving an additive kinetic energy term of the single particle density.
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The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model describing both system and apparatus and consisting of a harmonic oscillator coupled to a field. The equation of motion is a quantum stochastic differential equation. By solving it we establish the conditions ensuring that the two perspectives are compatible, in that the apparatus indeed measures the observable it is ideally supposed to.
The problem of reconstructing information on a physical system from data acquired in long sequences of direct (projective) measurements of some simple physical quantities - histories - is analyzed within quantum mechanics; that is, the quantum theory of indirect measurements, and, in particular, of non-demolition measurements is studied. It is shown that indirect measurements of time-independent features of physical systems can be described in terms of quantum-mechanical operators belonging to an algebra of asymptotic observables. Our proof involves associating a natural measure space with certain sets of histories of a system and showing that quantum-mechanical states of the system determine probability measures on this space. Our main result then says that functions on that space of histories measurable at infinity (i.e., functions that only depend on the tails of histories) correspond to operators in the algebra of asymptotic observables.
We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbolic motion group of the plane.
The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauers principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Arakis perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauers bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared.
The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schroedinger equation. The result is different from that given in [K. Kowalski, J.Rembielnski, Ann. Phys. 329 (2013) 146]. A comparison of the different outcomes is provided.
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