The theoretical apparatus of semantic realism: A new language for classical and quantum physics

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a realistic way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which applies both to classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language L_v which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and L_e hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and L_e. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenbergs uncertainty principle.     

Pragmatic versus semantic contextuality in quantum physics

An approach to quantum physics (QP) is proposed that is characterized by the attempt to give up the verificationist theory of truth underlying the standard interpretation of QP. As a first step, anobservatively minimal language L is constructed that is endowed with a Tarskian truth theory. Then, a set of axioms is stated by means of L that hold both in classical physics and in QP, and the further language L_e of all properties is constructed. The concepts ofmeaning andtestability do not collapse in L and L_e, hence quantum logic is interpreted as a theory of testability in QP, and QP turns out to be semantically incomplete. Furthermore, semantic and pragmatic compatibility of physical properties are distinguished in L_e, and the concepts of testability and conjoint testability of statements are introduced. In this context some known quantum paradoxes can be avoided, and a new general principle (MGP) characterizes the truth mode of empirical physical laws. MGP invalidates the Bell theorem and, presumably, the Bell-Kochen-Specker theorem, and introduces apragmatic contextuality in QP in place of thesemantic contextuality that should occur because of these theorems.     

Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ _e (τ,L)~× {1/σ _e (−τ,L)~⁻¹=σ _e ² (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p _c )/p _c , and p _c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ _e (τ)σ _e (−τ])=σ _e ² (τ=0)= σ ₁ σ ₂. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures. Zh. éksp. Teor. Fiz. 113, 1484–1490 (April 1998)     

Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs

We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi reservoirs ?₁, ?₂, which are in thermal equilibrium at inverse temperatures β₁≠β₂. We prove that, at small coupling, the combined quantum system ?+?₁+?₂ has a unique non-equilibrium steady state (NESS) and that the approach to this NESS is exponentially fast. We show that the entropy production of the coupled system is strictly positive and relate this entropy production to the heat fluxes through the system. A part of our argument is general and deals with spectral theory of NESS. In the abstract setting of algebraic quantum statistical mechanics we introduce the new concept of the C-Liouvillean, L, and relate the NESS to zero resonance eigenfunctions of L ^*. In the specific model ?+?₁+?₂ we study the resonances of L ^* using the complex deformation technique developed previously by the authors in [JP1]. Dedicated to Jean Michel Combes on the occasion of his sixtieth birthday Received: 12 July 2001 / Accepted: 11 October 2001     

Scattering of short ultrasonic pulses by thin cylindrical shells; Generation of guided waves inside the shell

We have studied the backscattering of short ultrasonic pulses by solid elastic cylindrical shells at high values of ka. When the thickness e of the shell is larger than the mean value of the wavelength λ_L for longitudinally polarized waves, the scattered echoes are well explained by a geometrical theory and their interpretation is trivial. Much more interesting is the case of very thin shells (e < λ_L) where we have observed the generation of two kinds of guided waves reradiating in the outer liquid and also in the inner liquid when present. For these shells five different sets of echoes corresponding to distinct propagation procedures have been identified.     

Classical foundations of quantum logic

We construct a languageL for a classical first-order predicate calculus with monadic predicates only, extended by means of a family of statistical quantifiers. Then, a formal semantic model is put forward forL which is compatible with a physical interpretation and embodies a truth theory which provides the statistical quantifiers with properties that fit their interpretation; in this framework, the truth mode of physical laws is suitably characterized and a probability-frequency correlation principle is established. By making use ofL and , a set of basic physical laws is stated that hold both in classical physics (CP) and in quantum physics (QP), which allow the selection of suitable subsets of primitive predicates ofL (the set _P of pure states; the sets _o and _E of operational and exact effects, respectively) and the introduction on these subsets of binary relations (a preclusion relation # on _P , an order relation < on _E . By assuming further physical laws, ( _E , <) turns out to be a complete orthocomplemented lattice [mixtures and atomicity of ( _E , <) also can be introduced by means of suitable physical assumptions]. Two languagesL _E ^x andL _E ^S are constructed that can be mapped intoL; the mapping induces on them mathematical structures, some kind of truth function, an interpretation. The formulas ofL _E ^x can be interpreted as statements about properties of a physical object, and the truth function onL _E ^x is two valued. The formulas ofL _E ^S can be endowed with two different interpretations as statements about the frequency of some physical property in some class (state) of physical objects; consequently, a two-valued truth function and a multivalued fuzzy-truth function are defined onL _E ^S . In all cases the algebras of propositions of these logics are complete orthocomplemented lattices isomorphic to ( _E , <). These results hold both in CP and in QP; further physical assumptions endow the lattice ( _E , <), henceL _E ^x andL _E/S , with further properties, such as distributivity in CP and weak modularity and covering law in QP. In the latter case,L _E ^S andL _E ^S , together with their interpretations, can be considered different models of the same basic mathematical structure, and can be identified with standard (elementary) quantum logics. These are therefore founded on the classical extended languageL with semantic model .     

Flavor symmetry L μ-L τ and quasidegenerate neutrinos

Current data implies three simple forms of the neutrino mass matrix, each corresponding to the conservation of a nonstandard lepton charge. While models based on L _e and L _e-L _μ-L _τ are well known, little attention has been paid to L _μ-L _τ. A low-energy mass matrix conserving L _μ-L _τ implies quasidegenerate light neutrinos. Moreover, it is μ-τ symmetric and therefore (in contrast to L _e and L _e-L _μ-L _τ) automatically predicts maximal atmospheric neutrino mixing and zero U _e3. A seesaw model based on L _μ-L _τ is investigated and testable predictions for the neutrino mixing observables are given. Renormalization group running below and in between the seesaw scales is taken into account in our analysis, both numerically and analytically. The text was submitted by the authors in English.     

Thickness and angular dependence of the L‐edge X‐ray absorption of nickel thin films

We report on the near‐edge X‐ray absorption fine structure spectroscopy of the L₃ (2p_3/2) and L₂ (2p_1/2) edges for ferromagnetic pure nickel transition metal and show that the L_2,3 edge peak intensity and satellite feature at ~6 eV above the L₃ edge in nickel increase with increasing nickel film thickness both in the total electron yield and transmission modes. The absorption spectra of nickel metal, however, exhibit strong angular‐dependent effects when measured in total electron yield mode. In addition, we calculated the mean electron escape depth of the emitted electrons (λ_e), which was found for pure nickel metal to be λ_e=25 ± 2 Å. We point out the advantages of the total electron yield technique for the study of the L‐edge of 3d transition metals. Copyright © 2011 John Wiley & Sons, Ltd.     

Spin-orbit coupling in the ground and low-lying excited states of HF<Superscript>+</Superscript> and HF<Superscript>-</Superscript>

Electronic structure and spectroscopic properties B _e, ω_e, ω_e x _e, α_e, T _e of ground state and the low-lying excited states of HF⁺ and HF^- molecular ions were investigated within scalar relativistic multireference configuration interaction with single and double excitations framework using the GAMESS-US program package. All potential energy curves (PECs) were calculated using the relativistic complete active space self-consistent field/spin-orbit multi-configuration quasi-degenerate perturbation theory (CASSCF/SO-MCQDPT). The curves are all fitted to the analytical potential energy function (APEF), from which accurate spectroscopic constants are derived. The spin-orbit splitting was also been studied, the split value of X²P^{2}{\rm \Pi} state of HF⁺ is determined to be 288.38 cm^-1. The calculated properties are in good agreement with the available experimental value. Spectroscopic constants of the ground states of HF^- that have never been observed in experiment are obtained. These curves provide an interpretation of the known experimental observations on this system and suggest a number of further experiments which possible provide a critical test of this data.     

Rank of quantized universal enveloping algebras and modular functions

We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groupsU _q (g). As a function ofq the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U _q (su(3))) and rank (U _q (e ₈)). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove ofg.     

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution function also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^−1/2f(h_m L^−1/2) for all L>0 where the function f(x) is the Airy distribution function. This result is valid for both the Edwards–Wilkinson (EW) and the Kardar–Parisi–Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^−1/2F(h_m L^−1/2), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the EW interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [S.N. Majumdar and A. Comtet, Phys. Rev. Lett. 92: 225501 (2004)].     

e -μ+→e +μ- process in a model with theSU(2)L×SU(2)R×U(1)B−L gauge group

A model based on theSU(2)_L×SU(2)_R×U(1)_B−L gauge group is used to study the lepton recharging processe ^-μ⁺→e ⁺μ^-. It should be possible to observe this process on a muon collider in the fixed-electron-target regime or the electron-beam regime. It is shown that the given process can be used to measure not only the characteristics of physical Higgs bosons, but also the parameters of neutrino oscillations. Grodno University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 83–88, November, 1998.     

Sterile neutrino in a minimal three-generation see-saw model

We investigate symmetries in Dirac and Majorana mass matrices of neutrinos in a three-generation scenario. We show that if we invokeL _e +L _μ-L _τ x S _2R symmetry, one combination of right-handed neutrino states remains massless which can be interpreted as a sterile neutrino. Next we consider a SU2_L x U(1)_y x U(l)_R gauge model and show how higher-dimensional operators can induce mixing between left- and right-handed states which explains solar, atmospheric and LSND experimental results.     

Amplification in one-dimensional random active medium near the lasing threshold

We studied the transmittance of a random amplifying medium near the lasing threshold by using the convergence criterion proposed by Nam and Zhang [Phys. Rev. B 66 73101, 2002] that allows separating the physical solutions of the time-independent Maxwell equations from the unphysical ones and describing critical size L _c of a random system in statistical terms. We found that the dependence of the critical gain ∈ ^″ _c (at which the lasing threshold occurs) as a function of number of layers is configuration-dependent and thus the lasing condition for random media is described by means of the probability of finding of physical solutions and evaluated by averaging over the ensemble of random configurations. By employing this approach we inspect the validity of the two-parameter scaling model by Zhang [Phys. Rev. B 52 7960, 1995], according to which the behavior of the random system with gain is described by relation 1/ξ = 1/ξ ₀ + 1/l _g, where ξ and ξ ₀ are localization length with and without gain, respectively, and l _g = 2/ω∈ ^″, is gain length, where ∈ ^″ is imaginary part of the dielectric constant that represents gain. We show that the range of validity of this relation depends on the ratio of both lengths and also affects the slope of the ln Λ_c(q) (where Λ_c ≡ L _c/ξ ₀ is normalized critical size and q ^?1 ≡ l _g/ξ ₀ is dimensionless gain length). We extend the study of the relation for the critical size L _c by inspecting the dependence of the slope of the ln Λ_c(q) on the strength of the randomness. We interpret its behavior in terms of the statistical properties of the localized states. Namely, by studying of the variance of the Lyapunov exponent λ (the inverse of the localization length ξ ₀) we have found that the slope of the ln Λ_c(q)) reflects the transition between two different regimes of localization with Anderson and Lifshits-like behavior that is known to be indicated by peak in var(λ). We discuss the generalization of two-parameter scaling model by implementing revisited single parameter scaling (SPS) theory by Deych et al. [Phys. Rev. Lett. 84 2678, 2000] which allows describing non-SPS regime in terms of a new scale l _s.

     

The electron transport properties of pure liquid metals

Progress in the theory of the electrical conductivity and other ordinary transport properties of liquid metals since 1961 is reviewed. After a brief account of the basic nearly-free-electron diffraction formula, the quantitative comparison of this formula with experiment is discussed.

For the alkali metals, the agreement is adequate, given the uncertainty of the pseudopotentials, although there is controversy about the calculation of the temperature coefficient of ρ _L. To explain the observed volume dependence of ρ _L, and the thermoelectric power, it also seems necessary to allow for the variation of the pseudopotential with the positions of the Fermi level and the core levels relative to the bottom of the conduction band.

Quantitative results for the noble and polyvalent metals are meagre, and although calculations of ρ _L for Al and Zn are in excellent agreement with experiment there may be other cases where the basic formula is not adequate. The general question of the structure and convergence of the perturbation series for ρ _L is discussed, and it is suggested that corrections for higher order terms can be minimized by making the pseudopotential as near as possible to the t-matrix of an ion.

The anomalous properties of Hg are then discussed, in the light of the work of Mott (1966). In this connection it is shown that Edwards' formula (1962) for ρ _L, in which the Fermi velocity, v _F, is taken to be that of a free electron, ?k _F/m, despite deviations from the free-electron curve for ?(k), can be derived by using the expectation value of the current operator in place of e v _F in the Boltzmann equation. This modification of the elementary theory allows the Hall constant of a liquid metal to deviate from 1/nec, as found experimentally.     

Investigation of the multiplet features of SrTiO3 in X‐ray absorption spectra based on configuration interaction calculations

Synchrotron‐based L_2,3‐edge absorption spectra show strong sensitivities to the local electronic structure and chemical environment. However, detailed physical information cannot be extracted easily without computational aids. Here, using the experimental Ti L_2,3‐edges absorption spectrum of SrTiO₃ as a fingerprint and considering full multiplet effects, calculations yield different energy parameters characterizing local ground state properties. The peak splitting and intensity ratios of the L₃ and L₂ set of peaks are carefully analyzed quantitatively, giving rise to a small hybridization energy around 1.2 eV, and the different hybridization energy values reported in the literature are further addressed. Finally, absorption spectra with different linearly polarized photons under various tetragonal crystal fields are investigated, revealing a non‐linear orbital–lattice interaction, and a theoretical guidance for material engineering of SrTiO₃‐based thin films and heterostructures is offered. Detailed analysis of spectrum shifts with different tetragonal crystal fields suggests that the e_g crystal field splitting is a necessary parameter for a thorough analysis of the spectra, even though it is not relevant for the ground state properties.