What is the Partition Bundle?

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometrical data. We discuss the nature of the object in such a theory that generalizes the partition function of a more conventional quantum field theory.     

How particular is the physics of the free energy principle?

The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. Although, in theory, the FEP applies to a wide variety of systems, there has been almost no direct exploration or demonstration of the principle in concrete systems. In this work, we examine in depth the assumptions required to derive the FEP in the simplest possible set of systems – weakly-coupled non-equilibrium linear stochastic systems. Specifically, we explore (i) how general the requirements imposed on the statistical structure of a system are and (ii) how informative the FEP is about the behaviour of such systems. We discover that two requirements of the FEP – the Markov blanket condition (i.e. a statistical boundary precluding direct coupling between internal and external states) and stringent restrictions on its solenoidal flows (i.e. tendencies driving a system out of equilibrium) – are only valid for a very narrow space of parameters. Suitable systems require an absence of perception-action asymmetries that is highly unusual for living systems interacting with an environment. More importantly, we observe that a mathematically central step in the argument, connecting the behaviour of a system to variational inference, relies on an implicit equivalence between the dynamics of the average states of a system with the average of the dynamics of those states. This equivalence does not hold in general even for linear stochastic systems, since it requires an effective decoupling from the system's history of interactions. These observations are critical for evaluating the generality and applicability of the FEP and indicate the existence of significant problems of the theory in its current form. These issues make the FEP, as it stands, not straightforwardly applicable to the simple linear systems studied here and suggest that more development is needed before the theory could be applied to the kind of complex systems that describe living and cognitive processes.     

What is the Relativistic Volterra Lattice?

We develop a systematic procedure of finding integrable 6ldquo;relativistic” (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problem, which can be, in turn, interpreted as a new discrete time system. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then “relativistic”, the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the “relativistic” deformations were not known previously. Received: 1 April 1998 / Accepted: 21 July 1998     

Why is GeV physics relevant in the age of the LHC?

The contribution that Jefferson Lab has made, with its 6 GeV electron beam, and will make, with its 12 GeV upgrade, to our understanding of the way the fundamental interactions work, particularly strong coupling QCD, is outlined. This physics at the GeV scale is essential even in TeV collisions.     

What is the Cause of Inertia?

The question of the cause of inertial reaction forces and the validity of Mach's principle are investigated. A recent claim that the cause of inertial reaction forces can be attributed to an interaction of the electrical charge of elementary particles with the hypothetical quantum mechanical zero-point fluctuation electromagnetic field is shown to be untenable. It fails to correspond to reality because the coupling of electric charge to the electromagnetic field cannot be made to mimic plausibly the universal coupling of gravity and inertia to the stress-energy-momentum (i.e., matter) tensor. The gravitational explanation of the origin of inertial forces is then briefly laid out, and various important features of it explored in the last half-century are addressed.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Observation of anomalously fast diffusion in 3He–4He solid solutions near the BCC-HCP transition

The pulsed NMR technique was used to investigate diffusion on the BCC-HCP phase-equilibrium and melting curves of a dilute solution of ³He in ⁴He. The contributions from all coexisting phases were identified using the spin-echo method. It is established that, along with the contributions from the equilibrium BCC and HCP phases or from bulk liquid (in the melting curve measurements), there is an additional diffusional process that is characterized by an anomalously high diffusion coefficient. It is found that the latter is close to the diffusion coefficient in liquid helium, while the diffusion itself is spatially restricted. The observed effect may be caused by the formation of liquid droplets in the course of the BCC-HCP transition.     

3He–HeII Mixtures in the Static Approximation

We have applied, for the first time, the so-called static approximation (SA) on the ³He–HeII mixtures to calculate their thermodynamic properties under different conditions. For that, we have first obtained the so-called self-consistent long-range-equation. The essence of this approximation is to replace the true quantum-mechanical spectrum of the local-field operator with a distribution around the expectation value of the local-field operator. The distribution function of the fermionic particles has been found to be almost a step function up to 0.1 K. The chemical potential, pressure, and the mean internal energy per unit volume have been calculated in this temperature range with different values for the volume differential coefficient and the effective mass m ₃*. We have found that the thermodynamic properties of this system are temperature independent.     

What is the ground-state structure of the thinnest Si nanowires?

Pristine silicon whiskers are compared through energy analysis by separating the surface, edge, and bulk contributions, and by energy computation for a variety of structures and diameters d. It is shown that for d<6 nm a polycrystalline wire of five-fold symmetry, rather than single-crystal types, represents the ground state. It remains stable in molecular dynamics tests up to approximately 1000 K. Its specific surface reconstruction also stands out in that it favors kinetics of whisker growth and thus appears potentially realizable.     

T invariance and polarization effects in the reactions p+3He → π++4He and π++4He → p+3He

On the basis of T invariance, it is established that the dependence of the effective cross section for a binary reaction of the a+b → c+d type on the polarization vectors of primary particles a and b determines completely the polarization vectors and spin correlations for the same particles in the inverse reaction c+d → a+b induced by collisions between unpolarized primary particles c and d. By using the formalism of helicity amplitudes, polarization effects are studied in the process p+³He → π⁺+⁴He and in the inverse process π⁺+⁴He → p+³He. It is shown that, in the reaction π⁺+⁴He → p+³He, the spins of the final-state particles (proton and ³He nucleus) are strongly correlated. An expression for the correlation tensor is obtained for arbitrary values of the (p, ³He) emission angle.     

What is a photon?

Certain properties of photons viewed as quanta (particles of an electromagnetic field) are discussed. Specifically, the nature of localization (size) of photons along and across the direction of wave propagation is examined.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.