Does the topology of space fluctuate?

Evidence is presented that the singularities induced in causal Lorentzian spacetimes by changes in 3-space topology give rise to infinite particle and energy production under reasonable laws of quantum field propagation. In the case of the gravitational field, if 3-space is compact the total energy must vanish. A topological transition therefore induces a violent collapse that effectively aborts the transition, since the collapse mode is the only mode carrying the negative energy needed to compensate the associated infinite energy production. The existence of the Hamiltonian constraint of general relativity suggests that topological stability is a local property of the quantum theory that is maintained even when 3-space is noncompact.Supported in part by National Science Foundation Grant No. PHY-8318635.     

Periodic Monopoles with Singularities and 𝒩=2 Super-QCD

 We study solutions of the Bogomolny equation on ℝ²×𝕊¹ with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperk?hler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain 𝒩=2 d=4 supersymmetric gauge theories on ℝ³×𝕊¹. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ²×𝕊¹. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane. Received: 9 March 2001 / Accepted: 15 January 2002 Published online: 20 January 2003     

Cosmic strings in a space with topology M2 × V2

For the case of a space-time with topology M₂×V₂, we show that the equation of motion of an infinitely thin string has solutions that can naturally be called the laws of motion of a straight string. For the case of a locally plane conical space, the solutions are written explicitly. We show that such motions of a test string are not followed by gravitational radiation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 75–79, November, 1991.     

A dynamical topology for the space of states

A new topology is introduced on the space of states of a physical system. This topology is given by dynamics, every state has a neighbourhood consisting of states which are connected by the time evolution only. All conservation laws can be treated as topological ones with respect to the new topology.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.     

Real space and configuration space wave function in the intermediate valence problem

This paper analyses the behavior of intermediate valence compounds, from the point of view of wave functions. They are expressed in a linear combination of cellular orbitals (LCCO) basis for SCF plus correlation introduced in the configuration interaction (CI) scheme, suitable to describe the different spatial extension in real space and the correlation between different fⁿ possibilities. This allows the discussion of the large variety of interesting phenomena which arises from the changes of the f electron configuration space wave functions: fⁿ → fⁿ⁺¹ of from the changes of the electronic charge from atomic-like to the different condensed matter-like boundary conditions. In particular an analysis is included of the correspondence between the actual properties in this type of materials and the amount of atomic-like f character n_f^atomic ?n_f^total in some rare earth and actinide compounds, concluding that the experimental evidence is consistent with a large distortion of the actual f-wave functions from their atomic-like forms.     

Delays, connection topology, and synchronization of coupled chaotic maps

We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian. Consequently, scale-free and random networks are capable of synchronizing despite the delayed flow of information, whereas regular networks with nearest-neighbor connections and their small-world variants generally exhibit poor synchronization. On the other hand, connection delays can actually be conducive to synchronization, so that it is possible for the delayed system to synchronize where the undelayed system does not. Furthermore, the delays determine the synchronized dynamics, leading to the emergence of a wide range of new collective behavior which the individual units are incapable of producing in isolation.     

Probability densities in configuration space and the Hamilton-Jacobi equation

The characteristic solutions of the Hamilton-Jacobi equation give the energies of conservative physical systems as functions of position and time. It is shown that these expressions are useful in the formation of probability densities in configuration space for canonical ensembles. Applications are given and discussed.     

Effective operators and the truncation of shell model configuration space

An alternative derivation of the projection method for constructing effective operators in the truncated shell model space is presented. The results of explicit numerical calculations in three different nuclear regions are discussed. Non-hermiticity of the effective Hamiltonian and various hermitisation procedures are investigated in detail.     

The Wigner-Newton state localization and the commutativity of the configuration space

The commutativity requirement of the components of the position operator is implicitly included in the set of the Wigner-Newton postulates defining the localized state of the relativistic particle. By omitting this constraint, we obtain a more general concept of localization based on the representation of the Poincare group.     

Calculation of the two-body scattering T-matrix in configuration space

In order to carry out a solution of the three-body Faddeev integral equations in configuration space, the calculation of the two-body scattering T-matrices and related integrals are required as an input. The formulation of the three-body Faddeev solution, as well as the computational steps used for the calculation of the T-matrices are presented, and results for the latter are illustrated for the case of the scattering of two helium atoms.     

Momentum space topology of fermion zero modes brane

We discuss fermion zero modes within the 3+1 brane, i.e., the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by a nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.     

EMCD real space maps of Magnetospirillum magnetotacticum

In this study we combine energy loss magnetic circular dichroism (EMCD) and energy filtered transmission electron microscopy (EFTEM) to map magnetic properties of nanoparticles. We show that it is a functional tool for investigating the magnetic behaviour of bio-mineralized magnetite crystals of Magnetospirillum magnetotacticum. We find that the spatial resolution of our experimental set-up is in the range of less than 2 nm. The results are compared with EMCD studies of abiogenic magnetite.