Two-parametric zeta function regularization in superstring theory

In this paper some quite simple examples of applications of the zeta-function regularization to superstring theories are presented. It is shown that the Virasoro anomaly in the BRST formulation of (super)strings can be directly computed from the original expressions of the operators as well as normal ordering constants and masses of ground levels. Hawking's zeta regularization is recognized as an efficient tool for direct calculations, bringing no ambiguities. Possible implications for global GSO operators' phases definitions (maybe ensuring modular invariance) will be discussed elsewhere.Comment: 13 pages, standard LaTeX, printing two A5's per one sheet recom., cut to 80 chars/lin

Toward unification: the dimensionless equation of motion

We demonstrate that if masses and charges figuring in the equation of motion including both Newton gravitational and Coulomb electrostatic force laws are divided by mass and charge, respectively, which are derived using the relations contaning only the fundamental physical and mathematical constants (like relations defining the Planck's mass, length, and time), then the gravitational constant and permitivity of vacuum can be eliminated from the equation. In addition, the equation becomes dimensionless containing only the ratios of distances, velocities, masses, and electric charges. The ratios of masses and charges can further be replaced with the ratios of wave-lengths or frequencies. The corresponding equation of motion implies that the fundamental physical constants as the gravitational constant, permitivity of vacuum, and Planck constant are, likely, mere the transformation constants between artificial quantities as mass and electric charge, which were established by man to communicate some concerning things and events in every-day life, and natural physical quantities as wave-length or frequency of oscillations of waving space-time.Comment: a brief report; 3 pages in RevTEX style; no figures or tables; submitted to Physical Review

Structure of fermion nodes and nodal cells

We study nodes of fermionic ground state wave functions. For 2D and higher we prove that spin-polarized, noninteracting fermions in a harmonic well have two nodal cells for arbitrary system size. The result extends to other noninteracting/mean-field models such as fermions on a sphere, in a periodic box or in Hartree-Fock atomic states. Spin-unpolarized noninteracting states have multiple nodal cells, however, interactions and many-body correlations generally relax the multiple cells to the minimal number of two. With some conditions, this is proved for interacting 2D and higher dimensions harmonic fermion systems of arbitrary size using the Bardeen-Cooper-Schrieffer variational wave function. Implications and extent of these results are briefly discussed.Comment: 4 pages, 2 figure

Proposals on nonperturbative superstring interactions

We show a possibility that the matrix models recently proposed to explain (almost) all the physics of M-theory may include the superstring theories that we know perturbatively. The ``1st quantized'' physical system of one IIA string seems to be an exact consequence of M(atrix) theory with a proper mechanism to mod out a symmetry. The central point of the paper is the representation of strings with P^+/epsilon greater than one. I call the mechanism ``screwing strings to matrices''. I also give the first versions of the proof of 2/3 power law between the compactification radius and the coupling constant in this formulation. Multistring states are involved in a M(atrix) theory fashion, replacing the 2nd quantization that I briefly review. We shortly discuss the T-dualities, type I string theory and involving of FP ghosts to all the systems including the original one of Banks et al.Comment: plain LaTeX, 22 pages, 1st revision: another proof of the R=g^{2/3} law and references and acknowledgements added. 2nd revision: origin of level-matching conditions explaine

Quaternions and M(atrix) theory in spaces with boundaries

A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The construction causes the elements of matrices to be equivalent to real numbers or quaternions and the symmetry U(2N) of the original model is reduced to O(2N) or USp(2N)=U(N,H). We also show that membranes end on the boundary of the spacetime correctly in this construction.Comment: plain LaTeX, 15 pages, 1st revision: references, school info and notes added (real matrix case, Mobius membranes and so on...) 2nd revision: notes on originators of idea

Fermion nodes and nodal cells of noninteracting and interacting fermions

A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion nodes of fermionic ground state wave functions for a number of systems. For several models we demonstrate that noninteracting spin-polarized fermions in dimension two and higher have closed-shell ground state wave functions with the minimal two nodal cells for any system size and we formulate a theorem which sumarizes this result. The models include periodic fermion gas, fermions on the surface of a sphere, fermions in a box. We prove the same property for atomic states with up to 3d half-filled shells. Under rather general assumptions we then derive that the same is true for unpolarized systems with arbitrarily weak interactions using Bardeen-Cooper-Schrieffer (BCS) variational wave function. We further show that pair correlations included in the BCS wave function enable singlet pairs of particles to wind around the periodic box without crossing the node pointing towards the relationship of nodes to transport and many-body phases such as superconductivity. Finally, we point out that the arguments extend also to fermionic temperature dependent/imaginary-time density matrices. The results reveal fundamental properties of fermion nodal structures and provide new insights for accurate constructions of wave functions and density matrices in quantum and path integral Monte Carlo methods.Comment: 17 pages, 10 figure

Controlling congestion on complex networks: fairness, efficiency and network structure

We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow allocation, and the location of bottleneck edges. The more realistic proportional fairness and max-min fairness algorithms have similar throughput, but path flow allocations are more unequal in scale-free than in random regular networks. Scale-free networks have lower throughput than their random regular counterparts in the uniform-flow algorithm, which is favoured in the complex networks literature. We show, however, that this relation is reversed on all other congestion control algorithms for a region of the parameter space given by the degree exponent $\gamma$ and average degree ${k}$. Moreover, the uniform-flow algorithm severely underestimates the network throughput of congested networks, and a rich phenomenology of path flow allocations is only present in the more realistic $\alpha$-fair family of algorithms. Finally, we show that the number of paths passing through an edge characterises the location of a wide range of bottleneck edges in these algorithms. Such identification of bottlenecks could provide a bridge between the two fields of complex networks and congestion control.Comment: publishe

Structural (B1 to B8) Phase Transition in MnO under Pressure: Comparison of All-electron and Pseudopotential Approaches

We employ the density functional theory to study a structural transition of MnO from B1 (rocksalt) to B8 (NiAs) structures that was observed experimentally at pressures around 100 GPa. We utilize all-electron description as well as norm-conserving pseudopotentials and demonstrate that these two approaches can significantly differ in quantitative predictions. We explicitly show that even small-core pseudopotentials exhibit transferability inaccuracies for quantities sensitive to the energy differences between high- and low-spin polarizations of valence electrons.Comment: 5 pages, 3 figures, REVTeX

Business cycle synchronization within the European Union: A wavelet cohesion approach

In this paper, we map the process of business cycle synchronization across the European Union. We study this synchronization by applying wavelet techniques, particularly the cohesion measure with time-varying weights. This novel approach allows us to study the dynamic relationship among selected countries from a different perspective than the usual time-domain models. Analyzing monthly data from 1990 to 2014, we show an increasing co-movement of the Visegrad countries with the European Union after the countries began preparing for the accession to the European Union. With particular focus on the Visegrad countries we show that participation in a currency union possibly increases the co-movement. Furthermore, we find a high degree of synchronization in long-term horizons by analyzing the Visegrad Four and Southern European countries' synchronization with the core countries of the European Union.Comment: 21 page

Applications of quantum Monte Carlo methods in condensed systems

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.Comment: 34 page