Geometry and duality in supersymmetric σ-models

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson fermion symphysis of the dual transition, and on the new geometry of the DSM.     

Equivalence principle,the general theory of relativity,ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with valve properties -a one-way exchange of information—contradicts the equivalence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–15, January, 1984.     

Large-scale–small-scale duality and the cosmological constant

We study a model of quantum cosmology originating from a classical model of gravitation where a self-interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical signature changing solutions, one at large scales and the other at small scales. It is possible to fine-tune the physics in both scales with an infinitesimal effective cosmological constant.     

A principle in dynamic coarse graining–Onsager principle and its applications

Dynamic coarse graining is a procedure to map a dynamical system with large degrees of freedom to a system with smaller degrees of freedom by properly choosing coarse grained variables. This procedure has been conducted mainly by empiricisms. In this paper, I will discuss a theoretical principle which may be useful for this procedure. I will discuss how to choose coarse grained variables (or slow variables), and how to set up their evolution equations. To this end, I will review the classical example of dynamic coarse graining, i.e., the Brownian motion theory, and show a variational principle for the evolution of the slow variables. The principle, called the Onsager principle, is useful not only to derive the evolution equations, but also to solve the problems.     

Equivalence of Ensembles,Condensation and Glassy Dynamics in the Bose–Hubbard Hamiltonian

Journal of Statistical Physics - We study mathematically the equilibrium properties of the Bose–Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the...     

Concavity of the QQ̄ potential in N=4 super Yang-Mills gauge theory and AdS/CFT duality

We derive a generalised concavity condition for potentials between static sources obtained from Wilson loops coupling both to gauge bosons and a set of scalar fields. It involves the second derivatives with respect to the distance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretical condition as a nontrivial consistency check of the AdS/CFT duality.     

On the “Equivalence” of the Maxwell and Dirac Equations

It is shown that Maxwell's equation cannot be put into a spinor form that is equivalent to Dirac's equation. First of all, the spinor in the representation of the electromagnetic field bivector depends on only three independent complex components whereas the Dirac spinor depends on four. Second, Dirac's equation implies a complex structure specific to spin 1/2 particles that has no counterpart in Maxwell's equation. This complex structure makes fermions essentially different from bosons and therefore insures that there is no physically meaningful way to transform Maxwell's and Dirac's equations into each other.     

New search for processes violating the Pauli exclusion principle in sodium and in iodine

In this paper a new search for non-Paulian nuclear processes, i.e. processes normally forbidden by the Pauli Exclusion Principle (PEP), is presented. It has been carried out at the Gran Sasso National Laboratory of the INFN by means of the highly radiopure DAMA/LIBRA set-up (sensitive mass of about 250 kg highly radiopure NaI(Tl)). In particular, a new improved upper limit for the spontaneous non-Paulian emission rate of protons with energy E _p ≥ 10 MeV in ²³Na and ¹²⁷I has been obtained: 1.63 × 10⁻³³ s⁻¹ (90% C.L.). The corresponding limit on the relative strength (δ ²) for the searched non-Paulian transition is δ ²≲(3–4)×10⁻⁵⁵ (90% C.L.). Moreover, PEP-violating electron transitions in iodine atoms have also been investigated. Lifetimes shorter than 4.7×10³⁰ s are excluded at 90% C.L.; this allows us to derive the limit δ _e ²<1.28×10⁻⁴⁷ (90% C.L.). This latter limit can also be related to a possible finite size of the electron in composite models of quarks and leptons providing superficial violation of the PEP; the obtained upper limit on the electron size is r ₀<5.7×10⁻¹⁸ cm (energy scale of E≳3.5 TeV).     

Sigma models withA k singularities in Euclidean spacetime of dimension 0 ≤D < 4 and in the limitN → ∞

For the case of the single-O(N)-vector linear sigma models the critical behaviour following from anyA _k singularity in the action is worked out in the double scaling limitN→∞,f _r →f _r ^c , 2≤r≤k. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for allA _k and spacetime dimensions 0≤D<4. There appear exceptional spacetime dimensions where the degreek of the singularityA _k is more strongly constrained than by the renormalizability requirement.     

Properties of the decay H→γγ using the approximate α_s~4 corrections and the principle of maximum conformality

The decay channel H→γγ is an important channel for probing the properties of the Higgs boson.In this paper,we analyze its decay width by using the perturbative QCD corrections up to the α_s~4 order with the help of the principle of maximum conformality(PMC).PMC has been suggested in literature for eliminating the conventional renormalization scheme-and-scale ambiguities.After applying PMC,we observe that an accurate renormalization scale independent decay width Γ(H→γγ) up to the N~4 LO level can be achieved.Taking the Higgs mass,M_H = 125.09±0.21 ±0.11 GeV,given by the ATLAS and CMS collaborations,we obtain Γ(H→γγ)|LHC = 9.364_(0.075)~(0.076) KeV.     

Detection of a Physical Difference between the CDM Halos in Simulation and in Nature

Numerical simulation is an important tool that is helpful for us to understand the process of structure formation in the universe. However, many simulation results of cold dark matter （CDM） halos on a small scale are inconsistent with observations： the central density profile is too cuspy and there are too many substructures, Here we point out that both the problems may be connected with a hitherto unrecognized bias in the simulated halos. Although CDM halos in nature and in simulation are both virialized systems of collisionless CDM particles, gravitational encounter cannot be neglected in the simulated halos because they contain many fewer particles. We demonstrate this by two numerical experiments, showing that there is a difference on the microcosmic scale between the natural and simulated halos. The simulated halo is more akin to globular clusters where gravitational encounter is known to lead to such drastic phenomena as core collapse. Such an artificial core collapse process appears to link the two problems together in the bottom-up scenario of structure formation in the ACDM universe. The discovery of this bias also has implications on the applicability of the Jeans theorem in galactic dynamics.     

Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena

This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities （the same as the surface elevation）, i.e. Iω -ω^-3-5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of ‘narrowband pumping＇ for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.     

Brillouin light scattering in LiKSO4 between 20 and 80°C

Elastic constants of LiKSO₄ crystals have been measured at room temperature and over the temperature range 20–80°C by Brillouin scattering. No anomaly has been found near 60°C, in disagreement with the results of a previous Brillouin study which suggested a new phase transition.     

Maximum information entropy principle and the interpretation of probabilities in statistical mechanics − a short review

In this paper an alternative approach to statistical mechanics based on the maximuminformation entropy principle (MaxEnt) is examined, specifically its close relation withthe Gibbs method of ensembles. It is shown that the MaxEnt formalism is the logicalextension of the Gibbs formalism of equilibrium statistical mechanics that is entirelyindependent of the frequentist interpretation of probabilities only as factual (i.e.experimentally verifiable) properties of the real world. Furthermore, we show that,consistently with the law of large numbers, the relative frequencies of the ensemble ofsystems prepared under identical conditions (i.e. identical constraints) actuallycorrespond to the MaxEnt probabilites in the limit of a large number of systems in theensemble. This result implies that the probabilities in statistical mechanics can beinterpreted, independently of the frequency interpretation, on the basis of the maximuminformation entropy principle.     

Optical bistability and multistability in a three-level Δ-type atomic system under the nonresonant condition

Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level Δ-type system by using a microwave field to drive a hyperfine transition between two upper excited states inside a unidirectional ring cavity. We find that the optical bistability and multistability behaviours can be controlled by adjusting the intensity of the microwave field or the intensity of the coherent coupling field. Furthermore, our studies show an interesting phenomenon of the transition from the optical bistability to the optical multistability only by changing the negative detuning of the coupling field into the positive detuning of the coupling field.