V. V. Papoyan

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary conditions. We prove that the so defined update leads to a stationary state in which all possible particle configurations have equal probabilities. Using the exact analytical expression for the propagator, we find the generating function for the conditional probabilities, average velocity and diffusion constant at all stages of evolution. An exact and explicit expression for the stationary velocity of TASEP on rings of arbitrary size and particle filling is derived. The evolution of small systems towards a steady state is clearly demonstrated. Considering the generating function as a partition function of a thermodynamic system, we study its zeros in planes of complex fugacities. At long enough times, the patterns of zeroes for rings with increasing size provide evidence for a transition of the associated two-dimensional lattice paths model into a clustered phase at low fugacities.

CONFORMAL UNIFICATION OF GENERAL RELATIVITY AND STANDARD MODEL

Abstract The unification of general relativity and standard model for strong and electro-weak interactions is considered on the basic of the conformal symmetry principle. The Penrose-Chernikov-Tagirov Lagrangian is used to describe the Higgs scalar field modulus and gravitation. We show that the procedure of the Hamiltonian reduction converts the homogeneous part of the Higgs field into the dynamical parameter of evolution of the equivalent reduced system. The equation of dynamics of the “proper time” of an observer with respect to the evolution parameter reproduces the Friedmann-like equation, which reflects the cosmological evolution of elementary particle masses. The value of the Higgs field is determined, at the present time, by the values of mean density of matter and the Hubble parameter in satisfactory agreement with the data of cosmological observations.

Two-dimensional random walk and critical behavior of double-strand DNA

The phase behavior in a double-strand homopolynucleotide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of base pairs between the complementary units. We obtain a completely denatured state below the finite temperature Tc. It was shown that Tc is the point of the infinite-order phase transition. The specific behavior of the order parameter, free energy and correlation functions has been addressed.

Two-dimensional random walk and loop factor in helix-coil transition theory of DNA

Theory of helix-coil transition in double-stranded homopolypeptides is considered. The theory develops an approach, which takes into account fundamental properties of the system (loop formation under complementary binding). Calculations are done in the framework of random walk theory. Partition function of the system is obtained in terms of arbitrary and first returns. It is shown that the loop factor of the theory has a power law behavior depending on the length of the chain.

The melting phenomenon in random-walk model of DNA

The melting phenomenon in a double-stranded homopolypeptide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the two competing interactions of monomers inside the chains, we obtain a completely denatured state at finite temperature Tc.

Cosmological Creation of Matter in Conformal Cosmology

The effect of rapid cosmological creation of vector W and Z bosons is studied in the framework of conformal cosmology, which unifies the general theory of relativity and the standard model for strong and electroweak interactions.

Dynamics of proper time in the theory of gravitation and conformal unification of interactions

The work is devoted to a description of the dynamics of proper time as a function of the evolutionary parameter,which can be separated from the Dirac-ADM metric in the Hamiltonian version of the general theory of relativity (GTR) and in conformally invariant, Lichnerowicz variables. In these variables, the GTR is equivalent to the conformally invariant, Penrose-Chernikov-Tagirov, scalar-field theory, with a quantity proportional to the scale factor playing the role of the scalar field. Identifying such a scalar field with the modulus of the Higgs field in the standard model, which unifies the electrvweak and strong interactions, makes it possible to formulate a unified,conformally invariant theory in which the vacuum average of the scalar field is determined by integrals of motion of cosmological evolution.

Temperature of the Cosmic Microwave Background Radiation in Conformal Cosmology

A scheme is proposed for explaining the origin of the observed temperature of the cosmic microwave background (relict) radiation in which this radiation is treated as a product of the decay of primordial vector bosons in the framework of the Hoyle-Narlikar conformal cosmology.

Gravitational Waves and the Reparameterization-Invariant Hamiltonian Formalism

A consistent perturbation theory is formulated on the basis of a recently proposed method of reparameterization-invariant Hamiltonian reduction, and a linearized limit in the oscillator approximation of General Relativity is considered. Possible physical consequences of interpreting the nonzero local Hamiltonian as the gravitational field energy are discussed. The physical and geometrical meanings of reduced action variables are investigated. A qualitative conclusion is drawn about the dependence of the distribution of phases of relict gravitational waves at the current epoch on the initial conditions at the time of the Big Bang.

Einstein Representation of the Jordan-Brans-Dicke Theory of Gravitation

Various representations of the Jordan-Brans-Dicke (JBD) theory arising in conformal transformations of the metric are considered. Propositions are formulated that establish the mathematical equivalence of these representations, making it possible from known exact solutions in one representation to generate new ones in another. It is shown, in particular, how to obtain new solutions in the general theory of relativity from known solutions in the JBD theory and vice versa.