David B. Saakian

Phase diagram for the Eigen quasispecies theory with a truncated fitness landscape.

David B. Saakian , Christof K. Biebricher,Chin-Kun Hu Yerevan Physics Institute, Alikhanian Brothers St. 2, Yere van 375036, Armenia, Institute of Physics, Academia Sinica, Nankang, Taipei 115 29, Taiwan, 3 National Center for Theoretical Sciences:Physics Divisio n, National Taiwan University, Taipei 10617, Taiwan, Max-Planck-Institute for Biophysical Chemistry, D-37070 Göttingen, Germany Center for Nonlinear and Complex Systems and Department of P hysics, Chung-Yuan Christian University, Chungli 320, Taiwan (Dated: August 14, 2009)

Phase structure of string theory and the Random Energy Model

The results by E. Gardner and B.Derrida have been enlarged for the complex temperatures and complex numbers of replicas. The phase structure is found. There is a connection with string models and their phase structure is analyzed from the REMs point of view.We solve a random energy model with complex replica number and complex temperature values, and discuss the ensuing phase structure. A connection with string models and their phase structure is analyzed from the REM point of view. The REM analysis yields a few integer dimensions as special points of the REM phase diagram. For N = 1 superstrings, there is a distinguished dimension 5.

Random energy model at complex temperatures

The complete phase diagram of the random energy model is obtained for complex temperatures using the method proposed by Derrida. We find the density of zeroes for the statistical sum. Then the method is applied to the generalized random energy model. This allowed us to propose an analytical method for investigating zeroes of the statistical sum for finite-dimensional systems.

Accessible Information in Multi-access Quantum Channels

The accessible information in multi-access quantum channels are considered. Classical messages from independent sources, which are represented as some quantum states, are transported by a channel to one address. The messages can interact with each other and with external environment. After statement of problem and proving some general results we investigate physically important case when information is transported by states of an electromagnetic field. One-way communication by noisy quantum channels is also considered.

Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics

We formulate the Crow-Kimura, discrete-time Eigen model, and continuous-time Eigen model. These models are interrelated and we established an exact mapping between them. We consider the evolutionary dynamics for the single-peak fitness and symmetric smooth fitness. We applied the quantum mechanical methods to find the exact dynamics of the evolution model with a single-peak fitness. For the smooth symmetric fitness landscape, we map exactly the evolution equations into Hamilton-Jacobi equation (HJE). We apply the method to the Crow-Kimura (parallel) and Eigen models. We get simple formulas to calculate the dynamics of the maximum of distribution and the variance. We review the existing mathematical tools of quasi-species theory.

Hierarchic trees with branching number close to one: Noiseless Kardar-Parisi-Zhang equation with additional linear term for imitating two-dimensional and three-dimensional phase transitions.

An imitation of two-dimensional (2D) field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to 2D correlator ones. Such a model carries on some features of the original model for certain scale invariant theories. The renormalization group equation for the free energy is the noiseless Kardar-Parisi-Zhang equation with an additional linear term.

SPIN-GLASS MODEL WITH PARTIALLY ANNEALED ASYMMETRIC BONDS

We have considered the two-spin interaction spherical spin-glass model with asymmetric bonds (coupling constants). Besides the usual interactions between spins and bonds and between the spins and a thermostat with temperature

Strengthened Lindblad Inequality: Applications in Non-equilibrium Thermodynamics and Quantum Information Theory

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Approximate calculation of the ground-state energy for Potts spin-glass models.

there is also an additional factor: the bonds are not assumed random {it a priori} but interact with some other thermostat at the temperature

Statistical mechanics and financial markets: antagony between derivatives and market self-regulation

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