312,277 research outputs found
Out of equilibrium quantum field dynamics in external fields
The quantum dynamics of the symmetry broken \lambda (\Phi^2)^2 scalar field
theory in the presence of an homogeneous external field is investigated in the
large N limit. We consider an initial thermal state of temperature T for a
constant external field J. A subsequent sign flip of the external field, J to
-J, gives rise to an out of equilibrium nonperturbative quantum field dynamics.
We review here the dynamics for the symmetry broken lambda(\Phi^2)^2 scalar N
component field theory in the large N limit, with particular stress in the
comparison between the results when the initial temperature is zero and when it
is finite. The presence of a finite temperature modifies the dynamical
effective potential for the expectation value, and also makes that the
transition between the two regimes of the early dynamics occurs for lower
values of the external field. The two regimes are characterized by the presence
or absence of a temporal trapping close to the metastable equilibrium position
of the potential. In the cases when the trapping occurs it is shorter for
larger initial temperatures.Comment: LaTeX, 3 pages, 2 figures. Presented at the IVth International
Conference on Quarks and Nuclear Physics (QNP06). Selected to appear in Eur.
Phys. J.
Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm
An efficient quantum modular exponentiation method is indispensible for
Shor's factoring algorithm. But we find that all descriptions presented by
Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark
that some experimental demonstrations of Shor's algorithm are misleading,
because they violate the necessary condition that the selected number ,
where is the number of qubits used in the first register, must satisfy , where is the large number to be factored.Comment: 12 pages,5 figures. The original version has 6 pages. It did not
point out the reason that some researchers took for granted that quantum
modlar exponentiation is in polynomial time. In the new version, we indicate
the reason and analyze some experimental demonstrations of Shor's algorithm.
Besides, the author Zhenfu Cao is added to the version for his contribution.
arXiv admin note: text overlap with arXiv:1409.735
Phase Transition in Evolutionary Games
The evolution of cooperative behaviour is studied in the deterministic
version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff
parameter is set at the critical region , where clusters of
cooperators are formed in all spatial sizes. Using the factorial moments
developed in particle and nuclear physics for the study of phase transition,
the distribution of cooperators is studied as a function of the bin size
covering varying numbers of lattice cells. From the scaling behaviour of the
moments a scaling exponent is determined and is found to lie in the range where
phase transitions are known to take place in physical systems. It is therefore
inferred that when the payoff parameter is increased through the critical
region the biological system of cooperators undergoes a phase transition to
defectors. The universality of the critical behaviour is thus extended to
include also this particular model of evolution dynamics.Comment: 12 pages + 3 figures, latex, submitted to Natur
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