Non-transitivity can arise in games with three or more strategies $A,B,C$ , when $A$ beats $B$ , $B$ beats $C$ , and $C$ beats $A$ , ( $A>B>C>A$ ). An example is the children's game \textquotedblleft rock, scissors, paper" ( $R,S,P$ ) where $R>S>P>R$ . We discuss the conditions under which quantum versions of $R,S,P$ retain the non-transitive characteristics of the corresponding classical game. Some physical implications of non-transitivity in quantum game theory are also considered.Non-transitivity can arise in games with three or more strategies $A,B,C$, when $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$, ($A>B>C>A$). An example is the children's game \textquotedblleft rock, scissors, paper" ($R,S,P$) where $R>S>P>R$. We discuss the conditions under which quantum versions of $R,S,P$ retain the non-transitive characteristics of the corresponding classical game. Some physical implications of non-transitivity in quantum game theory are also considered.

arXiv:quant-ph/0307072FizBJul 9, 20035 citations

Reply to “Comment on ‘Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field’ ”

Ram K. Varma, A. M. Punithavelu, S. B. Banerjee

The so-designated ``complete classical explanation'' by Unnikrishnan in the preceding Comment, of the macroscopic wave beats reported by us recently, is based on an assumed physical mechanism that has no experimentally established basis. Through this assumed physical process and the focusing properties of an electron beam in a magnetic field, he produces what are essentially ``particle beats'' as against the ``wave beats'' observed by us. Even assuming that such a physical process does exist, the consequences of his mechanism are shown here to be in serious contradiction with our experimental observations, thereby invalidating the claim that his model explains, in purely classical terms, our observations exhibiting the existence of macroscopic matter wave beats in the charged particle motion along a magnetic field.The so-designated ``complete classical explanation'' by Unnikrishnan in the preceding Comment, of the macroscopic wave beats reported by us recently, is based on an assumed physical mechanism that has no experimentally established basis. Through this assumed physical process and the focusing properties of an electron beam in a magnetic field, he produces what are essentially ``particle beats'' as against the ``wave beats'' observed by us. Even assuming that such a physical process does exist, the consequences of his mechanism are shown here to be in serious contradiction with our experimental observations, thereby invalidating the claim that his model explains, in purely classical terms, our observations exhibiting the existence of macroscopic matter wave beats in the charged particle motion along a magnetic field.

Physical Review EAug 30, 20044 citations

Quantum Mechanics and Classical Physics

N. Rosen

Jan 1, 19900 citations

Classical and Quantum Physics

R. Asokamani

Elsevier eBooksOct 2, 20260 citations

Effect of a magnetic flux line on the quantum beats in the Hénon–Heiles level density

M. Brack, R. K. Bhaduri, J. Law +2 more

The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the changes can be easily understood in terms of the Aharonov-Bohm effect. However, we find that the standard periodic orbit theory does not reproduce the diffraction-like quantum effects on those classical orbits which intersect the singular flux line, and argue that corrections of relative order variant Planck's over 2pi are necessary to describe these effects. We also discuss the changes in the distribution of nearest-neighbor spacings in the eigenvalue spectrum, brought about by the flux line. (c) 1995 American Institute of Physics.The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the changes can be easily understood in terms of the Aharonov-Bohm effect. However, we find that the standard periodic orbit theory does not reproduce the diffraction-like quantum effects on those classical orbits which intersect the singular flux line, and argue that corrections of relative order variant Planck's over 2pi are necessary to describe these effects. We also discuss the changes in the distribution of nearest-neighbor spacings in the eigenvalue spectrum, brought about by the flux line. (c) 1995 American Institute of Physics.

arXiv:chao-dyn/9312002Chaos An Interdisciplinary Journal of Nonlinear ScienceMar 1, 199522 citations

Non-transitivity can arise in games with three or more strategies

A,B,C

, when

A

beats

B

B

beats

C

, and

C

beats

A

, (

A>B>C>A

). An example is the children's game \textquotedblleft rock, scissors, paper" (

R,S,P

) where

R>S>P>R

. We discuss the conditions under which quantum versions of

R,S,P

retain the non-transitive characteristics of the corresponding classical game. Some physical implications of non-transitivity in quantum game theory are also considered.