The rationality of irrationality in the Monty Hall problem

The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for its superiority. Many people, if given the choice to switch, think the chances are fifty-fifty between their options, but still strongly prefer to stay with their initial choice. Is there some sense behind these irrational feelings? We entertain the possibility that intuition solves the problem of how to behave in a real game show, not in the abstract textbook version of the Monty Hall problem. A real showmaster sometimes plays evil, either to make the show more interesting, to save money, or because he is in a bad mood. A moody showmaster erases any information advantage the guest could extract by him opening other doors which drives the chance of the car being behind the chosen door towards fifty percent. Furthermore, the showmaster could try to read or manipulate the guest's strategy to the guest's disadvantage. Given this, the preference to stay with the initial choice turns out to be a very rational defense strategy of the show's guest against the threat of being manipulated by its host. Thus, the intuitive feelings most people have about the Monty Hall problem coincide with what would be a rational strategy for a real-world game show. Although these investigations are mainly intended to be an entertaining mathematical commentary on an information-theoretic puzzle, they touch on interesting psychological questions.Comment: 4 pages, no figures, revised articl

Development of the critical exponent at the antiferromagnetic phase transition of YbRh2Si2 under chemical pressure

We present specific-heat measurements in the vicinity of the antiferromagnetic phase transition on single crystals of the alloy Yb(Rh_{1-x}Co_x)2Si2 for x<= 0.38. This study was motivated by the violation of critical universality in the undoped YbRh2Si2 (Krellner et al., Phys. Rev. Lett. 102, 196402) where we have found a large critical exponent a=0.38. For Co-doped samples we observe a drastic change of the critical fluctuations resulting in a negative a, explainable within the universality classes of phase transitions. The development of a under chemical pressure gives strong indication that the violation of critical universality in YbRh2Si2 is due to the nearby quantum critical point.Comment: Accepted for the QCNP proceedings 200

Feynman integrals for a class of exponentially growing potentials

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schroedinger equation. The Morse potential is considered as a special case

Effect of chemical substitution and pressure on YbRh2Si2

We carried out electrical resistivity experiments on (Yb,La)Rh2Si2 and on Yb(Rh,Ir)2Si2 under pressure and in magnetic fields. YbRh2Si2 exhibits a weak antiferromagnetic transition at atmospheric pressure with a N\'eel temperature of only T_N = 70 mK. By applying a small magnetic field T_N can be continuously suppressed to T=0 at B_c = 60 mT (B_|_c) driving the system to a quantum critical point (QCP). On applying external pressure the magnetic phase is stabilized and T_N(p) is increasing as usually observed in Yb-based heavy-fermion metals. Substituting Yb by La or Rh by Ir allows to create a negative chemical pressure, La (Ir) being smaller than Yb (Rh), and eventually to drive YbRh2Si2 to a pressure controlled QCP. In this paper we compare the effect of external hydrostatic pressure and chemical substitution on the ground-state properties of YbRh2Si2.Comment: 4 pages, 5 figures, proceedings paper of the QCNP0