An Exact Solution for Quantum Tunneling in a Dissipative System

Applying a technique developed recently [1,2] for an harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The result shows that while the dissipation tends to suppress the tunneling, the Brownian motion tends to enhance the tunneling. Whether the tunneling rate increases or not would then depend on the initial conditions. We give a specific formula to calculate the tunneling probability determined by various parameters and the initial conditions.Comment: The reference 2 is changed to Phys. Lett. from Phys. Rev. Let

Evolution of cooperation in spatial traveler's dilemma game

Traveler's dilemma (TD) is one of social dilemmas which has been well studied in the economics community, but it is attracted little attention in the physics community. The TD game is a two-person game. Each player can select an integer value between $R$ and $M$ ($R < M$) as a pure strategy. If both of them select the same value, the payoff to them will be that value. If the players select different values, say $i$ and $j$ ($R \le i < j \le M$), then the payoff to the player who chooses the small value will be $i+R$ and the payoff to the other player will be $i-R$. We term the player who selects a large value as the cooperator, and the one who chooses a small value as the defector. The reason is that if both of them select large values, it will result in a large total payoff. The Nash equilibrium of the TD game is to choose the smallest value $R$. However, in previous behavioral studies, players in TD game typically select values that are much larger than $R$, and the average selected value exhibits an inverse relationship with $R$. To explain such anomalous behavior, in this paper, we study the evolution of cooperation in spatial traveler's dilemma game where the players are located on a square lattice and each player plays TD games with his neighbors. Players in our model can adopt their neighbors' strategies following two standard models of spatial game dynamics. Monte-Carlo simulation is applied to our model, and the results show that the cooperation level of the system, which is proportional to the average value of the strategies, decreases with increasing $R$ until $R$ is greater than the threshold where cooperation vanishes. Our findings indicate that spatial reciprocity promotes the evolution of cooperation in TD game and the spatial TD game model can interpret the anomalous behavior observed in previous behavioral experiments

Electroweak radiative corrections to triple photon production at the ILC

In this paper, we present the precision predictions for three photon production in the standard model (SM) at the ILC including the full next-to-leading (NLO) electroweak (EW) corrections, high order initial state radiation (h.o.ISR) contributions and beamstrahlung effects. We present the LO and the NLO EW+h.o.ISR+beamstrahlung corrected total cross sections for various colliding energy when $\sqrt s \ge 200 {\rm GeV}$ and the kinematic distributions of final photons with $\sqrt s = 500 {\rm GeV}$ at ILC, and find that the NLO EW corrections, the h.o.ISR contributions and the beamstrahlung effects are important in exploring the process $e^+e^- \to \gamma\gamma\gamma$.Comment: 6 pages, 8 figures, accepted for publication in Physics Letters