Metal-Insulator Transition of the Quasi-One Dimensional Luttinger Liquid Due to the Long-Range Character of the Coulomb Interaction

An instability of the quasi-1D Luttinger liquid associated with the metal - insulator transition is considered. The homogeneous metal ground state of this liquid is demonstrated to be unstable and the charge-density wave arises in the system. The wavevector of this wave has nonzero component both along the direction of the chains and in the perpendicular direction. The ground state of the system has a dielectric gap at the Fermi surface, the value of this gap being calculated.Comment: RevTex, 10 page

Excitonic Instability and Origin of the Mid-Gap States

In the framework of the two-band model of a doped semiconductor the self-consistent equations describing the transition into the excitonic insulator state are obtained for the 2D case. It is found that due to the exciton-electron interactions the excitonic phase may arise with doping in a semiconductor stable initially with respect to excitonic transition in the absence of doping. The effects of the strong interactions between electron (hole) Fermi-liquid (FL) and excitonic subsystems can lead to the appearance of the states lying in the middle of the insulating gap.Comment: 2 pages with 2 figures available upon request, LaTex Version 3.0 (PCTeX), to appear in the Proceedings of the M2S-HTSC IV Conferenc

Query Complexity of Approximate Nash Equilibria

We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an $\varepsilon$-well-supported Nash equilibrium is exponential in $n$. One of the consequences of this result is an exponential lower bound on the rate of convergence of adaptive dynamics to approxiamte Nash equilibrium

Axiomatic Approach to Solutions of Games

We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest notion of individual rationality restricts the set of solutions to be equilibria. This observation holds for all types of solutions: in pure-strategies, in mixed strategies, and in correlated strategies where the corresponding notions of equilibria are pure-Nash, Nash and coarse-correlated. An action profile is (strict) simultaneous maximizer if it simultaneously globally (strictly) maximizes the payoffs of all players. - If we require that a simultaneous maximizer (if it exists) will be a solution, then the solution contains the set of pure Nash equilibria. - There is no solution for which a strict simultaneous maximizer (if it exists) is the unique solution

Query Complexity of Correlated Equilibrium

We study lower bounds on the query complexity of determining correlated equilibrium. In particular, we consider a query model in which an n-player game is specified via a black box that returns players' utilities at pure action profiles. In this model we establish that in order to compute a correlated equilibrium any deterministic algorithm must query the black box an exponential (in n) number of times.Comment: Added reference