The method of positive commutators, developed for zero temperature problems over the last twenty years, has been powering progress in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of l...

We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s). The moments...

Statistical equilibrium is a short-run, temporary equilibrium model of market exchange which replaces the Walrasian picture of the market in equilibrium as a budget hyperplane defined by equilibrium relative prices with a scalar field of transactions probabilities. Statistical equilibrium synthesizes the classical notion of competition as a market with a large number of traders with the idea of...

Weprovide an alternative proof of QIP=PSPACE to the recent breakthrough result [JJUW09]. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one QIP-Complete problem which computes the diamond norm between two admissible quantum channels. The key observation is that we can convert the computation of the diamond no...

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium. Equilibrium refinements can mend this issue, but have experienced little practical adoption. This is largely due to a lack of scalable algorithms. Sparse iterat...

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion proper...

in this paper, we study a class of methods for solving the management equilibrium model. We first give an estimate of the error bound for the model, and then, based on the estimate of the error bound, propose a method for solving the model. We prove that our algorithm is quadratically convergent without the requirement of existence of a non-degenerate solution. Keywords—Management equilibrium m...